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Longitudinal research using structural equation modeling applied in studies of determinants ofpsychological well-being and personal initiative in East Germany after the unification
Garst, G.J.A.
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Citation for published version (APA):Garst, G. J. A. (2000). Longitudinal research using structural equation modeling applied in studies ofdeterminants of psychological well-being and personal initiative in East Germany after the unification.
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Download date: 07 Jul 2020
Longitudinal research
using Structural Equation Modeling
applied in studies of determinants of
psychological well-being and personal initiative
in East Germany after the unification
Harry Garst
Longitudinal research using Structural Equation Modeling
applied in studies of determinants of
psychological well-being and personal initiative
in East Germany after the unification
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam
op gezag van de Rector Magnificus
Prof.dr. J.J.M. Franse
ten overstaan van een door het college voor promoties ingestelde
commissie, in het openbaar te verdedigen in de Aula der Universiteit
op
donderdag 15 juni 2000, te 10.00 uur
door
Gerhard Jan Aalbert Garst
geboren te Warnsveld
Promotor: Prof. dr. M. Frese
Co-promotor: Prof. dr. P.C.M. Molenaar
Faculteit: Maatschappij- en Gedragswetenschappen
Promotiecommissie: Prof. dr. C.K.W. de Dreu
Prof. dr. H. van der Flier
Prof. dr. J. Hox
Prof. dr. G.J. Mellenbergh
Prof. dr. C.G. Rutte
Acknowledgements
In the first place I want to thank my promotor, Michael Frese. Although it wasn’t
always easy for both of us and we sometimes spoke different languages, we
succeeded to finish this project. In many ways I learned a lot from Michael. Next, I
want to thank my co-promotor, Peter Molenaar for his methodological support.
Part 1 of this dissertation improved considerably by the helpful comments of Conor
Dolan.
Part 2 of this dissertation is based on data from the project AHUS (Aktives Handeln in
einer Umbruch-Situation - active actions in a radical change situation). This project
was supported by the Deutsche Forschungsgemeinschaft (DFG, No Fr 638/6-5)
(principal investigator: Prof. Frese) from 1990-1998. Continuation of the project was
made possible by the programmagroep work and organizational psychology,
University of Amsterdam. Members of the AHUS project were D. Fay, S. Hilligloh,
C. Speier, T. Wagner and J. Zempel, student members were C. Dormann, M.Erbe-
Heinbokel, T. Hilburger, J. Grefe, M. Kracheletz, K. Leng, K. Plüddemann, V.
Rybowiak, and A. Weike (Giessen) and R. Bamesberger, A. Dehnelt, G. Engstle, M.
Fontin, B. Hartmann, J. Haushofer, B. Immler, E. Kahl, M. Eichholz, S. Kemmler, C.
Lamberts, R. Lautner, A. Röver, B. Schier, S. Schmider, D. Schweighart, H. Simon,
B. Waldhauser, T. Weber, B. Winkler (Munich). Especially, I want to thank Doris
Fay, my former roommate and fellow member of the AHUS project in the last stage.
I thank the following persons for reviewing parts of this dissertation: Kathy Klein,
Elizabeth Morrison, Andreas Utsch, and Dieter Zapf (Chapter 3), Frans Oort, Doris
Fay and Mike Rovine (Chapter 4), Sabine Sonnentag (Chapter 4 and 5), and Jasper
Klapwijk (Summary).
Finally, I owe much to Frans Oort and Wim de Haan who both guided me through the
field of methodology for many years.
Contents Chapter 1 Introduction 1
PART 1
Chapter 2 A General Longitudinal Model 7
PART 2
Chapter 3 Control and Complexity in Work and the Development of
Personal Initiative (PI): A 5-Wave Longitudinal Structural
Equation Model of Occupational Socialization
73
Chapter 4 The Temporal Factor of Change in Stressor-Strain Relationships:
A Growth Curve Model on a Longitudinal Study in East
Germany
119
Chapter 5 Optimism and Subjective Well-being in a Radical Change
Situation in East Germany 163
Chapter 6 Summary and conclusion 221
Appendix A 235
Appendix B 237
Appendix C 245
Appendix D 250
Appendix E 255
Summary in Dutch 263
Chapter 3 is based on:
Frese, M., Garst, H., Fay, D. Control and complexity in work and the development of
personal initiative (PI): A 5-wave longitudinal structural equation model of
occupational socialization. Manuscript submitted for publication
Chapter 4 of this thesis has been accepted for publication:
Garst, H., Frese, M. & Molenaar P.C.M. (in press). The Temporal Factor of Change in
Stressor-Strain Relationships: A Growth Curve Model on a Longitudinal Study in
East Germany. Journal of Applied Psychology.
Chapter 5 is based on:
Garst, H & Frese, M. Optimism and Subjective Well-being in a Radical Change
Situation in East Germany. Manuscript submitted for publication.
ISBN 90-5470-091-2
1
Chapter 1
Introduction
Structural Equation Modeling is especially well suited for analyzing longitudinal data since
it allows the inclusion of many repeatedly measured variables into a single model. Moreover, since
both observed and latent variables can be included, relations between latent variables over time can
be studied. Using Structural Equation Modeling the processes of how psychological well-being and
personal initiative unfold over time can now adequately be tested.
Both theory and applications of longitudinal Structural Equation Modeling will be treated
and therefore this dissertation is composed of two parts. Part 1 introduces a new general
longitudinal model and describes how several well-known models can be treated as its special
cases. Part 2 consists of three longitudinal studies on a sample from former East Germany. These
studies are part of a larger project that started immediately after the unification 1990 and stretched a
period of five years with six measurement occasions.
In Part 1 a hierarchy of longitudinal models will be described and it is shown that different
classes of models (autoregressive versus latent growth curve models) are based upon different
assumptions of the underlying change processes.
The data in Part 2 were analyzed using Structural Equation Modeling. Both autoregressive
and latent growth curve models have been tested. Some of the models are innovative by combining
autoregressive and growth curve models into a single model. Also the inclusion of a measurement
model in growth curve models is new in the literature (to the best of my knowledge).
The studies in Part 2 belong to the field of industrial and organizational psychology,
although the third study is also rooted in the field of social psychology.
The data on which the studies in Part 2 are based were gathered in the AHUS project
(AHUS: Aktives Handeln in einer Umbruch-Situation - active actions in a radical change situation).
A representative sample of (former East-German) workers participate in a longitudinal investigation
into the transition from a planned economy to a market economy. Questionnaire and interview data
were obtained from an average of 540 respondents. The 1st wave was directly after economic
unification in July, 1990; the 2nd after the political unification in November and December, 1990;
the 3rd in July, 1991; the 4th in September and October, 1992; and the 5th in August and
September, 1993 and the sixth in august and September 1995.
2
The central concern of the AHUS study was how much did people cope with the many
changes in these revolutionary times and which people changed the most and what were the major
determinants for these changes? How can we understand that some people changed for the best
while other suffered and grew bitter? Is it fair to speak from winners and losers of the German
unification? Did the winners possess important personality traits? Did they use different coping
styles? Did they use more personal initiative? Or were external circumstances the key determinants?
Other AHUS studies reported on personal initiative (Frese, M., Kring, W., Soose, A. & Zempel, J.
,1996; Speier, C. & Frese, M., 1997; Frese, M., Fay, D., Hilburger, T., Leng, K., Tag, A. 1997);
error orientation (Rybowiak, V., Garst, H., Frese, M. & Batinic, B. (1999), social support
(Dormann, C., & Zapf, D., 1999).
The AHUS data are unique in many respects. First, its longitudinal design: it included six
measurement waves stretching a period of five years. Most field studies in IO psychology use cross-
sectional designs and longitudinal studies are relatively rare and almost always limited to a few
measurement occasions. Further the length of the period of study made it possible to study effects
with a long time lag. Both the number of waves and the length of the period of this study allowed
decomposing changes into state and trait components. Traits are by definition relatively stable, but
may show changes in a long-time frame. Second, the sample size was impressive: 684 subjects
participated at least one measurement occasion. Third, the sample consisted of subjects with various
occupations. Too often studies in the field of organization and work psychology make use of
convenience samples, including subjects with the same occupation or working in the same
company. Generalizing the results of these studies are severely limited. Fourth, in this study a large
array of constructs relevant for industrial and organizational and social psychology were measured.
This made it possible to test for hypothesis controlling for variables known to affect the outcomes
also. Fifth, many constructs in this study have great societal relevance as well. Working
characteristics and work stressors have well documented effects on both performance as many other
psychological constructs (e.g., subjective well-being, strains). Personal initiative, coping styles and
resilience constructs like optimism are central in theories about how to function optimal in an
adverse environment. Sixth, the measurements were not restricted to questionnaires, but also
included interviewer observations by trained interviewers. Especially the measurement of personal
initiative used a situational interview procedure, where in a standardized procedure hypothetical
problems were offered and the responses of the subjects were recorded. Finally, this study took
place in a period in which drastic changes took place. Since human behavior is supposed to be
affected by a great number of determinants the isolated effects of a single determinant is frequently
3
of modest size. In high change environments many processes are stirred up and this is to some
extent comparable with manipulations in field experiments.
In Chapter 3 an occupational socialization model will be presented. This model describes the
relationships between work characteristics (job control and job complexity), mastery orientation
(including control appraisals, self-efficacy, and control aspirations), and personal initiative (PI).
In Chapter 4 several theoretical models about how stressor-strain relationships unfold in
time will be tested using multivariate latent growth curve models.
In Chapter 3 and 4 work conditions (job characteristics, like job control and job complexity,
and work stressors) were included to explain psychological processes. In Chapter 5 the focus was
on factors within the person: Optimism and pessimism. Several models of the relation between
optimism/pessimism and subjective well-being will be tested and the mediational role of coping
styles will be investigated.
In Chapter 6 the results will be summarized and the overall conclusion will be discussed in
light of the specific political and economical context of this historical period. Chapter 6 ends with a
discussion of some methodological issues.
References
Dormann, C., & Zapf, D. (1999). Social support, social stressors at work and depressive symptoms:
Testing for moderator effects with structural equations in a 3-wave longitudinal study. Journal of
Applied Psychology, 84, 874–884.
Frese, M., Kring, W., Soose, A. & Zempel, J. (1996). Personal initiative at work: Differences
between East and West Germany. Academy of Management Journal, 39, 37-63.
Speier, C. & Frese, M. (1997). Generalized self-efficacy as a mediator and moderator between
control and complexity at work and personal initiative: A longitudinal field study in East Germany.
Human Performance, 10, 171-192.
Frese, M., Fay, D., Hilburger, T., Leng, K., Tag, A. (1997). The concept of personal initiative:
Operationalization, reliability and validity in two German samples. Journal of Organizational and
Occupational Psychology, 70, 139-161.
Rybowiak, V., Garst, H., Frese, M. & Batinic, B. (1999). Error Orientation Questionnaire (EOQ):
Reliability, validity, and different language equivalence. Journal of Organizational Behavior, 20.
527-547.
4
5
Part 1
6
7
Chapter 2 A General Longitudinal Model
Introduction
Over the years many authors have consistently pleaded for making more use of longitudinal
designs. Despite the consensus on the importance of longitudinal studies, the question of how to
study change over time is long debated and have led to much controversy in the social sciences
(Cronbach & Furby, 1970; Rogosa, 1980). Not only has the longitudinal literature been rife with
conflict and controversy, also remarkable advances have been made in developing powerful
methods of analyzing change. Latent Growth Curve Models (Muthén, 1997; Muthén & Curran,
1997) and Hierarchical Linear Models (Bryk & Raudenbush, 1991) are major contributions.
Pioneers like Meredith and Tisak (1990) introduced the Latent Growth Curve Model and authors
like Browne (1993), Muthén (1997), and Willett and Sayer (1994, 1995) wrote influential papers
about this subject. However, the introduction of Latent Growth Curve Models also led to new
controversies (Stoolmiller, 1995) e.g., about the ability to distinguish empirically between the
Latent Growth Curve Model and the more conventional Quasi-Markov Simplex (Rogosa & Willett,
1985, Mandies, Dolan & Molenaar, 1994, Raykov, 1998). Both models and the differences between
them are excellent explained by Curran (1998).
In order to give some oversight to the wide array of existing longitudinal models I present in
this paper a new general model and I will show how existing models can be fit into this framework
by treating them as special cases of this general model.
The general model that will be described in this paper is a higher order factor model. The
relationship between several longitudinal models and factor models is well known in the literature.
Jöreskog (1970) showed that a quasi-simplex can be parameterized as a factor model (see also
Browne, 1992, McCloy, Campbell & Cudeck, 1994). Two decades later Meredith and Tisak (1990)
demonstrated that latent growth models can also be specified as a factor model. Recently Curran
and Bollen (1999) introduced a longitudinal model which can be viewed as a hybrid of the latent
growth curve model and the quasi-simplex.
Although a general longitudinal model will be presented, I will show that a special case of
this model is already sufficiently general in scope to encompass several longitudinal models as
special cases. However, more complex longitudinal models cannot be treated as special cases of this
submodel. These models should be instead considered as submodels of the general longitudinal
8
factor model. The similarities and differences between all longitudinal submodels will be described
and it will be shown how these models are based upon different assumptions about the underlying
developmental process. Although many well-known longitudinal models can be considered as
descendents of the general longitudinal model, the conventional specification of these models
differs sometimes greatly from the specification of the model as a special case of the general
longitudinal model. In order to study the interrelations of the longitudinal models it is necessary to
translate them in a more general presentation. However, the equivalence between the various
presentations of the models will be demonstrated extensively, although in some cases the
technicalities had to be transferred to the Appendices.
All models include latent variables. It is assumed that an acceptable measurement model is
known and that the requirement of measurement invariance over time holds. The unique terms of
identical items may correlate over time and the covariance matrix of the unique terms may be a
banded or block-diagonal matrix.
In this paper the modeling of the means will not be described as our presentation does not
provide new insights to the mean part and the topic of incorporating structured means in
longitudinal models is already well treated in Bast & Reitsma (1997) and Mandys, Dolan &
Molenaar (1994).
This paper is organized as follows: First the general longitudinal model and the submodel
will be described. Second, the least restricted submodel of the general longitudinal model will be
presented: The Latent Difference Model. It will be shown that linking this model to the time-
dimension yields an equivalent model: the smallest Piecewise Latent Growth Curve Model which
allows the slopes for each individual to be different for each time-interval. Third, constraining the
slopes to be equal for all time-intervals leads to the Linear Growth Curve Model. A special case of
this model is the Random Intercept Model and a further restriction, assuming equal residual
variances, yields the Equal Variance Covariance Model. A special case of the Latent Difference
model is the Quasi-Wiener Simplex Model which can be derived from the Latent Difference Model
by restricting the covariance matrix to be diagonal. Next, the First Order Moving Average
Difference Model will be presented. What follows are three equivalent first order autoregressive
models (further denoted as AR(1) models). An extension of this model is the second order
autoregressive model (AR(2)). A new model will be presented by autoregressing latent differences
on preceding latent differences. It will be demonstrated that this model can also be estimated as a
special case of an AR(2) model. An overview of the General Longitudinal Model and the
submodels is shown in Figure 1. The reader may find it helpful to consult Figure 1 in the next
section where the models will be discussed in detail.
9
General M
odel
εΘ
ΛΨ
∆Φ
∆Λ
Σ+
+
∏
∏=
−=
−=
''
11
11
qtt
qtt
2
A
R(2) m
odel
subm
odel
∏ −=
11
qtt
∆
ΚΤΗ
∆=
∏ −=
11
qtt
free parameters in row
t and column t –1
()
εΘ
ΛΨ
ΚΤ
ΗΚ
ΤΗΦ
ΛΣ
++
='
''
'2
and in t –2 (except if t = 2).
m
odels Κ = Ι
models Κ
≠ Ι
Figure 1. Family of L
ongitudinal Models
10
Figure 1. Continued
models Κ
≠ Ι Q
uasi Markov Sim
plex
Autoregressive effects for latent differences
Κ =
Ζ; Η
= Ζ
-1; Ψ= 0
; Φ2 =
diagonal, free
Κ
= ΤΖ
; Η =
Ζ-1; Ψ
= 0; Φ
2 = diagonal, free
Ζ =
diagonal, fixed parameter at value 1 at
first row and first colum
n, all other parameters free:
products of autoregressive coefficients
11
Figure 1. Continued
models Κ
= Ι
Latent D
ifference Model
Linear G
rowth C
urve Model
First Order M
oving Average
Κ =
Η = Ι ; Ψ
= 0; Φ
2 = sym
metric, free
(conventional version: Ψ= diagonal, free
D
ifference Model
to allow for tim
e-specific disturbances)
Η is q ×q m
atrix with fixed
equal slopes for each subject
elem
ents: 1’s at the
()
εΘ
ΛΨ
ΤΗ
ΤΗΦ
ΛΣ
++
='
''
4
diagonal, -1 at second band below
''Ν
ΗΦ
ΝΗ
Φ1
21
4−
−=
main diagonal
Ν =
fixed matrix of 0’s and 1’s
Ψ= 0
; Φ2 =
diagonal, free, Κ = Ι
R
andom Intercept M
odel ϕ
11 and ϕ21 in Φ
4 fixed to zero
Equal V
ariance Covariance M
odel
In addition: all parameters in Ψ
equal
12
Figure 1. C
ontinued L
atent Difference M
odel
Sm
allest Piecewise L
inear Grow
th Model
εΘ
ΛΤ
ΗΗ
ΦΤΗ
ΗΛ
Σ+
=−
−'
''
'12
1
Η =
diagonal, fixed timesteps on diagonal
Q
uasi-Wiener Sim
plex
L
inear Grow
th Curve M
odel
Κ =
Η = Ι; Ψ
= 0; Φ
2 = diagonal, free
(restricted version: Ψ
= 0)
equal slopes for each subject
()
εΘ
ΛΤ
ΗΤΗ
ΦΛ
Σ+
='
''
4
''Ν
ΗΦ
ΝΗ
Φ1
21
4−
−=
Ν =
fixed matrix of 0’s and 1’s
13
After the presentation of the basic longitudinal models we will introduce some more
complex models. First, the hybrid model of Curran and Bollen (1999) will be described as a
synthesis of the AR(1) and Linear Growth Curve Model. These last models were previously
considered as distinct models. Second, multivariate models, describing multiple series of latent
constructs, will be treated hereafter. Finally, for the Linear Growth Models the relationship with
time will be explored. The invariance of the model parameters under a linear transformation of the
time scale will be discussed.
The General Longitudinal Model
All longitudinal models described in this paper refer to latent variables. Therefore we start
with a description of the measurement model. For an arbitrary subject the measurement model for a
single latent construct, repeatedly measured by the same set of items, can be expressed as follows:
ittiiity εηλτ ++= , (1)
where τi refers to the item intercept and λi to the factor loading of item i (i ∈ 1,2,…, p) on factor
ηt at measurement occasion t. Note that times t are discrete (t ∈ 1,2,…, q). Because measurement
invariance (Oort, 1996) is assumed no occasion indices were added to the item intercepts and factor
loading. The unique factor is denoted by εit. To simplify the notation no subject indices are added.
In matrix form (1) can be expressed as
y ++= ΛΛ , (2)
where y is a pq × 1 vector of observed variables, is a pq × 1 vector of item intercepts, Λ is a pq ×
q matrix of factor loadings, η is a q ×1 vector of latent constructs and ε is a pq × 1 zero mean
vector of unique factors. These matrices are specified as follows:
14
+
+
=
pq
q
p
q
p
p
p
p
p
pq
q
p
y
y
y
y
ε
ε
ε
ε
η
η
λ
λ
λ
λλ
λ
τ
τ
τ
τ
..
..
..
..
..00
....00
..00
........
0..0
0....0
0..0
0..0
0..0..
0..0
..
..
..
..
..
..
1
1
11
1
1
1
1
1
1
1
1
11
The covariance structure for model (2) (Jöreskog & Sörbom, 1989) is:
εΘΛΛΦΣ += '1 , (3)
given that Cov[ηη] = Φ1, E[εε] = Θε, and E[ηε] = 0. The covariance matrix of the
unique factors, Θε can be specified as either banded error or as block diagonal (Vonesh &
Chinchilli, 1997).
A second order factor model can be formulated by specifying relations between the first and
the second order factors. This can be described as follows:
ζ+= Γ (4)
In (4) the q × r matrix Γ contains the second order factor loadings and the q × 1 vector ζ containing
unique factors. If we define E[ζζ]= ψ, E[ξξ]= Φ2 then, under the assumption of E[ζε]=
0, E[ξε]= 0, and E[ζξ]= 0 . The covariance matrix of the second order factor model is:
( ) εΘΛΨΓΓΦΛΣ ++= ''2 (5)
15
Φ2 is the r × r covariance matrix of the second order factors. Finally, Ψ is a q × q matrix of the
unique factors, determining the first order factors. Restricting Γ to equal a q × q identity matrix and
Ψ to a zero matrix reduces (5) to (3).
The structure of higher order factors influencing lower order factors can be used for
longitudinal models. If we define the matrix of second order loadings in (5) as the product of q – 1
matrices, where q is the number of measurement occasions and t = q – j + 1, as follows:
∏=−
=
1
1
q
jt∆Γ , (6)
then our general model can be described as:
εΘΛΨ∆Φ∆ΛΣ +
+
∏
∏=−
=
−
=
''
1
1
1
1
q
jt
q
jt 2
. (7)
The specification of each of the matrices ∆t is a function of the measurement occasion and
the specific longitudinal model under consideration. The number of waves (denoted as q) minus 1
determines the total number of these matrices.
A submodel of the general model (7) can be obtained by imposing the following restrictions
on the ∆t matrices: Each ∆t can be decomposed into three matrices Αt Μt Ωt, specified as follows.
The matrices Αt and Ωt are both diagonal matrices of order q × q and the matrices Μt can be
specified as q × q identity matrices except for one single element in row r = t and column c = t –1
which is fixed to the value 1. Thus, the matrices Μt are specified as follows:
16
=
=
= −
100..00
010..00
001..00
............
000..11
000..01
....;;
100..00
011..00
001..00
............
000..10
000..01
;
11..000
01..000
............
00..100
00..010
00..001
21 ΜΜΜ qq
j = 1 j = 2 j = q – 1
t = q – j + 1 = q t = q – j + 1 = q –1 t = q – j + 1 = 2
r = t = q r = t = q –1 r = t = q –1 = 2
c = t – 1= q –1 c = t – 1= q – 2 c = t – 1 = 1
With some algebraic manipulations the product
222333111 .... ΩΜΑΩΜΑΩΜΑΩΜΑ −−− qqqqqq (8)
can be written as
( ) qqqqqq ΥΥΥΥΜΜΜΜΧΧΧΧ 132231132 .......... −−− (9)
All Αt matrices, placed between the Μt matrices, have been replaced by premultiplying with a
suitable matrix Χt. In similar vein, all Ωt matrices, placed between the Μt matrices, have been
replaced by postmultiplying with a suitable matrix Υt. The algebraic derivation of (9) can be found
in Appendix A. The following identity can easily be verified:
ΤΜ =∏−
=
1
1
q
jt (10)
where T is lower q × q triangular matrix with all elements fixed to the value of 1.
17
=
1..111
..........
0..111
0..011
0..001
Τ (11)
We show the equivalence 2345 ΜΜΜΜΤ = for a 5-wave study:
Μ5 Μ4 Μ3 Μ2 Τ
=
11111
01111
00111
00011
00001
10000
01000
00100
00011
00001
10000
01000
00110
00010
00001
10000
01100
00100
00010
00001
11000
01000
00100
00010
00001
If we define:
qq ΧΧΧΧΚ 132 ... −=
qq ΥΥΥΥΗ 132 ... −=
we can write the covariance structure for this submodel as:
( ) εΘΛΨΚΤΗΚΤΗΦΛΣ ++= ''''2 (12)
If ΚΤΗ is replaced by Γ the model (12) reduces to a second order factor model described in (5).
Central to longitudinal models is the principle that ‘the past influences the present in a
particular manner’ and that ‘innovation’ or ‘change’ may take place. If we define one factor as
representing ‘initial status’ and all subsequent factors as ‘change’ factors, we can interpret a higher
18
order factor model as a longitudinal model. This concept is displayed as a SEM graph in Figure 2.
The model is a factor model, because higher order factors influence lower order factors (top-down
direction in display). At the same time it is a longitudinal model, because initial status and change
factors influence present and all subsequent lower order factors (time dimension in left-right
direction in display).
Transmission matrix Τ (all elements fixed to 1)
π1 π2 π3 π4 π5
ω1 ω2 ω3 ω4 ω5
initial status factor
change factors
Time
T1
T2
T3
T4
T5
Figure 2. Longitudinal model specified as a factor model.
The model can be described with the following equations:
11 ωπ =
212 ωωπ += (13)
3213 ωωωπ ++=
.. .. .. ..
qq ωωωωπ +++= ...321
In a more general form (13) can be expressed as:
∑==
t
jjt
1ωπ
(14)
19
The matrix representation uses the q × q lower triangular matrix Τ with all elements fixed to
the value of 1.
Τ= , (15)
where π and ω are q × 1 vectors of, respectively, higher and lower order factors. The function of
the matrix Τ is to transmit information to the present and all subsequent waves. The first column
refers to the effects of the first wave to all the other waves (including the first wave itself). The
matrix Τ only accomplishes a one to one transmission of information of higher order factors (initial
status and subsequent changes) to the lower order factors (latent constructs). In order to transform
this information the model have to be extended with two new sets of factors. The relations between
the factors can be specified as:
Η= , (16)
+= ΚΚ , (17)
where ξ and η are q × 1 vectors of higher and lower order factors, respectively, and Η and Κ are
q × q factor loading matrices and ζ is a q × 1 vector of residuals. The matrix ζ introduces additional
time-specific variances at the lowest structural level. Its function will be discussed when describing
the specification of growth curve models. Note that in equations (16) and (17) no vectors of
residuals were added, so only linear transformations of the ξ and ω factors are considered. The
relationship between the highest and lowest order factor is now:
+= ΚΤΗΚΤΗ (19)
The covariance matrix of (19) is the same as (12). The specification of the matrices Κ, Η, Φ2 and
Ψ will yield several longitudinal models presented in this paper.
20
The submodel (12) of the general model is displayed in Figure 3. The function of the
transformation matrices is visualized by introducing auxiliary variables without residual variances
(similar to phantom variables; Rindkopf, 1984; for a similar SEM display: see Neale (1999, p.112)
explaining the Cholesky decomposition). In Figure 3 the matrices Κ and Η are specified as
diagonal, which will be the case in almost all models. Figure 3 can best be interpreted starting from
top to bottom and from left to right. Initial status information is transmitted to all lower variables,
although possibly transformed by the matrices Κ and Η. During the developmental process new
information can be brought into the system through the change factors (also called innovation
terms). However, these effects may be again transformed and hence will be different for subsequent
lower variables. The transformation process can either have an explicit relationship with the factor
time or the process may only implicitly be related with the time dimension. The innovation terms
have a stochastic nature. In addition to these innovation terms, time-specific residuals reside on the
lowest level of the structural part of the model, only influencing the variable of one measurement
occasion. Only in a small subset of the models to be presented will these residuals be required.
In summary, a general longitudinal model (7) and a submodel (12) of this model were
specified as factor models. In the next section it will be explained that this submodel (12) is itself
sufficiently general to encompass several longitudinal models. However, some longitudinal models
cannot be treated as a special case of the submodel (12), but should be considered as a distinct
submodel of the general model (7) itself.
21
η1 η2 η3 η4 η5
y13 y23 y33
Transmission matrix Τ (all elements fixed to 1)
measument
model Λ
Transformation matrix Η
Transformation matrix Κ
π1 π2 π3 π4 π5
ω1 ω2 ω3 ω4 ω5
Covariance matrix Φ2
ξ1 ξ2 ξ3 ξ4 ξ5
time-specific disturbance term
time-specific unique i tem factors
Figure 3. Submodel (12); measurement model partly shown; covariances between unique factors of
identical items omitted.
22
Latent Difference Model
A special case of the submodel (7) is the Latent Difference Model. This model can be
obtained from the submodel (7) by specifying Κ and Η as identity matrices and Ψ as a zero
matrix. Strictly, the Latent Difference Model is not a model in the sense of imposing further
restrictions on the (co)variances of the latent constructs, but is in fact only a transformation of those
latent constructs. It differs from the model proposed by Steyer, Eid & Schwenkmezger (1997). They
specified a restricted latent difference model by imposing certain restrictions on the factor loadings.
However, the Latent Difference Model described here, does not concern itself with the specification
of the measurement model.
The following transformation yields a vector of latent difference scores (except for the first
element which remains η1):
1−= ΤΤ (20)
This is immediately apparent if we show the matrices with the elements:
−
−
−
=
−
−
−
=
−1
23
12
1
3
2
1
3
2
1
....
11..00
..........
00..10
00..11
00..01
..
qqqq ηη
ηη
ηη
η
η
η
η
η
ξ
ξ
ξ
ξ
(21)
Premultiplying both sides of (20) with Τ yields:
Τ= (22)
We defined ( ) 2Φ='E , and now we can write
( ) ( ) ( ) '''''' EEE ΤΤΦΤΤΤΤ 2=== (23)
23
Thus, if the matrices Κ and Η are specified as identity matrices and Ψ is a zero matrix the
submodel (7) reduces to:
( ) εΘΛΤΤΦΛΣ += ''2 (24)
This model is only a linear transformation of the original latent variables and is thus saturated with
respect to the structural part. In Figure 4 the model is shown as a SEM path model1.
η1 η2 η3 η4 η5
η1 η2−η1 η3−η2 η4−η3 η5−η4
Covariance matrix Φ2
Transmission matrix Τ (all elements fixed to 1)
y13
y23
y33
Figure 4. Latent Differences Model); measurement model partly shown; covariances between
unique factors of identical items omitted.
The Latent Difference Model can also be specified using the general model (7) by
specifying ∆t = Μt and all matrices Αt and Ωt are identity matrices. Using (10) the present
specification of (7) reduces to the model described in (24).
1 For a two wave model with difference scores: see McArdle & Nesselroade (1994).
24
Latent Difference Model as a Piecewise Linear Growth Model
Rogosa, Brandt, & Zimowski (1982, p. 730) showed that a difference score can be
considered as the slope (divided by the elapsed time) in a two-wave linear growth model. This can
be extended to more waves as illustrated in Figure 5.
d i ff e re nc e s c or e
t im e : T 3 - T 2
T 2 T 1 T 3 T 4 T 5 T 6
b 0
b 2
η
Figure 5. Score pattern for a single subject;
Note: slope b2 is equal to the ratio difference score/elapsed time
A simple reformulation of the equations of the latent difference model allows us to
demonstrate the similarities between the least restricted case of the Piecewise Linear Growth Model
and the Latent Difference Model. The least restricted Piecewise Linear Growth Model allows the
individual slopes to be different for each time-interval. Here are the equations:
11 ηη =
( )( )1212
1212 tt
tt−
−−+= ηηηη (25)
( )( ) ( )( )2323
2312
12
1213 tt
tttt
tt−
−−+−
−−+= ηηηηηη
… … ... … …
( )( ) ( )( ) ( )( )11
123
23
2312
12
121 ... −
−
− −−−
++−−−+−
qqq tt
tttt
tttt
tt
ηηηηηηηη
25
The matrix Η was specified as an identity matrix in the Latent Difference Model, but if the
specification of Η is modified in:
−
−−
=
−1
23
12
..000
0........
0..00
0..00
0..001
qq tt
tt
tt
Η, (26)
then (25) can be written in matrix form as follows:
11 −−= ΤΤΤΗΗ (27)
which is equivalent to
−−
−−−−
−−−
−−−
=
−
−−
1
1
23
23
12
12
1
12312
2312
12
3
2
1
......1
0.........1
0...1
0...01
0...001
...
qqqqq
tt
tt
tt
tttttt
tttt
tt
ηη
ηη
ηηη
η
ηηη
,
whereby the right side of the equation is presented by the product of matrix ΤΗ and vector
11 −− ΤΗ , respectively.
It is straightforward to demonstrate the equivalence between the Latent Difference Model
and the least restricted Piecewise Model. Since in (20) ξ was defined as
1−= ΤΤ , (20)
we can write (27) as:
26
ΤΤΗΗ == −1, (28)
and the covariance matrix of the least restricted piecewise model is:
εΘΛΤΗΗΦΤΗΗΛΣ +
= −− ''''12
1 (29)
The covariance matrix (29) is of course the same as the covariance structure of the Latent
Difference Model (24):
( ) εΘΛΤΤΦΛΣ += ''2 (24)
Thus, the Latent Difference Model is equivalent to the least restricted version of a Piecewise
Linear Growth Model. No restrictions are imposed on the structural part of the SEM model and
hence the goodness of fit of the Latent Difference Model and the least restricted Piecewise linear
growth model is completely determined by the measurement part of the model.
Linear Growth Curve Model
The slopes in the piecewise model (with different slopes for each time-interval for each
individual) are simple transformations of the latent difference scores. However, if we restrict the
piecewise slopes to be equal (see Figure 6) for each subject and at the same time allow for time-
specific residuals (denoted as ζ t), we obtain the Linear Growth Curve Model. The time-specific
residuals, ζ t , represent the deviations of each subject around his/her linear growth curve.
If we denote ξ1
* as the intercept factor score and ξ
2
* as the slope factor score for an arbitrary
person, the equations can be described as follows:
27
t1 t0 t2 t3 t4 t5
b0
Figure 6. Linear growth curve for a single subject
1*11 ζξη +=
( ) 212*2
*12 ζξξη +−+= tt
( ) ( ) 323*212
*2
*13 ζξξξη +−+−+= tttt (30)
… … … … …. ….
( ) ( ) ( ) qqqq tttttt ζξξξξη +−++−+−+= −1*223
*212
*2
*1 ...
which can be simplified:
1*11 ζξη +=
( ) 212*2
*12 ζξξη +−+= tt
( ) ( ) 313*2
*132312
*2
*13 ζξξζξξη +−+=+−+−+= tttttt (31)
… … … … …. ….
( ) ( ) qqqqqq tttttttt ζξξζξξη +−+=+−++−+−+= − 1*2
*112312
*2
*1 ...
28
In matrix formulation we can express the equality restriction on the slopes for each subject
as follows:
( )( )( )( )( )
( )( )
−−
−−−−
=
−
−
−
1
1
23
23
12
12
1
1
...
tt
tt
tt
ηη
ηη
ηηη
Η
==
*2
*2
*2
*1
*
...
ξ
ξ
ξ
ξ
(32)
We now define the covariance matrix for the growth curve factors Φ3 as:
''E 12
1**3
−−=
= ΗΗΦΗΦ (33)
The assumption of equal slopes reduces the rank of the q × q matrix Φ3 in (33) to 2 and the
rank deficiency can be prevented by premultiplying and postmultiplying Φ3 by Ν and Ν
respectively, whereby Ν is a q by 2 matrix of fixed factor loadings, specified as follows:
=
10
....
10
10
01
Ν (34)
Let define the full rank version of Φ3 as Φ4:
'ΝΝΦΦ 43 = (35)
The reducing of the rank of Φ3 can be illustrated by showing the matrices including the elements:
29
=
=
2222222221
22222221
22222221
12121211
3
..........
..
..
..
φφφφφ
φφφφ
φφφφ
φφφφ
Φ
1..110
0..001
10
....
10
10
01
2221
2111
φφ
φφ (36)
This results in the following model
( ) εΘΛΨΤΗΝΤΗΝΦΛΣ ++= ''''4 (37)
It is straightforward to show that this is the familiar linear latent growth model (with a
measurement model included) by defining ΤΗΝ as T*. Instead of using timesteps the relationship
with time is specified as the length of time that passed from the first measurement occasion.
( ) εΘΛΨΤΦΤΛΣ ++= ''** 4 (38)
ΤΗΝ=
30
=
−
−−
− 10
......
10
10
01
...0000
..................
0...000
0...000
0...0001
1...1111
..................
0...0111
0...0011
0...0001
1
23
12
qq tt
tt
tt
−
−−
=
−−−−
−−−
− 1
13
12
1342312
2312
12
1
......
1
1
01
10
......
10
10
01
...1
..................
0...01
0...001
0...0001
tt
tt
tt
tttttttt
tttt
tt
qqq
(39)
The equivalence of models with the sum of time steps and models with the elapsed time is
demonstrated in Figure 7a and 7b.
1
1 1
1 1
t5-t4 t4-t3 t3-t2 t2-t1
1 1 1 1
η1 η2 η3 η4 η5
slope factor
intercept factor
y13 y23 y33
Figure 7a
31
1
t5-t1
t4-t1
t3-t1
t2-t1
1 1 1
1
η1 η2 η3 η4 η5
slope factor intercept factor
y13 y23 y33
∗ ξ1 ∗ ξ2
Figure 7b Figure 7a and b. Two equivalent specifications of a Linear Growth Curve Model: Figure 7a: time
steps; Figure 7b: elapsed time from first measurement occasion. Measurement model partly shown;
covariances between unique factors of identical items omitted.
Equal Variance-Covariance Baseline Model
McArdle & Aber (1990) suggest before testing change models one should first reject the
following baseline model which they call the Equal Variance-Covariance Baseline Model. This
model predicts equal variances and covariances and excludes the existence of change factors. They
note that this model is equivalent with a one-factor model with equal factor loadings and equal
unique variances. The model is a special case of the Linear Growth Curve model described in (37).
This can by shown by fixing both ϕ22
and ϕ21
in (36) to zero. The matrix Ψ in (37) should be
specified as a diagonal residual matrix with all elements restricted to be equal. Freeing in (38) the
elements in T* and Ψ (except those for identification purposes) yields a conventional second
order factor model.
32
The Equal Variance Covariance Model is also known as the Random Intercept Model (see
Figure 8), although the restriction of equal variances is here usually not made. This model specifies
that each individual trajectory can be described by an individual baseline and uncorrelated time-
specific deviations around this baseline.
The Random Intercept Model is also equivalent with a one factor repeated measures
ANOVA (Bryk & Raudenbush, 1992). An advantage of the SEM approach is that the random
intercepts refer to the latent constructs if a measurement model is included.
Figure 8. Random Intercept Model
Note: not shown autocorrelations between unique factors of identical items.
Quasi-Wiener simplex
If the matrix Φ2 in Model (24) is restricted to a diagonal matrix, the resulting model is
known as the Quasi-Wiener simplex (Jöreskog, 1970). This model may be appropriate for a
stochastic process if the only source of change consists of uncorrelated time-specific increments.
The model is displayed in Figure 9.
1 1 1 1 1 1
ξ
η1 η2 η3 η4 η5 η6
33
1 1 1 1 η1 η2 η3 η4 η5
η5 η4 η3 η2 η1
η2−η1 η1 η3−η2 η4−η3 η5−η4
Figure 9. Quasi-Wiener simplex; top panel reparameterized as a second order factor model, bottom
panel conventional SEM diagram; measurement model partly shown (only for T3); covariances
between unique factors of identical items omitted.
First Order Moving Average Difference Model
McArdle & Aber (1990) describe a model which they attribute to Wold. This is a first order
moving average or random shock model. In this model only adjacent waves share a common factor
34
and this makes the model highly restrictive, because it predicts a zero covariance between waves
that are more than one measurement occasion apart. A graphical display is shown in Figure 10.
measument model
Transformation matrix Η
Transmission matrix Τ (all elements fixed to 1)
1 1 1 1 1
-1 -1 -1
η1 η2 η3 η4 η5
y31 y32 y33
measument model η1 η2 η3 η4 η5
y31 y32 y33
ζ1 ζ2 ζ3 ζ4 ζ5
1 1 1 1 1 1 1 1 1
1 1 1 1 1
π1 π2 π3 π4 π5
Transformation matrix Κ
ω1 ω2 ω3 ω4 ω5
ξ1 ξ2 ξ3 ξ4 ξ5
Figure 10. First order moving average model; top panel reparametrized as a special case of model
(12); bottom panel conventional diagram; measurement model partly shown (only for T3);
covariances between unique factors of identical items omitted.
35
By specifying the elements of the matrix Η as follows:
−
−
−=
1..1000
............
0..1010
0..0101
0..0010
0..0001
Η
, (40)
the product TH yields the desired permutation matrix:
TΗ =
−−
−
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
1 1 1 1 1
1 0 0 0 0
0 1 0 0 0
1 0 1 0 0
0 1 0 1 0
0 0 0 1 1
...
...
...
...
... ... ... ... ... ...
...
...
...
...
...
... ... ... ... ... ...
...
=
1 0 0 0 0
1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 0 1
...
...
...
...
... ... ... ... ... ...
...
The function of matrix Η is ‘to break the chain’ and hence this model violates the principle that all
subsequent measurement waves are affected by previous measurement occasions.
The covariance for the First Order Moving Average Difference Model is:
( ) εΘΛΤΗΤΗΦΛΣ += '''2 (41)
The model can also be specified as a submodel of the general model (7) by specifying the
matrices ∆t as identity matrices except for the elements below the main diagonal in column t – 1.
These elements are fixed to –1(–1)(r-c), were r denotes the rth row and c the cth column and it
assumed that r > c. An example for a four-wave study is:
36
∆t = 4 ∆t = 3 ∆t = 2 ΤΗ
=
−
−
1100
0110
0011
0001
1001
0101
0011
0001
1010
0110
0010
0001
1100
0100
0010
0001
In this example the matrix to the left, corresponds with t = 4 and column t – 1 = 3. Below the main
diagonal is element 4,3, which is fixed to –1(–1)(4 - 3) = 1
Quasi Markov Simplex
In the Linear Growth Curve Model the piecewise slopes were restricted to be equal for each
subject. An alternative specification is that the piecewise slopes can be predicted by the latent score
on the preceding measurement occasion. If we denote the regressioncoefficients as ct, t-1 and the
disturbance term as ζt , we can write the equations as:
11 ζη = (43)
( )( ) 2121
12
12 ζηηη +=−−
ctt
( )( ) 3232
23
23 ζηηη +=−−
ctt
( )( ) 4343
34
34 ζηηη +=−−
ctt
…. …. …
( )( ) qqqq
qq ctt
ζηηη
+=−−
−−−
−11,
1
1
37
It is convenient to express (43) in matrix formulation:
C +=−− 11ΤΗ (44)
where is Η defined as in (27) and C as follows:
=
− 0000
..........
0..00
0..00
0..000
1,
32
21
qqc
c
c
C (45)
The reduced form of (44) can be derived as follows:
C =−−− 11ΤΗ
( ) C =−−− 11ΤΗ
( ) C111 −−− −= ΤΤΗ (46)
Equation (46) can also be written as:
( ) C ΗΗΤΗ 1111 −−−− −= (47)
Using ( ) 111 −−− = ΒΑΒΑΒΑ we can write (47) as:
38
( ) C ΗΤΗΗ111 −−− −= (48)
( ) C ΗΗΤ11 −− −= (49)
It is easy to verify that
( ) ( )*1 CC −=−− ΙΗΤ , (50)
where C* is defined as follows:
( )( )
( )
+−
+−+−
=
−− 01000
..........
0..010
0..001
0..000
11,
1232
0121*
qqqq ttc
ttc
ttc
C (51)
It may be helpful to show the specification of the matrices again:
=− *CΙ
−
−
−−
11..00
..........
00..10
00..11
00..01
−
−−
−1
23
12
..000
0........
0..00
0..00
0..001
qq tt
tt
tt
− 0000
..........
0..00
0..00
0..000
1,
32
21
qqc
c
c
If we now assume that all timesteps have equal length, we can use unit scaling and this turns Η into
an identity matrix. Now we define C** as:
39
+
++
=
− 01000
..........
0..010
0..001
0..000
1,
32
21**
qqc
c
c
C (52)
and we write (49) as:
( ) C1** −
−= ΙΙ (53)
This is equivalent to the reduced form of the conventional presentation of the quasi Markov
simplex:
( ) 1−−= ΒΒΙ , (54)
where Β is specified as:
=
− 0000
..........
0..00
0..00
0..000
1,
32
21
qqβ
ββ
Β (55)
and now we can conclude that:
**C=Β (56)
Because piecewise slopes can be obtained from the original latent scores by a simple
transformation and the timesteps are given and fixed, the model (43) is only a simple
reparametrization of the Quasi Markov Simplex Model.
40
Jöreskog (1970) described another interesting reparametrization of the Quasi Markov
Simplex. The submodel (12) reduces to (57) if we specify Ψ as a zero matrix and Κ as Ζ and Η as
Ζ-1:
εΘΛΖΤΖΦΖΤΖΛΣ +
= −− ''''12
1 (57)
The elements of Ζ are specified as follows:
∏
=
−
=+
1
1,1
3221
21
..000
..........
0..00
0..00
0..001
q
iii
Ζ (58)
The model (57) is similar to Jöreskog’s reparametrization of the Quasi Markov Simplex. The
equivalence between model (57) and the more conventional formulation (Bollen, 1989) in (59)
( ) ( ) εΘΛΒΙΦΒΙΛΣ +
−−= −− ''11
, (59)
where Β is again specified as in (55), can easily be verified by showing the identity between
ΖΤΖ-1and (Ι − Β)
-1. The details are described in Appendix B. Both the AR(1) model in (57) and
(59) are shown in Figure 11.
41
η1 η2 η3 η4 η5
y13 y23 y33
Transmission matrix Τ (all elements fixed to 1)
measument
model Λ
Transformation matrix Ζ
π1 π2 π3 π4 π5
ω1 ω2 ω3 ω4 ω5
ξ1 ξ2 ξ3 ξ4 ξ5
Transformation matrix Ζ−1 1 1/β21 1/β21β32 1/β21β32β43 1/β21β32β43β54
β21β32β43β54 β21β32β43 β21β32 β21 1
η1
η2
η3
η4
η5
y13
y23
y33
β21 β32 β43 β54
Figure 11. First Order Markov Simplex: top panel reparametrized model; bottom panel
conventional diagram; measurement model only shown for T3 and autocorrelation between unique
item factors not shown.
42
The First Order Autoregressive Model can also be specified using the general model (7) by
specifying ∆t as identity matrices except for element δ in row r = t and column c = t –1 in each
matrix. All δ’s are free parameters which are equal to the βs. A SEM display is shown in Figure 12.
measument model (including first order factor loading matrix)
second order factor loading matrix
η1 η2 η3 η4 η5
β21
β32
β43
β54
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
third order factor loading matrix
fourth order factor loading matrix
fifth order factor loading matrix
ζ1 ζ2 ζ3 ζ4 ζ5
Figure 12. AR(1) model as a general model (7)
43
In Appendix B the equivalence between the AR(1) formulation using model (7) and the
conventional formulation will be proven for a five-wave model. Here we only show the equivalence
between both versions of the AR(1) model:
∆5 ∆4 ∆3 ∆2 (60)
=
10000
01000
00100
0001
00001
10000
01000
0010
00010
00001
10000
0100
00100
00010
00001
1000
01000
00100
00010
00001
21
32
43
54
β
β
β
β
r = t = 5 r = t = 4 r = t = 3 r = t = 2
c = t – 1= 4 c = t – 1 = 3 c = t – 1 = 2 c = t – 1 = 1
=
1
01
001
0001
00001
54544343433254433221
434332433221
323221
21
ββββββββββ
ββββββ
βββ
β (61)
It is easily verified that the above matrix is the same as (Ι − Β)-1
if Β is specified as in (55).
Second Order Autoregressive Model
A Second Order Autoregressive Model (further denoted as AR(2)) cannot conveniently be
treated as a special case of submodel (12), but it fits nicely into the framework provided by the
general longitudinal model (7). The disadvantage of submodel (12) is that the transmission matrix is
inflexible and in cases where more complex forms of transmissions are needed there seems to be no
convenient way to treat these models as special cases of submodel (12). Transmission is more
complicated if more than one source of information partly travels along the same paths. Model (7)
44
is, however, easily adaptable. The second order structure can be incorporated by specifying ∆t as
identity matrices except for the following two elements δs in each matrix: The element in row r = t
and column c = t –1 and secondly the element in column c = t –2 (except if t = 2). All δs are free
parameters and equal to the βs in the conventional representation of the AR(2) model. A SEM
display both for a conventional and the alternative version of the AR(2) model is shown in Figure
13. We show the equivalence of both models for a five-wave study: ∏−
=+−
1
11
q
jjq∆ =
∆5 ∆4 ∆3 ∆2 (62)
=
10000
01000
00100
0001
00001
10000
01000
001
00010
00001
10000
010
00100
00010
00001
100
01000
00100
00010
00001
21
3231
4342
5453
β
ββ
ββ
ββ
r = t = 5 r = t = 4 r = t = 3 r = t = 2
c = t – 1 = 4;
c = t – 2 = 3
c = t – 1 = 3;
c = t – 2 = 2
c = t – 1 = 2;
c = t – 1 = 1
c = t – 1 = 1
It is easily verified that the same result will be obtained from (Ι − Β2)-1
whereby Β2 is
specified as follows:
=
100
010
001
0001
00001
5453
4342
3231
21
2
ββββ
βββ
Β (63)
Thus, ( ) ∏=−−
=+−
− 1
11
12
q
jjq∆ΒΙ
45
measument model (including first order factor loading matrix)
second order factor loading matrix
η1 η2 η3 η4 η5
β21
β31 β32
β42 β43
β54
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
third order factor loading matrix
fourth order factor loading matrix
fifth order factor loading matrix
ζ1 ζ2 ζ3 ζ4 ζ5
β53
η1 η2 η3 η4 η5
Figure 13. AR(2) model: top panel specified as a special case of general model (7); bottom panel conventional model.
46
Autoregressive Effects For Latent Differences
In the Linear Growth Model the piecewise slopes of each subject are assumed to be equal:
The growth of every subject is characterized by a constant rate of change. For some data sets this
assumption may be overly restrictive. This assumption may be alleviated by giving up the equality
constraints for the slopes, and instead only assuming that the slopes can be predicted by the slopes
on a previous measurement occasion. This means that changes can be predicted by previous
changes. For identification purposes we have to assume that this is a fixed regression. If the
prediction is perfect, then this model reduces to the Linear Growth Model.
One can decide whether to regress also the first latent difference on the latent scores of the
first measurement occasion or only use latent difference scores as predictors. First we describe the
model which includes an autoregression on the first latent score. Later we will show that only a
small adjustment in the model specification is needed if only autoregression is assumed on previous
latent differences and the first latent score is ignored. If we denote the fixed regressioncoeffients as
α’s and the disturbance term as ζ’s, the equations can be described as follows:
11 ζη = (64)
( )( ) 2121
12
12 ζηαηη +=−−
tt
( )( )
( )( ) 3
12
1232
23
23 ζηηαηη +−−=
−−
tttt
( )( )
( )( ) 4
23
2343
34
34 ζηηαηη +−−=
−−
tttt
…. …. …
( )( )
( )( ) q
qqqq
ttttζ
ηηα
ηη+
−−
=−−
−−
−−−
−
−
11
211,
1
1
The dependent variables, the piecewise slopes, can be transformed into latent scores by first
multiplying both sides of all equations (except the first equation) by the time step and next moving
the previous latent score to the right side. We show this for the third equation in (64). Both sides
multiplying by the timestep gives:
47
( ) ( ) ( )( )
+
−−−=− 3
12
12322323 ζηηαηη
tttt (65)
( )( )( ) ( ) 32312
23
2332 ζηηα tt
tt
tt −+−−−= ,
and moving 1η− to the right side gives:
( )( )
( )( ) ( ) 3231
12
233222
12
23323 ζηαηηαη tt
tt
tt
tt
tt −+−−−+
−−= (66)
To simplify (66) we can write:
*31
*3222
*323 ζηαηηαη +−+= = (67)
( ) *31
*322
*32 1 ζηαηα +−+ ,
where
( )( )12
2332
*32 tt
tt
−−= αα , and ( ) 323
*3 ζζ tt −= . (68)
If we assume that all timesteps have equal length, we can scale each timestep to the value of 1:
11 ζη = (69)
( ) 21212 1 ζηαη ++=
( ) 31322323 1 ζηαηαη +−+=
( ) qqqqqqqq ζηαηαη +−+= −−−− 21,11, 1
For deriving the covariance matrix of η it is more convenient to express (69) in matrix formulation:
+= 2Α , (70)
where Α2 is specified as:
48
+−
+−+−
+
=
−− 01..0000
................
000..0000
000..010
000..001
000..0001
000..0000
1,1,
4343
3232
21
2
qqqq αα
αααα
α
Α
(71)
The equations in (69) and the specification of Α2 in (71) show a second order autoregressive
structure, although we started in (64) with a first order autoregressive structure. The matrix
formulation of (64) is:
+= −−−− 111
11 ΤΗΑΤΗ , (72)
where Α1 is a matrix of first order autoregressive coefficients, defined as:
=
− 0..000
00..000
............
00..00
00..00
00..000
1,
32
21
1
qqα
αα
Α (73)
The relationship between the first and the second order autoregressive coefficients in this model can
be demonstrated by the following easily verifiable identity:
11
12
−− +−= ΤΤΑΤΙΑ (74)
49
We first derive the covariance matrix of η by using the first order autoregressive structure
of (74), and later show the equivalent matrix for the second order structure. To obtain the reduced
form of (74) some algebraic manipulations are needed: First the η vector on the right side have to
move to the left side:
=− −−−− 111
11 ΤΗΑΤΗ (75)
This can be simplified to:
( ) =− −− 111 ΤΗΑΙ (76)
Premultiplying both sides with ( ) 11
−− ΑΑΙΤΗ gives:
( ) 1
1−−= ΑΑΙΤΗ (77)
The covariance matrix for η is then:
[ ] ( ) [ ]( ) ''''' EE ΤΗΑΙΑΙΤΗ 11
11
−− −−= (78)
If we again define E[ζζ]= ψ, the covariance for y is then:
( ) ( ) εΘΛΤΗΑΙΨΑΙΛΤΗΣ +−−= −− ''''11
11 (79)
Using again Jöreskog’s parametrization of the first order autoregressive model, whereby Ζα is
defined as:
50
∏
∏
=
=+
−
=+
q
ttt
q
ttt
1,1
1
1,1
3221
21
0..000
0..000
............
00..00
00..00
00..001
α
α
αα
α
αΖ
, (80)
we can write:
( ) ( ) =−− −− '11
11 ΑΙΨΑΙ '''
αααα ΖΤΖΦΤΖΖ 14
1 −− (81)
Thus, (79) can be written as:
εαααα ΘΛΤΗΖΤΖΦΤΖΛΤΗΖΣ += −− ''''''14
1 (82)
The model (82) is displayed in Figure 14.
51
η1 η2 η3 η4 η5
y13 y23 y33 measument
model Λ
Transformation matrix Ζ−1
Transformation matrix Ζ
Transmission matrix Τ (all elements fixed to 1)
π1 π2 π3 π4 π5
ω1 ω2 ω3 ω4 ω5
ξ1 ξ2 ξ3 ξ4 ξ5
ρ1 ρ2 ρ3 ρ4 ρ5
Transmission matrix Τ (all elements fixed to 1)
Transformation matrix Κ
ϖ1 ϖ2 ϖ3 ϖ4 ϖ5
Figure 14. AR(1) structure imposed on Latent Difference Model
Next we show the equivalence between the covariance matrix in (82) using a first order
autoregressive structure and the covariance matrix based upon the second order structure.
We again show the identity in (74):
11
12
−− +−= ΤΤΑΤΙΑ (74)
52
Moving Α1 to the left side and Α2 to the right side gives:
12
11
−− +−= ΤΤΙΑΤΑ (83)
Postmultiplying both sides with Τ-1 gives:
ΤΤΤΤΑΑ 121
−+−= (84)
If we substitute (84) in ( ) 11
−− ΑΑΙ gives:
( ) =− −11ΑΙ =−+−
−−− 112
1 ΤΤΤΤΑΤΤ
( ) =−+−−−− 11
21 ΤΤΙΑΤ
( ) =− −12 ΤΑΙ
( ) 12
1 −− − ΑΑΙΤ (85)
Substituting this result into (79) with an additional assumption of equal time steps (Η = Ι), we can
write:
( ) ( ) εΘΛΤΤΑΙΨΑΙΛΤΤΣ +−−= −−−− '''' 112
12
1, (86)
which simplifies to:
( ) ( ) εΘΛΑΙΨΑΙΛΣ +−−= −− ''12
12 (87)
Formula (87) describes the covariance matrix for a second order autoregressive model.
53
So far we have discussed the option where the slopes of the first time interval are regressed
on the initial score. If we change this option into an alternative assumption which states that the first
slopes are only allowed to be correlated with the initial score, only some small adjustment have to
be made. The second equation in (64) has to be changed to:
( )( ) 2
12
12 ζηη =−−
tt (88)
Consequently, in (79) the matrices Τand Ζα have to be replaced by respectively:
=
1..110
..........
0..110
0..010
0..001
*Τ (89)
and
∏
∏=
=+
−
=+
q
ttt
q
ttt
1,1
1
1,1
32*
0..000
0..000
............
00..00
00..010
00..001
α
α
α
αΖ
.
The matrix Φ4 is no longer diagonal, since the parameter cov(ζ1, ζ2) has to be estimated.
54
Bollen and Curran Hybrid model:
A Synthesis between AR(1) and the Latent Growth Model
Recently Bollen & Curran (in press) introduced a synthesis between the AR(1) and the
Latent Growth Curve Model. The model is shown in Figure 15.
η1 η2 η3 η4 η5
y15 y25 y35
I S
1 1 1 1 1
t2
t3 t4 t5
Slope factor Intercept factor
Figure 15. Synthesis between Quasi Markov Simplex and Linear Growth Curve Model;
measurement model only shown for T3.
The Bollen and Curran hybrid model can also be specified using parts of submodel (12).
Since the hybrid model integrates two models based upon different concepts of change it is obvious
that it is not possible to treat this hybrid model as a special case of submodel (12). However, all that
is needed is a small modification of submodel (12): Only one additional equation is required. For
ease of presentation we present the linear growth curve specification in the simple form using ξ* as
in (32) and T* as in (38) and (39).
55
The relations between the factors for the hybrid model can be defined as:
+= **Τ , (91)
where ρ is a q × 1 vector of latent factors, T* is a q × 2 matrix of fixed basis coefficients2 as in
(39), ξ* is a 2 × 1 vector of growth curve factors (intercept and slope factor, respectively), and ξ is
a q × 1 vector of latent factors, necessary for the AR(1) specification. Equation (91) is the
modification needed to incorporate both models (note that the right side of (91) adds two vectors,
one for the growth part and one for the AR(1) part). The second equation is:
1−= ΖΖ , (92)
where ω is a q × 1 vector of latent factors as in (15) and Ζ is as a q × q diagonal matrix of products
of first order autoregressive coefficients in (58). The third equation is the same as in (15):
Τ= , (15)
where π is q × 1 vector of latent factors and T is lower q × q triangular matrix with all elements
fixed to the value of 1 as in (11). Finally, if we now specify ζ as a q × 1 zero vector, the last
equation changes to:
Ζ= (93)
Substituting (91) and (92) in (93) gives:
( ) += − **1 ΤΖΤΖ (94)
2 basis coefficients is the term used by Meredith & Tisak (1990) for denoting the factor loadings for growth curve models.
56
Assuming that the growth curve factors in ξ* are independent of the autoregressive factors in ξ the
covariance matrix of η is as follows:
( ) '''''Cov ΖΤΖΦΤΦΤΖΤΖ 12
*4
*1 −−
+= (95)
where Φ4 is a 2 × 2 covariance matrix of the growth curve factors as in (36) and Φ2 is a q × q
diagonal matrix of residual3 variances pertaining to the AR(1) part of the model as in (57).
The covariance matrix for the observed variables is:
( )( ) '' CovCov yy ++== ΛΛΣ =
εΘΛΖΤΖΦΤΦΤΖΤΖΛ +
+ −− ''''' 12
*4
*1 (96)
The derivation of (96) can be found in Appendix C. In Appendix C the equivalence between the
covariance structure of (96) and the conventional specification of the model (as shown in Figure 15)
is demonstrated.
The alternative specification of the Bollen and Curran Hybrid Model is displayed in Figure
16.
3 except that element (1,1) in (57) is the variance of the first latent construct of the AR(1) series and not a residual variance as in (95).
57
1/β21β32β43
β21β32β43
η5
Transmission
matrix Τ (all elements fixed to 1)
Transformation
matrix Ζ
π5
ω5
ρ5
Transformation
matrix Ζ−1
1/β21β32β43β54
β21β32β43β54
y13 y23 y33
η1
π1
ω1
ρ1
1
1
1/β21
η2
π2
ω2
ρ2
β21
η3
π3
ω3
ρ3
1/β21β32
β21β32
η4
π4
ω4
ρ4
1 1
1 1
t2-t1
t3-t1 t4-t1 t5-t1
Slope factor
ξ1∗
ξ2∗ Intercept factor
ξ2 ξ1 ξ4 ξ3 ξ5 1
1 1 1 1
1
Figure 16. Alternative specification of Bollen & Curran Model; measurement model only shown for T3.
58
Multivariate Models
Simple multivariate models, including more than one series of latent constructs, can be
formulated by extending the submodel (12). It is convenient to make use of partioned matrices. For
example, a cross-domain latent growth curve model, including two growth curves, can be specified
by replacing ΤΗΝ by:
222
111
ΝΗΤΝΗΤ
0
0 (94)
All other matrices should be partioned accordingly. The covariance matrix between the growth
curve parameters appear in the off-diagonal partition of Φ3.
However, more complex multivariate models are more easily specified by extending the
general model (7). Again, some new complexities, created by specifying relationships between the
sets of latent constructs, do not seem to fit well into submodel (12). Although it is possible to extend
submodel (12) for limited classes of relationships between the series, the causal structures needed
for many models are not easily specified as extension of model (12). The explanation for the
inflexibility of submodel (12) is the use of a direct form of transmission of information from earlier
to subsequent waves. Many complex models require indirect forms of transmission which can be
accomplished by dividing the transmission into multiple paths. In this way also relationships can be
specified which use only parts of the transmission.
To extend model (7) to a multivariate model only the matrix ∆ need to be partioned into
suitable specified submatrices. On the main diagonal the matrices for the univariate time series are
placed and on below the main diagonal the matrices specifying the paths between the series are
located. For a multivariate model, consisting of two time series, the model can be described as:
εΘΛ∆∆
∆Φ
∆∆∆
ΛΣ +
∏
∏
=
−
=
−
=
''
q
t tt
tq
t tt
t 1
12
1
1 2221
11
2221
1100
(95)
59
two time series with lagged effects for one of the variables. The model is shown in Figure 17 and in
Figure 18 as a conventional lagged AR(1) model.
ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8
1
ξ1 ξ2 ξ3 ξ4
1 1 1
ξ5 ξ6 ξ7 ξ8
1
β87
1 1
η1 η2 η3 η4
y13 y23 y33
η5 η6 η7 η8
y13 y23 y33
1 1 1 1
π1 π2 π3 π4 π5 π6 π7 π8
1 1 1
β21
β32
1
β43
β65
β76
1
β61
β72
β83
φ51
Figure 17. Model with two First Order Markov Simplexes with lagged effects of one variable;
measurement model only partly shown; η1 and η5 refer to T1, η2 and η6 refer to T2, etc.
60
β76 β87 β98 β10,9 η6 η7 η8 η9 η10
β21 β32 β43 β54 η1 η2 η3 η4 η5
β71 β82 β93 β10,4
Figure 18. Conventional SEM diagram of model including two AR(1) series with lagged effects;
measurement model only partly shown; η1 and η6 refer to T1, η2 and η7 refer to T2, etc.
Because the matrices on the main diagonal are specified as AR(1) matrices and equal to (60), and
given that the inverse of triangular matrices has a special structure, we only show the specification
of the off-diagonal matrices.
212121 234 ∆∆∆
0000
0000
000
0000
0000
000
0000
0000
000
0000
0000
0000
61
72
83
β
β
β
(96)
To demonstrate the equivalence between the model (95) and the conventional parametrization we
denoted the coefficients in (96) as betas. In Appendix D the equivalence of model (95) and the
conventional model is demonstrated.
61
Invariance of parameters in Latent Growth Curve Models
A problem of the specification of a Linear Growth Curve Model is that for most applications
in the social sciences the scaling of the time axis (fixing the basis coefficients) is arbitrary: Both the
origin and the metric is not inherently tied to the real timeframe for the data of the study. In the
following the (in)variance of the growth parameters for a cross-domain model (Linear Growth
Curve Model consisting of two growth curves, cf. Willett & Sayer, 1995) is investigated under a
linear transformation of the timescale.
jj tt βα +=* (97)
The implied covariance structure of the original scaling is (using a conventional specification and
ignoring the matrix of residuals):
'ΛΨΛΣ = , (98)
which matrices are specified as follows:
4321
4321
44434241
43333231
42322221
41312111
4
3
2
1
4
3
2
1
0000
11110000
0000
00001111
100
100
100
100
001
001
001
001
tttt
tttt
t
t
t
t
t
t
t
t
ψψψψψψψψψψψψψψψψ
(99)
A linear transformation of basis coefficients yields:
++++
++++
=
4
3
2
1
4
3
2
1
4
3
2
1
4
3
2
1
100
100
100
100
001
001
001
001
000
100
000
001
100
100
100
100
001
001
001
001
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
δγδγδγδγ
βαβαβαβα
δγ
βα
(100)
62
If we denote P as follows:
=
δ
γ
β
α
000
100
000
001
Ρ, (101)
Because estimation methods like Maximum Likelihood and Generalized Least Squares are scale-
free (Long, 1984, p.58) transformations of the factor loadings yield the same expected covariance
matrix, because the scale transformations can completely be absorbed by corresponding changes in
the factor (co)variances. Therefore, we can write:
''''' 1111 −−−− =⇒== ΨΡΨΡΡΦΛΡΨΡΛΡΡΛΨΛΣ (102)
where
1
1 0 0
10 0 0
0 0 1
10 0 0
α
β
β
γ
δ
δ
−
−
−
=
(103)
and the elements of this final matrix are: '11 −−= ΨΡΨΡΡΦ
63
Φ =
−−
+−+−+−−
−
+−
244
44243424241
442
2
4333423242413231
222
22221
222
2
2111
111
21
1
2
δψψ
δγψ
δψ
βδψ
βδαψ
δ
ψδγψ
δγψψ
βδγψ
βψ
δγ
βαψ
δγψ
βαψ
βψψ
βαψ
β
ψβαψ
βαψ
(104)
Of course one can transform the new parameters in Φ to obtain the old ones.
== 'ΡΦΡΨ
( )( )
( )
++++++++
+++
442
4443424241
442
4333423242413231
222
2221
222
2111
2
2
φδγφφδβδφδαφδφφγγφφγφφβγαφγφαφφ
φβαφφβφααφφ
(105)
In the case one is only interested in focusing on another zero timepoint, the matrix, used for
the linear transformation simplifies to:
=
1000
100
0010
001
α
α
Ρ (106)
and
−
−
=−
1000
100
0010
001
1
α
α
Ρ
(107)
so that:
64
++++
++++
=
4
3
2
1
4
3
2
1
4
3
2
1
4
3
2
1
100
100
100
100
001
001
001
001
1000
100
0010
001
100
100
100
100
001
001
001
001
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
αααα
αααα
α
α
(108)
Φ =
−−
+−+−+−−
−
+−
444443424241
442
43334232422
413231
222221
222
2111
2
2
ψαψψψαψψ
ψααψψαψψψααψαψψ
ψαψψ
ψααψψ (109)
As one can see the variances of both slopes are not affected by a translation on the time axis,
neither is the covariance between the slopes. Only if the variance of the slope factor is nonzero, the
covariance between the intercept factor and the slope factor changes by a translation on the time-
axis (cf. Rovine & Molenaar, 1998). This makes sense because the slope factor scores are constants
for each subject. However, the relative positions of the subjects change over time in the case there is
variance in slopes. So the subjects change into different directions and given a constant slope, the
covariance has to change as well. Equivalently, one can start reasoning with a given fixation
scheme of the basis coefficients, for instance fixing the first basiscoefficient to the value of zero.
Next one is interested in finding the covariance between the intercept factor and the slope factor at
an arbitrary time point t. The covariance equals COV(η1+tη2, η2) = COV(η1, η2) + tVAR(η2, η2) =
ψ21 + tψ22. The same result can be obtained by a translation on the time axis by α = −t. The
covariance is ψ21 − αψ22 = ψ21 − (−t)ψ22 = ψ21 + tψ22. In case the growths curves are not parallel,
the covariance between the intercept factor and slope factor can only be conditionally interpreted:
each time point yields a different covariance and represents the state of affairs at that particular
time. In the case of nonparallel slopes it is misleading to speak of the covariance between level and
shape, as sometimes appears in the literature: the level changes constantly if there are
interindividual differences in growth trajectories, so does the covariance.
65
Discussion
In this paper I presented a general longitudinal model and described how special cases of
this model yielded several well-known longitudinal models. In Figure 1 this family of longitudinal
models is displayed. The submodel (12) encompasses all models except the AR(2) model, which
should be regarded as a direct descendent of the general longitudinal model (7). The second order
autoregressive structure needs a mechanism of transmission which is more complicated than the
submodel (12) can provide. Therefore the broader model (7) was used.
The submodel can be divided into two categories: models that need the matrix Κ and
models and models that restrict this matrix to an identity matrix. Autoregressive models need the
matrix Κ in order to model the decaying of information over time (also called entropy by Dwyer,
1987). The effect of the same source of variance (initial or innovation) on a variable depends upon
the passing of time. Although time is not explicitly modeled in the AR models, it is shown that the
factor time can be incorporated if the piecewise slopes are used as dependent variables. Whatever
the exact functional relationship with time may look like, in many applications the secant line (a
line connecting two points on a curve; mathematical term for piecewise slope) might be a
reasonable approximation of the real curve (Rogosa, Brandt & Zimowski, 1982, p. 728; Willett,
1989). Although to the best of my knowledge autoregression for piecewise slopes has not been
described in the literature, this approach might be fruitful in cases where the time steps differ
among subjects. In this case the difference score divided by the elapsed time between the occasions
on which the subjects has been observed, may be a better estimate for modeling the developmental
process.
Another model which is, again to the best of my knowledge, unknown in the literature is the
autoregression on latent changes. Previous changes may predict later changes and this may or may
not be independent of the level of the score (note that two versions of this model have been
proposed). A developmental process, in which change is directional, may better be modeled by
predicting changes by previous changes. This model argues that change is both directional and
(partly) predictable. These characteristics are shared with the growth curve models, but unlike these
models random changes can be incorporated into the true scores and no functional relationship with
time has to be made. Directional change contrasts with the conventional AR models in which the
innovations are normally treated as independent of each other (but see Finkel, 1996).
66
The models that restricted the matrix Κ to an identity matrix were the Latent Difference
Model, the Linear Growth Curve Model and the First Order Moving Difference Model. One could
question if the Latent Difference Model (and also the equivalent Smallest Piecewise Linear Growth
Model) should be considered to be a model, since no further restriction are imposed and only a
transformation of the scores is obtained. This may be true, but the ‘model’ provides some major
advantages over more restricted models. First it does not depend on characteristics of data and they
can be used if the developmental process is unknown. In contrast, Growth Curve Models and first-
order Autoregressive Models make strong assumptions about the developmental process. Growth
Curve Models assume that the explicit relationship with time is tenable, and autoregressive models
assume that the innovations are stochastically independent of each other. Second, as Arminger
(1987, p. 339) argues that difference scores protect against misspecification of the model by
omitting stable variables: the estimation of the model is still consistent even though the model is
partly specified. This an important advantage of panel studies, since omitted variable bias is one of
the most severe threats for the validity of any model (Dormann, 1999). However, Arminger warns
(on p. 340) that this protection is no longer present if the lagged dependent variable is included in
the regression model (as in AR models). Third, latent difference scores may be better predictors
than the original scores in many panel studies. Models including multiple repeatedly measured
variables are often modeled as autoregressive models with an additional cross-lagged structure
explaining the causal effects upon each other. By partialling out the stabilities the predictors explain
residual changes. However the predictor itself is in this model not a change variable, but instead the
latent score is used. For some data sets it might be better to use the changes in one variable to
predict (residual) changes in another variable.
In the Latent Difference Model the covariance matrix was unconstrained, but restricting this
matrix as a diagonal matrix yields the Wiener Simplex. An interesting application of the Wiener
Simplex can be found in modeling individual change (Mellenbergh & Van de Brink, 1998).
The Smallest Piecewise Growth Curve Model is equivalent to the Latent Difference Model.
Restricting the slopes of each subject as equal assumes a constant rate of change for each subject
and this results in a restricted version of the Linear Growth Curve Model. This model is overly
restrictive, because it does not allow for deviations around the curves. Thus, the conventional
presentation of the Linear Growth Curve Model is not nested in the Latent Difference Model, but is
a special case of the submodel (12). One aspect of the Linear Growth Curve Model is its reduction
of dimensions: only two common factors (an intercept and a slope factor) are necessary to describe
the systematic part of the growth. However, for every measurement occasion time-specific residuals
67
are specified. In order to reduce the number of dimensions the matrix Ν is used: the submodel (12)
provides as many factors as there are measurement occasions, but the Linear Growth Curve Model
and also the First Order Moving Difference Model only need a few. So a provision is made in the
submodel to reduce the dimensions. A further reduction of dimensions of Linear Growth Curve
Model yields the Random Intercept Model: both the variance and the mean of the slope factor are
fixed to the value of zero. Of course these new restrictions make the relationship with the factor
time redundant.
A pedagogical advantage of presenting longitudinal models as factor models is that these
representations focus more clearly on the exogenous sources of variance which underlie all the
relationships between the latent construct over time. All longitudinal models start with initial
variance, which will is passed to present and future measurement occasions. Subsequently new
sources of information come into play and these have to be transferred again. The models differ in
how they picture these forms of input and how they transmit this information to the present and
subsequent waves.
The relation between longitudinal models and factor models has another interesting feature:
all longitudinal models reduce to one-factor models if the variance(s) of the change factor(s)
(innovation terms in the AR models and slope factor in the growth models) become(s) zero. In this
case the single common factor represents the initial scores. This one-factor model may include
time-specific disturbance terms which turns it into a random intercept model.
Paradoxically, although in the Latent Growth Curve Model the level 1 parameters are treated
as random and the autoregressive coefficients are fixed in the population, the assumptions about the
underlying developmental processes in both models are opposite: growth curves models assume a
constant, fixed process for each subject, whereas the autoregressive models assume a stochastic
process, where random changes are incorporated into the true scores for each subject.
Recently a synthesis between the seemingly antagonistic AR and Latent Growth Curve
Models were made. Interestingly, it was not possible to use submodel (12) to include both structures
into a single hybrid model, although both models could be fitted separately within this framework.
This can be explained by the different functions the factors have in the AR and Latent Growth
Curve Model. In the AR model the first factor represents the initial scores and all subsequent factors
are innovation terms. In contrast the first factor in the Latent Growth Curve Model represents the
start4 of the growth trajectories for each person and this is only one of the two components for the
initial score (the second is the time-specific residual). The slope factor is quite different from the
4 Assuming a conventional fixation scheme of fixing the first basis coefficient to “0”.
68
innovation terms in two ways: First it is tied to the time dimension and secondly it is usually
correlated with the intercept factor. Innovations terms have no relationship with the time factor and
are assumed to be independent of each other.
The interpretation of the Bollen & Curran model in terms of the underlying developmental
process seems rather complicated. Since two simultaneously operating processes are involved, the
interpretation of each process should account for the existence of the other. For ease of reasoning
one consider a two-stage procedure: One can either start from a Latent Growth Curve Model and
subsequently extend the model with an autoregressive structure or one can start with a first order
Autoregressive Model and later add an intercept and slope factor. Lets start with a linear Growth
Curve Model. Provided that a measurement model is included and the growth curves refer to the
true variates, for each subject the time-specific deviations around his/her growth curve can be
interpreted as caused by the particular state the subject was in at that moment (Garst, Frese,
Molenaar, in press; see also McArdle & Woodcock, 1997). Although states are by definition
transient they may show a regular pattern over time (e.g., oscillatory) and may influence the
outcome at the next measurement occasion. Thus, one interpretation of the Bollen & Curran model
is that development of the state components can be characterized by an autoregressive nature and in
this model stochastic time-specific changes can have a lasting (although decaying) effect on later
outcomes. If one compares Figures 15 and 16 one can notice that the disturbance terms in Figure 15
have been replaced by the autoregressive factors on top of Figure 16.
Alternatively, one can first conceive a first order autoregressive model and in a second stage
one can cancel the independence assumption for the innovation term by adding an intercept and a
slope factor. Innovation terms are deviations for each subject from the regression line (which is
assumed as fixed in the population). For each subject these innovations are now partly predictable
by his/her linear growth curve. Thus, the second interpretation of the Bollen & Curran hybrid model
is that it is a growth curve model for the innovation terms of a first order AR model.
In summary, the hybrid model decomposes change into three components: First, a
component which refers to a continuous underlying growth process which is constant for all
measurement occasions for each individual, and secondly, an autoregressive process which is time-
specific and constant for all subjects and finally a stochastic component which is both time-specific
and different for each subject.
The final question is: How flexible is the factor framework for longitudinal models? For
instance, in the multivariate models: Can also cross-lagged, synchronous and reciprocal effects be
specified? We think that the multivariate extension of the general model is flexible enough to fit
recursive models. However, in models including reciprocal relationships the matrix of structural
69
regression coefficients cannot be rearranged into a triangular form and it seems that these models go
beyond the structure of factor models as described in this paper.
References Bast, J.W., & Reitsma, P. (1997). Matthew effects in reading: A comparison of latent growth curve
models and simplex models with structured means. Multivariate Behavior Research, 32, 135-167.
Browne, M. W. (1993). Structured latent curve models. In C.M. Cuadras & C.R. Rao (Eds.),
Multivariate analysis: Future directions 2, (pp.171–197). New York: Elsevier Science Publishers.
Bryk, A.S. & Raudenbush, S.W. (1992). Hierarchical Linear Models: Applications and data
analysis methods. Newbury Park: Sage Publications.
Browne (1982). Covariance structures. In D.M. Hawkins (Ed.). Topics in Applied Multivariate
Analysis. Cambridge: Cambridge University Press.
Cronbach, L.J., & Furby, L. (1970). How we should measure "change" - or should we?
Psychological Bulletin, 74, 68-80.
Curran, P & Bollen, K. (in press). The best of both worlds: combining autoregressive and latent
curve models. To appear in A. Sayer & L.Collins (Eds.). New Methods for the Analysis of Change.
Dormann C. (1999). Modeling unmeasured third variables in longitudinal studies on organizational
stress. The case of social stressors at work, irritation, and depression. Doctoral Dissertation.
Johann Wolfgang Goethe Universität Frankfurt am Main.
Jöreskog, K.G. (1970). Estimation and testing of simplex models. British Journal of Mathematical
and Statistical Psychology, 23, 121-145.
Kenny, D.A., & Campbell, D.T. (1989). On the measurement of stability in over-time data. Journal
of Personality, 57, 445-481.
Long, S.C. (1984). Confirmatory factor analysis. Sage Universities Paper series on Quantitative
Applications in the Social Sciences, series no. 07-033.Beverly Hills and London: Sage Pubns.
Mandys, F., Dolan, C.V., & Molenaar, P.C.M. (1994). Two aspects of the simplex model:
Goodness of fit to linear growth curve structures and the analysis of mean trends. Journal of
Educational and Behavioral Statistics, 19, 201-215.
McArdle, J.J., & Nesselroade, J.R. (1994). Using multivariate data to structure developmental
change. In: S.H. Cohen & H.W. Reese (Eds.). Life-span developmental psychology: methodological
contributions (pp. 223-267). Hillsdale: Lawrence Erlbaum.
70
Mellenbergh, G.J., & Van den Brink, W.P. (1998). The measurement of individual change.
Psychological Methods, 3, 470-485.
McArdle, J.J., & Aber, M.S. (1990). Patterns of change within Latent Variable Structural Equation
Models. In: A. Von Eye (Ed.). Statistical methods in longitudinal research. Volume 1. Principles
and structuring change.(pp. 151-224). Academic Press: Boston
McArdle, J.J., & McDonald, R.P. (1984). Some algebraic properties of the Reticular Action Model
for moment structures. British Journal of Mathematical and Statistical Psychology. 37, 234-251.
McArdle, J.J., & Woodcock, R.W. (1997). Expanding test-retest designs to include developmental
time-lag components. Psychological Methods, 2, 403-435.
McCloy, R.A., Campbell, J.P., & Cudeck, R. (1994). A confirmatory test of a model of performance
determinants. Journal of Applied Psychology, 79, 493-505.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
Muthén, B.O., & Curran, P.J. (1997). General longitudinal modeling of individual differences in
experimental designs: A latent variable framework for analysis and power estimation.
Psychological Methods, 2, 371-402.
Rindskopf, D. (1984). Using phantom and imaginary latent variables to parameterize constraints in
linear structural models. Psychometrika, 49, 37-47.
Rogosa, D.R, Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurement of
change. Psychological Bulletin, 92, 726-748.
Rogosa, D., & Willett, J.B. (1985). Satisfying a simplex structure is simpler than it should be.
Journal of Educational Statistics, 10, 99-107.
Rovine, M.J. & Molenaar, P.C.M. (1998). The covariance between level and shape in the latent
growth curve model with estimated basis vector coefficients. Methods of Psychological Research,
3, 95-107.
Steyer, R., Eid, M., & Schwenkmezger, P. (1997). Modeling true intraindividual change: true
change as a latent variable. Methods of Psychological Research Online, 2, 21-33.
Stoolmiller, M. (1995). Autoregressive effects in structural equation models: Autoregressive effects
in structural equation models: We see some problems. In J.M. Gottmann (Ed). The analysis of
change (pp. 261-276). Mahwah, NJ: Erlbaum.
Vonesh E.F., & Chinchilli V.M. (1997). Linear and nonlinear models for the analysis of repeated
measurements. New York: Marcel Dekker.
Willett, J.B. (1989). Some results on reliability for the longitudinal measurement of change:
Implications for the design of studies of individual growth. Education and Psychological
Measurement, 49, 587-602.
71
Willett, J.B., & Sayer, A.G. (1994). Using covariance structure analysis to detect correlates and
predictors of individual change over time. Psychological Bulletin, 116, 363-381.
Willett, J.B., & Sayer, A.G. (1995). Cross-domain analysis of change over time: Combining growth
curve modeling and covariance structure analysis. In G.A. Marcoulides & R.E. Schumacker (Eds.).
Advanced structural equation modeling: Issues and techniques, (pp. 125-157). Mahwah, NJ:
Erlbaum.
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Part 2
Chapter 3 Control and Complexity in Work and the Development of Personal Initiative
(PI): A 5-Wave Longitudinal Structural Equation Model of Occupational
Socialization
Introduction
Personal initiative (PI) is a relatively new concept which we assume will become more
important in the future. Many companies are moving from stable structures to change oriented
organizations and the issue of PI is of high importance in any change process. People who just react
to change situations and just do what they have been ordered to do or what is necessary but do not
go “the extra mile” will not be able to carry changes actively forward and to make them work. To
do this they need initiative. Performance concepts that emphasize a proactive and self-starting
orientation are increasingly important with the advent of new production systems (e.g., Just in
Time, Total Quality Management, Advanced Manufacturing Technology), with new responsibilities
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assigned to rank and file workers (Wall & Jackson, 1995; Taira, 1996), with reduced supervision in
these new production systems (Womack, Jones, & Roos, 1990), with increased participation in
continuous improvement programs (Imai, 1994; Spreitzer, 1995), and with changes of the job
concept that require a more active orientation in the labor market (Bridges, 1995). Thus, industry
pushes employees to become more involved and active in their work (Lawler, 1992). Moreover, for
individuals, careers will depend more and more on initiative. The concept of PI may be an
important prerequisite for the issue of employability.
A practical and theoretically important question is which factors contribute to taking PI at
the work place. We would like to answer this question within a large five-wave longitudinal study
in East Germany. The longitudinal study allows us to study the development of PI as a function of
work place and personal characteristics. Moreover, it also makes it possible to study reciprocal
effects, such as the effects of work characteristics on PI and the effects of PI on changes in work
characteristics. An occupational socialization framework (Frese, 1982) is used to study these
developments. East Germany is a particularly interesting region to study PI, because a high amount
of changes in work and work places occurred and this lets us look at circular effects as well.
The Concept of Personal Initiative
PI consists of the following aspects (Frese et al., 1996, Frese, Fay, Hilburger, Leng & Tag,
1997): First, it is self-starting which means that goals are developed without external pressure, role
requirements, or instruction. Thus, PI is the pursuit for self-set goals in contrast to assigned goals.
An example is a blue-collar worker who attempts to fix a broken machine although this is not part
of his or her job description. Second, it is pro-active that is to prepare oneself for negative events
and prevent these from happening, for example when a blue collar worker attempts to prevent
breakdowns of the machine in the future. Third, it overcomes barriers on the way to the goals, that
is, goal pursuit is not stopped prematurely because problems appeared on the way towards the goal.
PI, as conceptualized for this article, consists of motivated behavior that leads in the long
term to positive outcomes for the individual and for the company. The long-term effects are
important here because in the short term, PI may even be negatively sanctioned by the organization
or by the supervisor because, initiatives tend to “rock the boat” and produce changes that are not
always welcome. If one defines motivation with (Ford, 1992), that it directs, energizes, and
regulates goal directed behavior, PI is reserved for those behaviors that are based on self-set goals
and that are energized to overcome many difficulties and that change the environment at least to a
certain extent. As any performance it should be affected by personality traits (for example proactive
75
personality, Crant, 1995), specific attitudes and orientations, and by situational parameters. A model
of how it develops with regard to work characteristics will be presented below.
Validity studies have been carried out and the validity of the PI concept is discussed next. PI
was shown to be related to the impression of PI by life partners (Frese et al., 1997). Another validity
issue was to distinguish the concept from organizational citizenship behavior. Conceptually, PI is an
aspect of contextual performance (Motowidlo, Borman, & Schmitt, 1997) because it does not
usually belong to the formalized job requirements of technical core performance. Organizational
citizenship behavior is the core concept of contextual performance. The major dimensions that
differentiate PI from organizational citizenship behavior is its proactive and self-starting nature.
Two aspects – altruism and generalized compliance have been studied in most detail within the
Organizational Citizenship Behavior paradigm (Smith, Organ, & Near, 1983). Fay (1998) has
shown that generalized compliance has a very different nomological net than PI; however there is
some overlap between altruism and PI. However, altruism can be shown in two forms: One is to
react to requests and obvious needs. In this case, there is an obvious conceptual difference of
altruism to PI. Another form of altruism requires initiative and is self-starting because it is not
salient for the other person involved that help is required. Thus, this form of organizational
citizenship behavior is self-starting. Thus, clearly, there is no overlap with generalized compliance
but there is one form of altruism – the one based on PI – that shows some overlap with PI. By
showing the usefulness of PI, this may also contribute to differentiating the concept of
organizational citizenship into forms that are based on PI and those that are not.
PI is a motivation concept that is action oriented and that should lead to higher
achievements. PI is, therefore, related to need for achievement but it is not identical to it (r=.20,
Frese et al., 1997). Conceptually, need for achievement can also be differentiated into a form that
relates to self-set goal and one related to other-set goals. Action orientation (Kuhl, 1992) is also
related but the two concepts are differentiated from each other as seen by their low correlation
(r=.20 in an East and r=.14 in a West German sample, Frese et al., 1997).
PI has been shown to be lawfully related to certain behaviors and to personal and firm
success in these validity studies: PI is related to developing career plans and, more importantly,
with executing them at a later stage (Frese et al., 1997). Moreover, unemployed with a high degree
of PI find a job more quickly than those with a lower degree of PI – PI was measured prior to
becoming unemployed (Frese et al., 1997). In a training, in which the task is to learn from
exploration, those students who have shown a higher degree of PI in their studies, seek less help and
reassurance from the trainer and overcome problems by themselves (Fay & Frese, 1998a). PI was
also measured in small scale entrepreneurs and was shown to be related to firm success in Uganda
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and Zimbabwe (Koop, De Reu & Frese, in press; Krauss, Frese & Friedrich, 1999) and in East
Germany (Zempel, 1999). Finally, a pro-initiative climate in companies, measured as a general
climate factor, is strongly related to the profitability of medium sized German firms; in addition,
there are interactions with process innovations: Those with many process innovations (e.g., total
quality management, re-engineering) are only profitable if they also have a pro-initiative climate in
their firm (Baer & Frese, 1999).
Occupational Socialization
Occupational socialization is defined as a developmental perspective that emphasizes "the
changes that take place in the person as a function of the job." (Frese, 1982, p. 209). Occupational
socialization theory (Frese, 1982; Kohn & Schooler, 1978; Semmer & Schallberger, 1996; Volpert,
1977) is concerned with the influence of control and complexity on long-range changes in people.
Examples of occupational socialization are the effects of non-control and stress on ill-health
(Gardell, 1971; Karasek, 1979, Karasek & Theorell, 1990), the effects of work complexity on
intellectual flexibility (Kohn & Schooler, 1978), on intelligence (Schallberger, 1988), and on values
and self-concept (Mortimer & Lorence, 1979a and b), and the effects of job characteristics on work
motivation (Hackman & Oldham, 1975).
There are three interfaces between the organization and the individual: The colleagues,
managers, and the work characteristics (including rules and procedures). The latter constitute the
substance of occupational socialization. Complexity and control at work are seen as
materializations of organizational decisions which have an influence on the development of the
person (Volpert, 1977). Occupational socialization is, thus, related to work design issues and
socialization of organizations is accomplished via work characteristics. Therefore, work
characteristics are used as independent variables. In contrast, organizational socialization (Chao,
O'Leary-Kelly, Wolf, Klein, & Gardner, 1994) is concerned with the other interfaces of the
organization and looks directly at what the organization does to socialize the person into the
organization, for example, socialization strategies that "break people in" (van Maanen, 1976).
We want to study PI within the occupational socialization framework and, therefore, look at
the effects of work characteristics on PI. Both organizational and occupational socialization
research emphasize that people are not just passive recipients of organizational and work input but
are also actively changing and selecting work environments. Thus, there are reciprocal relationships
between socialization and selection (Kohn & Schooler, 1978; Semmer & Schallberger, 1996) and
people are active participants ("...socialization is a process affected not only by organizational
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initiatives, but also by newcomer initiatives", Morrison, 1993, p. 173). Thus, PI should not only be
affected by the tasks at work but should in turn also influence which kinds of tasks are selected for a
person and by a person.
On a more general level Bandura (1997, p. 6) has argued with his concept of reciprocal
determinism that "internal personal factors in the form of cognitive, affective, and biological events,
behavior, and the environmental events all operate as interacting determinants that influence one
another bidirectionally." We would like to discuss theoretically and show empirically that PI
constitutes one important mechanism by which people change their (work-) environment. Because
of this, a concept of PI is central to the notion of reciprocal determinism.
The Theoretical Model
We would look at how occupational characteristics (in our case, control at work and
complexity of work) lead to personal initiative and vice versa. Our theoretical model is presented in
Figure 19.
Figure 19: Occupational Socialization Model of Initiative
A general occupational socialization framework (Frese, 1982; Semmer & Schallberger,
1996) is used to understand the development of initiative at work and hypothesized reciprocal
relations make it possible that PI increases control and complexity in one's works tasks (Kohn &
Schooler, 1978) and changes one's mastery orientation. In the following we shall walk along Figure
19 and start with the control and complexity.
Work characteristics
(Control, Complexity)
Mastery
Orientation
Initiative
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Control and Complexity as Work Characteristics. We restrict the analysis to the two work
characteristics control and complexity because they are related and are the core to occupational
socialization theory. A person has control at work when he or she "has an influence over his or her
actions and over the conditions" of work in accordance with his or her goals (Frese, 1989, p. 108).
Complexity has been defined by the number of elements that have to be considered in decisions
(Frese, 1987; Wood, 1986). Control and complexity are conceptually and empirically related as
both refer to decision making possibilities. Control and complexity are empirically related; for
example in one study the respective correlations between these two variables were .42 (control and
complexity measured on the level of job incumbents) and .70 (measured by observers’ ratings)
(Semmer, 1982). Control and complexity are, therefore, often combined into one factor (e.g., by
Frankenhaeuser & Gardell, 1976; Karasek, 1979). A more pragmatic reason to restrict the analysis
to two variables was that we needed to reduce the number of variables in the complex analysis of a
longitudinal study.
The notion that control and complexity are important work characteristics has been
theoretically and empirically supported by many authors (Gardell, 1971; Greenberger & Strasser,
1986; Karasek & Theorell, 1990; Kohn & Schooler, 1978; Kohn et al., 1997; Kornhauser, 1965 and
Spector, 1986) and is central to occupational socialization theory (Frese, 1982; Hacker, 1986; Kohn
& Schooler, 1978; Volpert, 1977). Job changes such as job enrichment or autonomous work groups
have emphasized changes in the level of control and complexity (Emery & Thorsrud, 1969;
Gulowsen, 1972; Jackson, et al., 1993; Wall & Clegg, 1981). The job characteristics model by
Hackman and Oldham (1975) presents convergent evidence. While this model is made up of five
variables, the central variables are autonomy and skill variety. Autonomy - control at work in our
terminology - is central to the 5 variables since it has the highest relationship with the overall job
motivation potential in Hackman and Oldham's (1975, r=.80) and in Wall, Clegg, and Jackson
(1978, r=.79) and with job satisfaction (Loher, 1985). Skill variety in Hackman and Oldham's
(1975) - a concept that is similar albeit not the same as complexity of work - is highly correlated
with autonomy (Wall et al., 1978) and it has been argued that job complexity is the core of
Hackman & Oldham's model (Gerhart, 1988).
The Influence of Control and Complexity on Mastery Orientation. Control and complexity
have been suspected to be direct predictors of performance (Frese, et al., 1996; Greenberger,
Strasser, Cummings, & Dunham, 1989; Wall & Jackson, 1995; Karasek & Theorell, 1990; Kohn &
Schooler, 1982; Spector, 1986). In contrast, our model (Figure 19) specifies that control and
79
complexity influence PI via mediators. There are three interrelated mediating mechanisms that
produce the relationship between control at work and PI: control aspirations (or lack of control
aspirations as in the case of helplessness), control appraisal, and self-efficacy.
First, whenever control is thwarted, helplessness appears. This implies negative
motivational consequences because the organism stops trying to control the environment when it
does not expect any positive outcomes from such attempts (Heckhausen & Schulz, 1995; Seligman,
1975; White, 1959). Seligman (1975) has argued that helplessness is related to control appraisals
and Abramson, Seligman, and Teasdale (1978) have shown that these expectations of non-control
can be generalized widely. Opposite ideas also exist: Lack of control may actually lead to higher
control aspirations because one is motivated to be in control again (cf. also Greenberger & Strasser,
1991). Reactance should follow when control is low. Wortman & Brehm (1975) have combined
reactance and helplessness theories. In the short term, lack of control can actually increase the
aspirations for control, as reactance theory suggests (Wicklund, 1974). However, if the attempts to
increase control get thwarted, learned helplessness develops (Wortman & Brehm, 1975). Thus, lack
of control leads to giving up wanting to have control and reduces control aspirations. A low level of
control aspirations leads people to show little PI.
Second, control appraisals relate to believing that one is able to influence decisions at work
(Folkman, 1984). If one has control at work, it is likely that one also expects the situation to be
controllable. If people expect that they can influence things at work, they are more likely to show
PI.
Third, Bandura (1997) argued that mastery experiences lead to higher self-efficacy which is
the expectancy that one is able to perform a certain action effectively. Control at work makes it
possible to have such mastery experiences which lead to self-efficacy. If people have a high degree
of self-efficacy, they will be more likely to show a high degree of PI because they have to rely on
their own effective actions when taking initiative.
As discussed above, there is theoretical and empirical overlap of control and complexity.
Complexity should also help in the development of these three mediators because complexity
increases the chances to have mastery experiences at work. Self-efficacy as perceived competence
requires the possibility to use skills and knowledge which can only be shown if a certain task
complexity exists (Bandura, 1997).
We measured all three variables but combined them into one general concept – mastery
orientation – for theoretical and practical reasons. The practical reason was to decrease the number
of variables in our complex LISREL modeling. The theoretical idea is that there is a common theme
of the three concepts – control aspirations, control appraisal, and self-efficacy are all related to
80
being able to master and to want mastery at work. We call it, therefore, mastery orientation.
Orientation (like an attitude) includes affective, conative, and cognitive components (Eagly &
Chaiken, 1993) (in terms of Hackman & Oldham, 1975, they are critical psychological states, albeit
Hackman & Oldham did not study these specific psychological states). The term orientation
signifies that it is a concept of medium specificity. It is not a very specific attitude but also not a
general personality trait. With Fishbein & Aijzen (1975) and Rotter (1972), we think that all person
concepts can be differentiated along the dimension of generality and that the generality of the
concept should fit the research question. We deal with an intermediate level of specificity as all
concepts are supposed to predict PI across a number of domains within the work setting. Thus, all
concepts used in our study are specific in so far as they refer to the work setting and mid-range as
they refer to broad categories of work, person, and behavior in the job.
We do not yet know enough about the time trajectory for these effects to appear. Control
and complexity can influence a person only given a certain exposure time. However, we do not
know whether these processes take months, half a year or a full year; therefore we shall contrast
models with short and long time lags (synchronous and lagged effects). In general, the timing of
effects due to working conditions is an issue that is very complicated and far from being resolved
theoretically or empirically (cf. Frese & Zapf, 1988 on time problems in a similar area).
Hypothesis 1: Control and complexity increase mastery orientation which consists of control
aspirations, control appraisals, and self-efficacy.
The Effects of Mastery Orientation on Initiative. A higher mastery orientation should
contribute to a more active approach and, thus, more PI. Potential processes are: People with high
mastery orientation should have a stronger sense of responsibility (Hackman & Oldham, 1975), they
should not give up easily when problems appear (Bandura, 1997; Folkman, 1984), they should
search more for opportunities to act (Bandura, 1997; Folkman, 1984), they should have higher
hopes for success and therefore take a long term perspective in goal setting and planning
(Heckhausen & Schulz, 1995), and should actively search for information (Ashford & Tsui, 1991),
which leads to better knowledge of where to show initiative. Indeed, self-efficacy has been shown
to be related to performance (Stajkovic & Luthans, 1998). All of these effects are supposed to be
immediate because attitudes and cognitions should have an immediate regulatory function on
actions (Miller, Galanter, & Pribram, 1960). The impact of mastery orientation on PI should,
therefore, be synchronous.
Thus, our hypothesis 2 is: Mastery orientation leads to a higher degree of personal initiative
synchronously.
81
Hypothesis 3: Mastery orientation functions as a mediator between work characteristics and
PI.
The Effects of Personal Initiative on Mastery Orientation. In the sense of reciprocal
determinism, PI should not only be determined by mastery orientation but should in turn also
determine mastery orientation (Bandura, 1997). Showing initiative provides the experience that one
has mastered difficulties and problems that appear after one has shown PI. For example, if a person
has implemented an idea to produce better quality with a new procedure, he or she will think of
him- or herself to be effective, to have control over the environment, and he or she will be
encouraged to assert control again. Therefore, such experiences function as a mastery experiences
and lead to higher mastery orientation (in the sense of higher expectations that one can master the
world and one's actions and that it is worthwhile). For this reason, Figure 1 displays reciprocal paths
between PI and mastery orientation.
Hypothesis 4: There is an effect of PI on mastery orientation.
The Effects of Personal Initiative on Control and Complexity. The reciprocal relationships
between work and behavior stands in contrast to some older approaches of occupational
socialization which assumed an influence of work on the person only (e.g., Frese, 1982 or Van
Maanen, 1976). However, the newcomer in a job changes the roles and the job content (Ashford &
Black, 1996; Ilgen & Hollenbeck, 1991; Staw & Boettger, 1990) and is, therefore, able to change
the job as well.
Thus, PI as an active approach to work, should eventually have an influence on work
characteristics. Two mechanisms may play a role here: First, people with high PI may produce some
added complexity and control in their given jobs. The tasks of a job are not completely fixed, once
and for all. There are always emergent elements to be developed (Hacker, 1986, Ilgen &
Hollenbeck, 1991). For example, by developing initiatives to improve productivity, the given job is
changed and control and complexity are increased. Work then becomes more interesting and one is
further encouraged to change it by developing better work procedures. Another examples shows
that the superiors can also be involved in this process: A secretary might have been originally hired
to be a typist; if she or he takes over more and more tasks in the organization of the group, the
superior will rely on him or her and in this way she or he actually increased control and complexity
of the job.
82
Second, another mechanism goes via job change. People with higher PI should use job
changes to get more challenging jobs. People with higher PI should also be more successful in
finding those jobs. Challenging jobs include tasks with a higher degree of control and complexity.
In the following we use the term job change to signify both mechanisms. Both mechanisms
need a certain amount of time to unfold. It is a slow process for the secretary described above to
convince the superiors that he or she should be approached for organizational tasks (and not just for
typing). Certain events, like reorganizations, new supervisors, etc. may help to speed up the process.
Similarly, giving up a job (or losing a job) and searching for another one is normally not a frequent
event and, thus, takes time to unfold. Kohn and Schooler (1978) found a lagged selection effect
with a time lag of 10 years. In a different area, Wilk, Desmarais, and Sackett (1995) found that
people gravitate to jobs commensurate with their ability within a five year period. We assume that
the stability of the economic situation of a country also influences the effective time lags (because
stability leads to more stable jobs). The time lags of 10 years (Kohn & Schooler, 1978) and 5 years
(Wilk et al., 1995) have been found in relatively stable economies. In a transitional economy, such
as East Germany, in which many more job changes occur (Frese et al., 1996), the time lag may be
much shorter.
Thus hypothesis 5 states: PI increases the degrees of control and complexity in the long run.
Hypothesis 6: PI is a mediator between mastery orientation and job change effects.
The Setting of the Study
Because of global competition and technological and organizational innovations, jobs
change their nature in today's Western economies (Bridges, 1995). Still, Western economies are
relatively stable in comparison to transitional ones which changed from socialist to market driven
economies (Kohn et al., 1997). We wanted to do this study in a high change situation and we picked
East Germany. In East Germany, many people have lost their jobs and had to find other ones. Even
those who did not lose their jobs experienced drastic changes in the technical lay-out and
organization of their jobs (and they could influence this process if they showed PI). In nearly every
company, new technology and new organizational structures were introduced. Thus, it is a situation
of revolutionary job change which affected nearly every East German (Nickel, Kühl & Schenk,
1994). Because of its dynamic situation, East Germany is a particularly good area to do research on
occupational socialization and selection effects. Occupational socialization research is better when
there is a natural "zero point", e.g., when all subjects start a given job. The natural "zero point" in
83
this study is the beginning of the transition from socialism to capitalism which started in Each
Germany at the time of unification of Germany. Additionally, PI is low in East Germany; in a
comparison of East and West Germans' PI, Frese et al. (1996) suggested that the differences in
control and complexity were important reasons for the higher degree of initiative in West Germany.
To test an occupational socialization model described in Figure 19, a longitudinal study in a
high change situation is needed. Ideally, the longitudinal study should have at least three
measurement points because identification problems are then reduced (Finkel, 1995). It is even
better to have more measurement points because then there is a chance to replicate the effects
several times and to study the exact nature of the effects. Additionally, it allows testing rather
complex models. In our case, we have used five waves.
Finally, we wanted to have as many sources of information as possible, not just
questionnaire responses. Unfortunately, it was not possible to observe people at work (companies
would not have given us their consent to do research at a time when they were scrambling to
survive; this was true at least for the first four years after the change over from socialism to a
market economy). A combination of behavioral interviews, questionnaire research, and ratings by
the interviewers was chosen.
Methods
Sample
The sample was drawn from Dresden, a large city in the south of East Germany; it is the
capital of Saxonia, houses a large Technical University and is relatively well-off in comparison to
other East German cities which are often quite poor. A "random walk sampling" was used by
randomly selecting streets, selecting every third house and in each house, every fourth apartment (in
smaller houses every third one). All people in this household between the ages of 18 and 65 with
full-time employment at T1 were asked to participate (thus, we sometimes had more than one
person per family). The refusal rate of 33% was quite low for a study of this kind. Confidentiality
was assured; if subjects preferred anonymity, this was done with the help of a personal code word.
In wave one (T1 for time 1) (July 1990), 463 people participated in Dresden. At wave two
(T2) (November, December, 1990) 202 additional people were asked to participate5. At wave three
(T3) (September 1991), the N was 543, at wave four (T4) (September 1992) the N was 506, at wave
5 Additional people were added to ascertain whether repeated participation had an influence on initiative. This is a worry in some developmental studies (Schaie, 1973). As we found that there was no such influence for T1 and T2, we discontinued to add further people in the other waves.
84
five (T5) (September 1993), N=478, at wave six (T6) (September 1995), N=4896. We did not
include wave one (T1) in our analysis and restricted our analyses to the five waves from T2 to T6.
We did this because we had added more subjects at T2 and, therefore, could use a larger N.
Experimental mortality did not prove to change the make-up of the sample. There were no
significant differences in the initiative variables between dropouts from T1 to T3 and full
participants. The sample is representative of the Dresden population on the relevant parameters (for
example, for age, social class, male/female percentage at work).
This article is based on a broad longitudinal study. Other publications of this study have
looked at the differences between East and West Germany (Frese et al., 1996), at the validity of PI
(Frese et al., 1997), at the relationship of conservatism and PI (Fay & Frese, in press), at the
function of self-efficacy at T3 and T4 of this study (Speier & Frese, 1997), at the relationship
between stressors and strain (Garst, Frese & Molenaar, in press) and at the moderating function of
social support on the stress process (Dormann & Zapf, in press). None of these papers have a
conceptually or methodologically done what the present paper attempts to achieve.
Interview Procedures
Structured interviews were used to measure personal initiative, with additional prompts
adapted by the interviewer to the particular answers provided. The interviews were carried out by
psychology and business students from Munich, Giessen, and Dresden trained during a two-day
course.
Subjects' answers were written down by the interviewers in a short form that was later
typed7 and used as the basis for a numerical coding system. After the short transcripts of the
interviews had been typed, they were coded by the interviewer him- or herself and by a second
coder. The coding system was either factual (for example, subject is unemployed or not - a
dichotomous variable), or it involved some kind of judgment (for example, to what extent does a
certain answer constitute initiative; usually a five point scale was used in these cases). Examples
were provided for the end points as anchors of the scales. All interviewers went to a two-day
training course that taught them the interview procedure and the use of the coding system.
6 N was higher at T6 because we made an extra effort to get at least questionnaire responses from those subjects who had moved to other parts of Germany. 7 For reasons of research economy, we did not use verbatim transcripts of the interviews. This was not necessary because the coding system was developed beforehand and the interviewers knew which answers had to be written down to make coding possible. However, the interviewers were also trained to write down the relevant responses as verbatim as possible; therefore, the records were not just a shorthand for coding.
85
After the interview, the subjects were given the questionnaires to fill them out at their
leisure (usually they were picked up one or two weeks afterwards). The work characteristics and the
mastery orientation variables were measured with the questionnaire. Immediately following the
interview, the interviewer evaluated the subject on a number of dimensions - this was deliberately
used as a subjective interviewer's response to the interviewee in question (we call it interviewer
evaluation and one of the measures of PI was taken from this). For this reason, no inter-rater
reliability was calculated here.
Measures
All measures were in German. In the questionnaire scales the response alternatives were
from 1 - 5 throughout; to make the scales comparable, the scale values were divided by the number
of items.
The work characteristics Control and Complexity were measured with four questionnaire
items each (Semmer, 1984; Zapf, 1993). Item examples are "Can you determine how you do your
work?" for control and "Can you learn new things in your work?" for complexity. Means (divided
by number of items) were 3.57 for control and 3.46 for complexity on average across the five
waves; the standard deviations were on average .80 for control and .68 for complexity across the
five waves. Complexity and control can be measured by questionnaires well because both variables
show high relationships of job incumbents’ self-reports with other people's judgments (Hackman &
Oldham, 1971; Semmer, 1982; Spector, 1992; Zapf, 1989).
The mediators were the questionnaire scales control appraisal, control aspiration, and
self-efficacy which were collapsed into one second order latent factor (see Introduction for our
theoretical and Results for the empirical arguments for collapsing these three variables into one
construct). Control appraisal measures how high one perceives one’s control with regard to work
with three items (Personally, my chance to influence ... things at the work place in general are very
good .... not at all good; ... climate in my department; ... decisions by the shop stewards [shop
stewards - Betriebsrat - is a decision body by law in all German firms]. Control aspirations was
developed by Frese (1984, printed in Frese et al., 1996 – then it was called control rejection; it is
now reversed scored) (7 items). Frese (1984) reported that he attempted at first to measure control
aspirations directly; but this resulted in little variance and a highly skewed distribution. Most people
at work wanted more control. He, therefore, measured whether or not people also accept the
potential negative consequences of control as well (e.g. higher responsibility for errors). This led to
a normal distribution and a more meaningful content of the scale (example, "I would rather be told
exactly what I have to do. Then I make fewer mistakes"). Self-efficacy is a work related generalized
86
scale with 5 items (similar to the one used by Schwarzer, Baessler, Kwiatek, Schroeder, & Zhang,
1997 and highly correlated with it) and shown to be useful in our context by Speier & Frese (1997).
The items are presented by Frese et al (1996) (sample item: "If I want to achieve something, I can
overcome setbacks without giving up my goal."). The Means (Standard Deviations) were 2.5 (.70)
for control appraisal on average across the five waves, 3.90 (.68) for control aspiration, and 3.55
(.51) for self-efficacy. Alphas were on average .61, .87, and.69 for control appraisal, control
aspiration, and self-efficacy respectively.
Personal Initiative was ascertained via a standardized interview and with an interviewer
evaluation at the end of the interview. We used three measures – Interviewer evaluation,
Overcoming barriers, and Active approach – with the latter two being condensed into one scale by
combining two items into one (so-called item parcels, March, Hau, Balla & Grayson, 1998). The 8-
item measure interviewer evaluation was filled out by the interviewer directly after the interview
as a subjective account of the degree of initiative that was shown by the particular interviewee
(degree of being active, goal oriented, independent, etc.). The interviewers were trained to use this
measure. The Alphas of this scale were around .92 for the five time periods, the mean was 3.6 on
average across the five waves and the SD was .9.
Overcoming barriers was based on a sort of situational interview (Latham & Saari, 1984).
The interviewees were asked to imagine having a certain problem, for example, a colleague who
always did his or her work sloppily, requiring additional effort from the interviewee. After the
interviewees suggested a way to deal with this situation, the interviewer would then present reasons
why that was not possible, thus presenting new barriers. After the third barrier (the question was
counted to be the first one), the respondents were asked whether they could think of additional
solutions. In this way we measured how many barriers the respondents were able to overcome.
Interrater agreement was r =.80 at T3. To overcome potential testing effects (Cook & Campbell,
1979 p. 52), we changed the problems three times, so that a repeat of the problem of T1 would
appear in T4, etc.
The scale Active approach was also based on this situational interview. Overcoming
barriers may be done more or less actively. Since proactivity is a core of personal initiative, it was
important to find out whether interviewees would just delegate a problem to other people (e.g., the
supervisor) or personally do something about the problems. The interviewers were asked (and
trained) to code how active an interviewee's propositions to overcoming barriers were. Overcoming
barriers and active approach were combined - in a scale called Situational interview; this
combined scale is based on 8 items and has an average alpha of .72 with a mean of 3.0 averaged
across the five waves and an SD of .71.
87
In principle we also ascertained other measures of PI in the interview who were shown to
correlate well with the measures used here (Frese et al., 1997, e.g., it is shown that these measures
also correlated well with partners’ estimates of PI and with a self-reported measure, as well with
giving suggestions at the work place and with participating in continuous education). We restricted
this analysis to three measures of PI. This was done because these three measures were consistently
used in all waves. Further, they are the best measures and they represent a good mix because they
combine an interview based performance measure (overcoming barriers) and two interviewer
estimates. Since they are based either on performance in the interview or on the interviewers'
judgments, they constitute a separate source from the questionnaire responses used for the
independent and moderator variables.
Models
Our overall model is displayed in Figure 19. From a methodological point of view, we have an
enormously complex array of potentially analyzable models because we have 5 different
measurement points and two levels of variables (first order constructs, second order latent
constructs) and several different causal time lags. In principle, one can always invent further
arrangements of the variables to produce other models. Therefore, we had to make certain decisions
to reduce the number of potential models.
In the following we shall first discuss the measurement models. Work characteristics are
frequently measured as latent constructs. Factor models assume that a latent common construct
determines the observed variables, that is the covariance among the observed variables (the items)
can be explained by this latent construct. However, the items of the work characteristics measures
control and complexity can also be conceived as the causes of a latent construct (Bollen & Lennox,
1991). A factor model implies, for example, that a change in the control over the timing of rest
periods is related to an equivalent change in the control over selecting one's methods of doing the
job. This does not have to be case. Therefore, a more reasonable model would consider both aspects
of control as causes for the latent control variable. In this "causal indicator model" a change in one
variable is not necessarily accompanied by a change in the other ones. The latent variable is then
only an abstraction of control in the sense that each specific instance of control added together leads
to overall higher control at work. Cohen, Cohen, Teresi, Marchi, and Velez (1990) criticized the
inappropriate use of confirmatory factor models by arguing similarly that in cases such as ours, one
should not develop latent construct to determine the observed variables. Therefore, the work
88
characteristics variables will not be fitted with a confirmatory factor analysis, because we prefer to
see them as causal indicators and not as effect indicators (Bollen and Lennox, 1991); we shall also
not calculate internal consistencies for the same reason (MacCallum & Browne, 1993)8. The causal
indicator model was calculated but it led to identification problems. Because we do not have good
theoretical reasons to weigh control and complexity, we used an equally weighted summation of the
two variables (McDonald, 1996). For reasons to keep a good variable to N ratio, it was also
necessary to decrease the number of variables in the model.
For mastery orientation, we chose a "banded error structure", which means that all unique
factors of identical items are correlated over time (Vonesh & Chinchilli, 1997). After the three
mastery orientation variables were treated as longitudinal measurement models9, the three measures
of mastery orientation - control appraisals, self-efficacy, and control aspirations - were modeled as a
second order construct. This was done for four reasons: First, the three mastery orientation variables
were significantly correlated (averaging across waves, the cross-sectional intercorrelations were .
34. Second, there is a coherent theme in these variables that makes it theoretically useful to
combine them (see our arguments above). Third, it was necessary to reduce the number of variables
for the structural equation analyses and, therefore, it was warranted to reduce these three mediators
to one. Fourth, the three variables produce a well fitting second order measurement model.
The PI scales were taken from different interviewers at different times; therefore, there is no
necessity for a banded error structure. In the structural model, these scales were also modeled as a
second order construct. This makes sense because they are well correlated (cf. also Frese, Fay et al.,
1997) and because a second order construct model has a good fit with the data.
To test for measurement invariance, we estimated models with free factor loadings and
alternative models with equal factor loadings over time (Pentzt & Chou, 1994).
The following structural models will be investigated (all of them shown in Figure 20). The
structural one-directional models are signified as I-models, and the reciprocal models as II- and III-
models. We used A, B, and C, to signify different time lags and arabic numbering for different lags
for the job change effects.
The Baseline Stability Model assumes that there are no causal relationships between the
variables except stabilities. It is used as a baseline model to test further structural causal models
(Hertzog & Nesselroade, 1987; Marsh 1993, Kenny & Campbell, 1989). Here each longitudinally
8 In earlier publications we did not yet think of this problem and have, therefore, calculated internal consistencies. The Alphas were for control .78 and for complexity .67 in Frese et al. (1996). 9 This means that the factor model is done for every time point within one model.
89
measured variable is repeatedly regressed on the same variable measured one wave before (Plewis,
1996).
The Fully Synchronous Socialization Model (I-A) is a longitudinal model in which
the working conditions impact on the mediating latent construct mastery orientation which in turn
impact on PI. Thus, it is an occupational socialization model because it assumes that work
conditions change person characteristics. It is fully synchronous because all the causal paths are
assumed to work at the same time. In this model the previous values of the dependent variables are
held constant so that we actually measure residual changes, as we do in all further models.
The Lagged-Synchronous Socialization Model (I-B) models a lagged effect from control
and complexity of work on mastery orientation and a synchronous effect of mastery orientation on
PI.
The Fully Lagged Socialization Model (I-C) is a model with time lags from work on mastery
orientation and from mastery orientation on PI.
From the 3 socialization models just described, we selected the empirically best fitting
model. This was then used a starting point for Models II and III which also involve reverse paths.
Model II is a Socialization Plus Job Change Model with reversed and direct paths from PI to work
characteristics. The reversed paths are assumed to be the result of job changes due to changing the
job or changing the content of one's work. We hypothesized this to be a slow effect. This implies
that this effect should be lagged. To be on the safe side, we calculated three models with a 3 to 4
years reverse effects lag, a two years lag and1 year lags (signified 3, 2, and 1).
From this we took the best II Model and used it as a starting point for Model III. The
Socialization Plus Job Change and Reciprocation Model (Model III) allows an additional
reverse path from PI to the mediators mastery orientation. The theoretical argument is that (at least
successful) personal initiative will lead to higher mastery orientation.
90
Baseline Stability Model
I-A Fully Synchronous Socialization Model
I-B Lagged Synchronous Socialization Model
I-C Fully Lagged Socialization Model
II-A-3 Socialization Plus Job Change Model (3 yr.)
II-A-2 Socialization Plus Job Change Model (2 yr.)
II-A-1 Socialization Plus Job Change Model (1 yr.)
III-A-1 Reciprocal Socialization Plus Job Change Model (1 yr.)
Figure 20: Structural Models (on Top, There is Personal Initiative, in the Middle Mastery Orientation, and at the Bottom Work Characteristics; from Left to Right: T2 to T6)
91
Statistical Analysis Method
Latent-variable models were first used to analyze the scales and in a second step (Anderson
& Gerbing, 1988, Jöreskog & Sörbom, 1993b p.113) structural equation models with simultaneous
estimates of the measurement and structural part of the model were done (Williams &.Podsakoff,
1989 p. 272) using LISREL VIII (Jöreskog & Sörbom, 1993a). Our models are complex not only
because they are longitudinal, but also because they test for mediation. Although many researchers
have used the Baron and Kenny's (1986) and James and Brett's (1984) approaches to test for
mediation, the use of structural equation modeling is a better strategy. The latter uses a simultaneous
estimate of the complete model and can deal with measurement error and nonrecursive parts of the
model as well (Brown, 1997).
Including the complete measurement model in the structural models would result in an
unfavorable subjects to variables ratio (Bentler and Chou,1987). To reduce the size of the structural
models factor scores and item parcels (Marsh, Hau, Balla, & Grayson, in press) were used. The
regression coefficients for the calculation of the factor scores were based upon longitudinal
measurement models after testing for equivalence of factor structure across time.
Model fit was assessed by the Root Mean Square Error of Approximation (RMSEA; Browne
and Cudeck, 1993) and the Comparative Fit Index (CFI, Bentler, 1990). Values of the RMSEA
lower than .05 indicate a good model fit and value of the CFI higher than .90 are desirable. Chi-
square values and degrees of freedom are also provided. We used the chi square difference test for
comparing nested models and the Expected Cross Validation Index (ECVI: Browne and Cudeck,
1993) and the Akaike (AIC, Akaike, 1987) for the non-nested models since these indicators show
how easy it is to cross-validate the models.
Treatment of Missing Cases
The N varies across the analyses. We, therefore, used covariance matrix based upon pairwise
deletion of the data was analyzed. Pairwise deletion is a more efficient method than list-wise
deletion and is preferred to listwise deletion (Roth, 1994). One reason for this procedure was
missing data as they appear in all studies of this type. However, a more important reason was that
people underwent strong changes and this led often to periods of unemployment, sabbaticals,
educational years, extended holidays, maternity leaves, extended lay-offs without being fired from
the job, etc. For example, of the 471 who had a job at wave 2, 97 did not work at wave 3 and of
those 428 with a job at wave 3, 91 did not have a job at wave 4. It was necessary to have a job to
answer the questions on the work related items. Given this picture across the different waves and
given that most people who lost a job at wave 3 had a job again at wave 4 (of those 97 not working
at T3, 46 had a job again at wave 4), a listwise missing data procedure would have led to a high loss
92
in N. Moreover, we would have lost precisely those people whose further fate was affected by PI,
for example, because they searched for a different job and got a job with higher (or lower) control
and complexity.
The sample size for the analyses was estimated as the median of different sample sizes used
for estimating the variances and the covariances. This leads to an N between 428 and 470 in the
measurement models and an N of 311 in the structural models. Whenever there were no data
available for the working conditions at a specific time (e.g. because of unemployment or maternal
leave), the data for PI and mastery orientation were ignored for this person for this wave. This was
done to prevent confounding with effects of unemployment.
Results
Confirmatory Factor Analysis
Table 1 provides the resulting fit indices of the longitudinal LISREL measurement models,
tested separately for free and equal factor loadings over time. All of the fit indices were very good.
There were no significant differences on the chi2 tests between free and equal factor loadings for the
first order mastery orientation variables: control appraisal, self-efficacy, and control aspiration. This
means that we can assume measurement invariance across time. These three variables were then
collapsed into one second order latent variable - mastery orientation - in the later models. This
second order latent variable also has good fit indices (chi2= 53.66, df= 58, p =.25).
Measurement equivalence tests were more difficult to do for the PI constructs, first because
the situational interview asked different questions at different times (and therefore, we cannot
assume complete measurement invariance for them) and there were only two repeats for them (T2
and T5, and T3 and T6 used the same items). In those cases that used the same items, the results
allow one to assume measurement equivalence.
For the interviewer evaluation of PI the equal loadings model had a worse fit than the free
loading model (significant difference). This is not surprising given the fact that the interviewer
evaluation is based on subjective interpretations and that different interviewers were used at
different waves. Partial measurement invariance is usually considered a sufficient condition for
using the measurement models in a longitudinal structural model (Pentzt & Chou, 1994).
93
Table 1
Goodness of F
it Measures of L
ISR
EL
Longitudinal M
easurement M
odels
M
odel χ
2 χ
2diff
d.f. ∆
d.f. RM
SEA
E
CV
I A
IC
CFI
Mastery
orientation
Control
Factor loadings free 37.49
50
.0000
.416 177.49
1.000 expectation
Equal factor loadings
42.35
58
.0000 .390
166.35 1.000
D
ifference
4.86
8
S
elf -efficacy Factor loadings free 321.32
215
.0325
1.154 541.32
.977
Equal factor loadings
342.93
231
.0321 1.132
530.93 .976
D
ifference
21.61
16
C
ontrol Factor loadings free
750.80
480
.0347 2.241
1050.80 .971
rejection E
qual factor loadings 778.31
504
.0341
2.200 1030.31
.971 D
ifference
27.51
24
Initiative
S
ituational Factor loadings free
190.58
160
.0206 .647
290.58 .985
interview
Pairs equal T
2=T
5; T3=T
6 194.44
166
.0195
.629 282.44
.986
Difference
3.86
6
Interview
er Factor loadings free
1283.74
720
.0428 3.467
1483.74 .952
evaluation E
qual factor loadings 1354.99
748
.0435
3.502 1498.99
.949 D
ifference
71.25*
28
*p < .05 (for difference χ
2 test).
94
Structural Models
Table 2 shows the intercorrelations of all the constructs/variables used in the structural
models (from the LISREL correlation matrix of Eta). This Table allows to do a first test of a
mediation effect for mastery orientation. All the prerequisites of Baron and Kenny (1986) are met
for all waves: There are sizeable correlations between work characteristics and the mediator mastery
orientation, between mastery orientation and PI and between work characteristics and PI. Further,
one can see that the correlations between work characteristics and PI are smaller than the ones
between work characteristics and the mastery orientation, and between mastery orientation and
initiative. Of course, the mediation test is done with LISREL in the following structural analyses.
Table 3 shows the fit indices for the structural models. The Baseline Model fits well but
clearly can be improved by allowing theoretically specified paths between the constructs.
Table 3 shows the best I - Model to be the Fully Synchronous Socialization Model (Model I-
A). Thus, the effects from work characteristics to mastery orientation and from mastery orientation
to PI are synchronous. This should not be interpreted to mean that there are no time lags for the
development of these effects. As Dwyer (1983, p.397) points out: "... the effects that are modeled as
synchronous are actually cross-lagged effects for which the appropriate lag is much shorter than the
period between waves of observation." Thus, strictly speaking it is not possible to prove
synchronous effects and we can only conclude from these results that the time lags are smaller than
1 year. Second, the model is a full mediation model: Mastery orientation completely mediates the
effects of work characteristics on PI. The modification indices showed no indication that there
should be a direct path from work characteristics to personal initiative.
95
Table 2
Correlations betw
een Latent C
onstructs for Maxim
um S
tructural Model
SD
1
2 3
4 5
6 7
8 9
10 11
12 13
14 15
1 T2 C
ontrol cognitions 0.26
1.00
2 T
3 Control cognitions
0.30 0.82
1.00
3 T4 C
ontrol cognitions 0.30
0.67 0.79
1.00
4 T
5 Control cognitions
0.28 0.60
0.64 0.82
1.00
5 T6 C
ontrol cognitions 0.30
0.56 0.54
0.72 0.72
1.00
6 T
2 Work characteristics
0.70 0.69
0.52 0.41
0.36 0.36
1.00
7 T3 W
ork characteristics 0.70
0.50 0.59
0.43 0.32
0.29 0.55
1.00
8 T
4 Work characteristics
0.72 0.49
0.54 0.73
0.51 0.54
0.46 0.47
1.00
9 T5 W
ork characteristics 0.66
0.38 0.44
0.62 0.66
0.55 0.41
0.42 0.67
1.00
10 T
6 Work characteristics
0.72 0.40
0.42 0.50
0.52 0.72
0.32 0.35
0.43 0.52
1.00
11 T2 Initiative
0.30 0.52
0.45 0.40
0.38 0.39
0.37 0.38
0.30 0.31
0.30 1.00
12 T3 Initiative
0.43 0.44
0.49 0.45
0.39 0.37
0.26 0.38
0.31 0.25
0.27 0.58
1.00
13 T4 Initiative
0.34 0.44
0.47 0.62
0.48 0.41
0.24 0.23
0.39 0.32
0.29 0.43
0.46 1.00
14 T5 Initiative
0.28 0.32
0.33 0.45
0.52 0.42
0.22 0.18
0.34 0.40
0.33 0.49
0.52 0.52
1.00
15 T6 Initiative
0.35 0.32
0.40 0.47
0.46 0.59
0.20 0.23
0.32 0.35
0.45 0.48
0.54 0.44
0.55 1.00
96
Table 3
Goodness of Fit M
easures of LISR
EL
Structural M
odels
Model
χ2
χ2
diff d.f.
∆d.f. R
MSE
A
EC
VI
AIC
C
FI
B
aseline Stability M
odel 1650.52
1125
.039
6.29 1950.52
.933 I-A
Fully S
ynchronous Socialization
1352.14
1117
.026 5.38
1668.14 .970
D
ifference Baseline Stability M
odel and I-A
298.38*
8
I-B
Lagged-Synchronous S
ocialization 1431.09
1117
.030
5.63 1747.09
.960
Difference B
aseline Stability Model and I-B
219.43*
8
I-C
Fully L
agged Socialization
1600.62
1117
.037 6.18
1916.62 .938
D
ifference Baseline Stability M
odel and I-C
49.90*
8
II-A-1
Socialization P
lus Job Change
1313.51
1113
.024 5.28
1637.51 .975
D
ifference I-A and II-A
-1 (1 yr.)
38.63*
4
II-A
-2 S
ocialization Plus Job C
hange 1331.57
1114
.025
5.33 1653.57
.972
Difference I-A
and II-A-2 (2 yr.)
20.57*
3
II-A-3
Socialization Plus Job C
hange 1336.26
1115
.025
5.34 1656.26
.972
Difference I-A
and II-A-3 (3 yr.)
15.88*
2
III-A-1 R
eciprocal Socialization Plus Job C
hange 1290.15
1109
.023
5.23 1622.15
.977
Difference II-A
-1 and III-A-1
23.36*
4
Note. N
= 311 for all models.
p < .00 for χ
2 test for all models.
*p < .05 (for difference χ
2 test).
97
The results up to this point suggest that we should use the Fully Synchronous Socialization
Model from here on. The next set of models includes the job change effects. This implies that
people with high initiative will eventually move to more responsible jobs with higher control and
complexity or create these kinds of jobs by changing the job content. These Socialization Plus Job
Change Models were tested with different time lags (note, that the time difference between T5 and
T6 is two years while all other time differences between the waves are 1 year each). All
Socialization Plus Job Change Models (II Models) were significantly better than our best
Socialization Model. This speaks for the reciprocal determinism concept in which both job change
and socialization effects can be observed. The decision which of these four Job Change Plus
Socialization Models is the best one is a "close call." Two arguments speak for Model II-A-1: First,
the job change effects stayed significant even when we assume the lag of only one wave. There
were four significant job change paths from T2 to T3, from T3 to T4, from T4 to T5, and from T5
to T6. This implies that the change situation in East Germany was strong enough to make it possible
for people to change their working conditions enough to produce an effect within a year. Second,
the fit indices including AIC and ECVI were slightly better for Model II-A-1 than for Models II-A-2
and 3. While the differences are not very large, this speaks again for taking the II-A-1 model as a
starting point for the last additional path.
Our last model - the Socialization Plus Job Change and Reciprocation Model (III-A-1) adds
one more path at each time period - the reciprocal path from personal initiative to mastery
orientation. This model was significantly better than the best fitting Model II.
The Best Fitting Structural Model: Reciprocal Socialization Plus Job Change
The best fitting model Reciprocal Socialization Plus Job Change is displayed in Figure 21.
The results are highly regular across time. While not each of the hypothesized paths was significant,
all of them were in the expected direction. There was the hypothesized effect of work characteristics
on mastery orientation which was significant in each case and rather large (standardized path
coefficients of .40 and above). Thus, occupational socialization has an important effect on mastery
orientation.
Further, the hypothesized effects of mastery orientation on personal initiative were
significant in three of the four cases with Betas of .32, .31 and .19 (one-sided significance tests
Figure 21. Reciprocal socialization plus job change m
odel (app: control appraisals; s-e: self efficacy; asp: control aspirations)
R2 = .49
R
2 = .65
R2 = .67
R
2 = .56
R2 = .70
R
2 = .87
R2 = .72
R
2 = .66
R2 = .35
R
2 = .26
R2 = .46
R
2 = .31
.46* .40*
.59* .43*
.53*
.32* .18*
.20* .45*
.56* .51*
.68* .52*
.19* .32*
.16 .31*
.40* .55*
.46*
WO
RK
CH
AR
AC
TE
RIST
ICS
MA
STE
RY
OR
IEN
TA
TIO
N
T2
T3
T4
T5
T6
T2
T3
T4
T5
T6
T6
T5
T4
T3
T2
.23* .20*
.16* .22*
.16* .38*
.35* .11
.60*
.38*
.75*
PE
RS
ON
AL
INIT
IAT
IVE
app s-e
asp app
s-e
asp
app
s-e
asp
app
s-e
asp
app
s-e asp
.55* .43*
.51*.54*
.51*
.61*
98
99
used). The hypothesized job change effect was also significant in all four waves, although it was not
as sizeable as the socialization effects - the paths were around .20. There was a synchronous
reciprocal effect in three of the waves (.38, .35 and .16). This means that PI also leads to higher
mastery orientation. This effect was about as large as the effect from mastery orientation to PI.
Figure 21 also shows the hypothesized mediation effect of mastery orientation. None of the
modification indices indicated that one would still need a direct path from work characteristics to
PI. This confirms that the mediation model fully explains that part of the correlations between work
characteristics and PI that was due to the socialization effect (of course, there is still the job change
effect from PI on work characteristics).
As one can see from Figure 21, the direct stabilities (as path coefficients) of work
characteristics signify that there were changes. The stabilities between T2 and T3 and T3 and T4
were lower than the stability for T4 to T5. This squares quite well with the informal observations
that work place changes were most dramatic directly after German unification (at T2) and then
leveled off two years later. The stability between T5 and T6 appears to be a little lower. Here one
has take into consideration that this time period is 2 years (in contrast to all other time lags which
are 1 year) (Arminger, 1987).
When interpreting the relatively low direct stability paths for the mediator mastery
orientation, one has to take into account that there were many indirect paths that also contributed to
the general stability. Table 2 shows that the stability-correlations for mastery orientation were
higher than the respective stability-paths in Figure 21.
Our model is able to explain a good part of the change processes. Figure 21 presents the
explained variance R2 coefficients. Between 66 and 87% of the variance of the mediator mastery
orientation was explained by our model. Between one-half and two thirds of the variance of
Personal Initiative was explained. This is certainly a high degree of explained variance in the social
sciences. Obviously, our model also includes stabilities and the stabilities make up a large part of
the explained variance.
Work characteristics showed the lowest degree of explained variance. Since we assume that
these variables are determined by a whole set of predictors in the outside world not modeled here
100
(e.g. organizational structure, career paths, management, delegation by supervisor, political /
economic developments, etc.), we are not surprised about this result.
Discussion
The model described in Figure 19 has fared quite well empirically. Most of the relationships
were synchronous. Our hypotheses were supported quite well. First, mastery orientation was
affected by the two work characteristics, control and complexity. Second, mastery orientation
(consisting of control appraisal, self-efficacy, and control aspiration) had an effect on PI and third,
mastery orientation mediated the socialization process. Fourth, there were lagged job change effects
of PI on work characteristics. Fifth, there were reciprocal effects of PI and mastery orientation. The
latter two findings confirmed the idea of reciprocal determinism (Bandura, 1997; Kohn & Schooler,
1978).
There were both synchronous as well as lagged processes. The effects of mastery orientation
on PI and from PI on mastery orientation were synchronous while the job change effect of PI on
work was lagged as hypothesized. It is important to keep in mind that a synchronous effect does not
mean that the effect is immediate. The synchronous effects found may be actually working within
the time frame of up to a year (the time between two waves) although we assume them to work
much faster from a theoretical perspective.
The predictive power of the model was high. Prediction of initiative was not just a matter of
the stability of initiative. This is encouraging because it suggests that one can change initiative by
changing the job content (control and complexity) and by increasing mastery orientation.
The data signify a vicious or benign cycle (depending upon one's perspective). Those who
show initiative eventually get complex and controllable work which in turn increases initiative. This
implies that those with little initiative may be on a downward spiral. These mechanisms should
eventually lead to a polarization into winners and losers in East Germany.
101
Limitations and Strengths
Obviously, one limitation of our study is that we do not have objective measures of work
characteristics. On the other hand, there is good theoretical thinking and empirical data in this area.
Theoretically, one can differentiate between different types of task characteristics. Hackman (1970)
and Wood (1986) have differentiated between tasks qua task, tasks as behavior requirements, tasks
as behavior descriptions, or as ability requirements. Underlying this differentiation is the dimension
from the most objective task characteristic (measured without any regard to the job incumbent) to
the most subjective one (measured based on the job incumbents' feelings). We conceptualize control
as opportunities and complexity as behavior requirements. "Because behavior requirements ... are a
relatively stable property of a given task, they can be described independently of the characteristics
of task performers." (Wood, 1986, p. 63). This implies that there is a certain objectivity to the task
situation.
Empirically, the two work characteristics studied show substantial correlations between job
incumbents and other raters of the task characteristics (cf. the meta-analysis by Spector, 1992).
Complexity ascertained by a questionnaire correlated .67 with observers' judgments and the
respective correlation for control at work was .58 (Semmer, 1982). Hackman & Lawler (1971)
similarly showed in their overview, that employees and their supervisors agreed highly when
judging variety (a concept similar to complexity) and autonomy; both showed the highest
correlations of all of Hackman & Lawler's variables; the correlations were on average around .90
for variety and .80 for autonomy (averaged by us after r-to-z transformation)(cf. also Gerhart,
1988). Zapf (1989) involving trained observers and job incumbents has shown that job incumbents'
perceptions of control and complexity were not influenced by ill-health variables in contrast to
stressors. Thus, for all practical purposes, control and complexity can be measured more objectively
than other work descriptors (such as stressors) (Zapf, 1989).
Our longitudinal design strengthens the conclusions to be drawn from this study. Since we
designed it with more than two waves, different time lags can be estimated and models with
reciprocal paths can be used without identification problems or non-theoretical constraints. In some
way, a long-term longitudinal study allows replicating the findings within its design - the same
relationships hold across different waves and, similarly, the measurement models can be upheld at
102
different time points. The longitudinal study allows to study processes and we hope to have shown
both (self-) selection and socialization processes in this study. However, we could not study micro-
processes with our design, for example, what happens immediately after a new supervisor is
introduced to a work place who supports PI or what happens, if somebody attempts to show
initiative and fails. It is of particular importance to look at failed initiatives. For example, we do not
think that the relationship between PI and increase of mastery orientation holds if an initiative fails.
The reason, why the relationship appears may be due to actual positive experiences that people have
once they showed PI or with positive bias memory effects. These micro-processes still await study;
there are some suggestions from recent studies on the psychology of volition that there is
considerable perseverance, once a person has set the course on showing initiative (Gollwitzer,
1993).
The longitudinal study also overcomes some of the problems of common method variance
because earlier levels of the variables were held constant; at least constant sources of common
method variance (e.g., negative affectivity) are ruled out in this way. Within wave common method
(e.g., state of mind or quickly fluctuating mood), may produce higher concurrent correlations.
Given the arguments on how well work characteristics can be described by people and given the
fact that there are also significant correlations between work characteristics and mastery orientation
across time, we think that the problem of within wave common method variance is probably of
minor importance for our design. This kind of within wave common method variance could only
influence the correlations between work characteristics and mastery orientation because PI
(measured by performance and interviewer) does not have common method variance with work
characteristics and mastery orientation (measured in the questionnaire).
The second feature of our study - the variable overcoming barriers which is a performance
variable ascertained within the interview - also works against percept-percept biases. Even the
subjective interviewer impressions (such as interviewer evaluation of PI) help to overcome the
percept-percept bias of questionnaire studies. Since the interviewers were trained and had a
common anchor point across different subjects, they do not have the problem of differential anchor
points that besets questionnaire research. Most of the interviewers errors (e.g., a halo effect) would
most likely work to decrease the relationships. On the other hand, the interviewer errors are
103
probably not very high because we found relatively high stabilities for PI (cf. Figure 21 – PI has
higher stabilities than mastery orientation and work characteristics) although different interviewers
did the interviews at different time points. Obviously our interviewer training was geared towards
keeping interviewer effects small.
The use of LISREL modeling has been quite useful in our study although it necessitated
some compromises. Rogosa (1995) and Stoolmiller (1995) criticized the autoregressive model. The
last author argues that if the dependent variable is highly stable, it is difficult to detect causal
relations with other variables. While this observation is certainly correct, the radical change
situation in East Germany - the site for this study - probably made it easier to detect significant
paths. The stability coefficients in our study were relative low – all lower than .70. Thus, the
historical change situation allowed us to use the autoregressive model in this case profitably.
One could argue that the specific historical situation of East Germany cannot be generalized
to the more stable market economies in Western Europe and in the U.S.A. And indeed, the specific
historical changes were reflected in our results. So, for example, the stabilities of work
characteristics are lower during the time of most rapid changes in the work places right after the
political unification of Germany (our waves T2 and T3). However, the relationships in our model
are regular across time suggesting that they would also hold (albeit maybe not as strongly and more
slowly) when the change situation is not quite so radical. One evidence for this is that the cross
sectional correlations between some of the variables discussed in our model are similar in East and
West Germany (Frese et al., 1996). Moreover, we think that even the more stable Western
economies are becoming more and more like East Germany with its high degree of turmoil on the
labor market and job changes. Obviously, our results bear on the situation of Asian countries at the
time of writing this article. Finally, all those countries that have recently changed from a more state
driven economy to a market economy (former Eastern bloc countries but also many developing
countries) find themselves in a similar situation as our study site (e.g., Kohn et al., 1997)
Theoretical Implications
The results confirm the view that occupational socialization has to incorporate both
processes: People actively change their work but the type of work they do also changes them. This
104
is of high theoretical importance because it calls into question all one-dimensional views which
assume either a simple influence of the person on the type of work one gets and of the work
imprinting the person without any activity from the side of the person.
Our results have some bearing on some influential theories on the effects of control. First,
they reinforce that the popular, however rarely studied, concepts of reciprocal determinism Bandura
(1997) or efficacy- performance cycles (Lindsley, Brass, & Thomas, 1995) are useful and operative
at the individual level. Second, Bandura (1997) argues that reciprocal determinism works via self-
efficacy. While our study was not concerned with self-efficacy per se (as discussed, we developed a
second order latent factor from the three mediators which included self-efficacy), our results
support the importance of the mediator PI. As shown in Figure 21, PI can be seen to mediate the
relationship of mastery orientation (which includes self-efficacy) with work characteristics. This
implies that simply having mastery orientation does not help one to change one's environment - one
has to show PI. For this reason, we think that the concept of PI may be an important "missing link"
to agency and self-efficacy theory. It may pay off to systematically integrate PI into these type of
theories. PI may be of particular importance to understand positive cycles of efficacy and
performance (Lindsley et al., 1995)
Third, Stajkovic & Luthans (1998) show that the relationship between self-efficacy and
performance is lowest in complex tasks. Our study points to some other issue of task complexity:
Task complexity itself can increase mastery orientation (self-efficacy) and, thereby, contribute to
higher performance. Moreover, mastery experience (self-efficacy) contributes to job changes that
lead to higher task complexity (via higher PI). This leads to the interesting hypothesis that self-
efficacy might become less and less effective to produce high performance as real life career
trajectories unfold.
Fourth, our results also bear on the interpretation of the control needs by Greenberger and
Strasser (1991). They argued that there is a consistent desire to have control that is independent of
the actual control one receives. In case control is lower than desired, compensatory areas of control
are sought; for example, an assembly line worker with little control at work would seek to have
control in his home life. While our study was not meant to test this hypothesis directly (our
longitudinal study started before Greenberger & Strasser's paper was published), our data show that
105
work characteristics change mastery orientation (and control motives are a part of mastery
orientation). Greenberger and Strasser (1991) did not directly discuss initiative, but their model
implies that lack of control at work should increase the degree of initiative because initiative is a
method to reassert control again. Our data show that this is not the case because lack of control and
complexity eventually decrease initiative. Thus, our data suggest that one should be skeptical
towards compensatory mechanisms.
Up to this point we have refrained from discussing PI as a personality construct; we simply
framed PI as a behavior. It makes sense that this behavior is related to such concepts as proactive
personality (Crant, 1995) or to a high activity level (Buss & Plomin, 1984). However, we do not
think that PI is a non-changeable trait. But there is no doubt that there are personality processes that
help in the development of showing PI-behavior. Personality processes could and should be
analyzed in the future within the 5-unit personality system suggested by Mischel & Shoda (1995).
One would look at the following processes: First, encoding of events, of situations and people can
be done from a self-starting and proactive viewpoint or from a purely order- or situation-driven and
reactive point of view. Perceiving action opportunities within the job situation is an important factor
that contributes to PI. We also think that the work characteristics control and complexity allow and
encourage the perception of action opportunities. Expectancies and beliefs (the second unit of the
personality system by Mischel & Shoda, 1995) have been in the foreground in this study. We do not
yet know a lot about the importance of affect (the third unit of Mischel & Shoda) for showing PI.
However, we assume that it will not be a purely positive affective state that contributes to PI-
behavior; first empirical results show that stressors actually increase the occurrence of PI (Fay,
1998). In terms of goals and values (the fourth unit), we assume that people who want to help the
company in the long run and who have long range goals and who have wider and more proactive
goals at the work place will show more PI at the work place (Parker, Wall & Jackson, 1997).
Finally, one needs specific competencies and self-regulatory plans (the fifth personality system unit
of Mischel & Shoda, 1995) to be able to show PI. We assume that it is important to deal with the
frustrations because of problems that appear whenever one attempts to show PI and persistence is
one aspect of PI. We do not know yet which competencies are important for PI but we assume that a
combination of cognitive ability (Fay, 1998) and practical intelligence (Sternberg & Wagner, 1986)
106
is important to show PI. We think of this article as one step in describing the dynamics of the
development of PI - behavior. It goes without saying that some situations are obviously more
conducive to showing PI-behavior than others and that people can differentially apply PI in different
areas of their life (e.g. social or achievement areas).
Practical Implications
We started out to be interested in this variable because East Germans had difficulties showing PI
(Frese et al., 1996). However, we are now convinced that the general add-on value of this variable
for industry and service is even more important than the study of this particular historical situation.
Many companies are moving from stable structures to change oriented organizations and the issue
of PI is of high importance in any change process. The concept of PI may also be an important
prerequisite for the issue of employability.
Our results have important practical implications. If managers want to achieve a higher
degree of PI, they have to break the vicious cycle of low control and complexity at work, low
mastery orientation, low PI, leading to lower control and complexity at work. Probably the best
strategy is to change the work conditions to increase control and complexity and at the same time to
increase control appraisal, control motives and self-efficacy. The latter can be changed by
reinforcing mastery experiences and by letting the employees know how much one can rely on
them. Additionally, training procedures can be developed to increase control appraisal, control
motives, and self-efficacy, mainly those that increase self-regulatory processes.
Our data have important implications for what companies can do to increase initiative.
Many companies that introduced lean production have told employees to be more daring. However,
the work characteristics of control and complexity were not necessarily changed much (Remdisch,
1998). An example is to keep the assembly line intact without any changes but to introduce quality
circles that are supposed to present initiatives to improve quality. Here control and complexity of
the work itself are not changed but people are encouraged to show initiative. This strategy may be
effective to a certain extent (and we see that mastery orientation and personal initiative feed upon
each other). However, as long as the work conditions stay constant, there will be a limit to this
strategy (Lawler, 1992). People who take more initiative may leave the work place to find other
107
work that allows more control and complexity (note, there is a path from PI to mastery orientation
which implies that one wants to have more control and responsibilities if one shows PI). Others may
not take initiative because they do not have enough mastery experiences in their jobs. We saw that
the influence of the work characteristics on mastery orientation was stronger and more consistent
than the other paths.
Our results support a pluralistic approach to encouraging initiative. There are various "entry
points" to change the cycles described. This may explain why different approaches to enhance
productivity report results of similar magnitude (Guzzo, Jette, & Katzell, 1985). One can start out
with improving the work characteristics, one can improve control appraisal, self-efficacy, and
enhance control aspirations, one can encourage initiative - since all of the paths feed upon each
other, the end result may be rather similar.
References
Abramson, L. Y., Seligman, M. E. P., & Teasdale, J. D. (1978). Learned helplessness in humans:
Critique and reformulations. Journal of Abnormal Psychology, 87, 49-74.
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317- 332.
Anderson, J.C., & Gerbing, D.W. (1988). Structural equation modeling in practice: A review and
recommended two step approach. Psychological Bulletin, 103, 411-423.
Arminger G. (1987). Misspecification, asymptotic stability, and ordinal variables in the analysis of
panel data. Sociological Methods & Research, 15, 336–348.
Ashford, S. J., & Black, J. S. (1996). Proactivity during organizational entry: The role of desire for
control. Journal of Applied Psychology, 81, 199-214.
Ashford, S. J., & Tsui, A. S. (1991). Self-regulation for managerial effectiveness: The role of active
feedback seeking. The Academy of Management Journal, 34, 251-280.
Austin, J. T., & Vancouver, J. B. (1996). Goal constructs in psychology: Structure, process, and
content. Psychological Bulletin, 120, 338-375.
108
Bandura, A. (1986). Social foundations of thought and action. Englewood Cliffs: Prentice-Hall.:
Prentice-Hall. Bandura, A. (1989). Human agency in social theory. American Psychologist, 44, 1175-1184.
Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman and Co.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social
psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality
and Social Psychology, 51, 1173-1182.
Bentler, P.M.(1990). Comparative fit indexes in structural models. Psychological Bulletin, 107,
238-246.
Bentler, P.M., & Chou, C. (1987). Practical issues in structural modeling. Sociological Methods and
Research, 16, 78-117.
Bollen, K. & Lennox, R. (1991). Conventional wisdom on measurement: a structural equation
perspective. Psychological Bulletin,110, 305-314.
Borman, W. C., & Motowidlo, S. J. (1993). Expansing the criterion domain to include elements of
contextual performance. In N. Schmitt & W. C. Borman (Eds.), Personnel selection in
organizations (pp. 71-98). San Francisco: Jossey-Bass.
Braverman, H. (1974). Labor and monopoly capital. New York: Monthly Review Press.
Bridges, W. (1995). Jobshift. London: Allen & Unwin.
Brief, A. P., Burke, M. J., George, J. M., Robinson, B. S., & Webster, J. (1988). Should negative
affectivity remain an unmeasured variable in the study of job stress? Journal of Applied
Psychology, 73, 193-198.
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J.
S. Long (Eds.), Testing structural equation models (pp. 136-62). Newbury Park, CA: Sage.
Brown, R.L. (1997). Assessing specific mediational effects in complex theoretical models.
Structural Equation Modeling 4,142-156.
Buss, A.H. & Plomin, R. (1984). Temperament: Early developing personality traits. Hillsdale, N.J.:
Erlbaum.
109
Campbell, J. P., McCloy, R. A., Oppler, S., & Sager, C. E. (1993). A theory of performance. In N.
Schmitt, W. C. Borman, & ass. (Eds.), Personnel selection in organizations (pp. 35-79). San
Francisco: Jossey-Bass.
Chao, G. T., O'Leary-Kelly, A. M., Wolf, S., Klein, H. J., & Gardner, P. D. (1994). Organizational
socialization: Its content and consequences. Journal of Applied Psychology, 79, 730-743.
Cohen, P., Cohen, J., Teresi, J., Marchi, M., Velez, C.N.(1990). Problems in the measurement of
latent variables in structural equations causal models. Applied Psychological Measurement, 14,
183-196.
Cook T.D., Campbell D.T. (1979). Quasi- Experimentation. Design & analysis issues for field
settings. Boston: Houghton Mifflin Company.
Crant, J. M. (1995). The proactive personality scale and objective job performance among real
estate agents. Journal of Applied Psychology, 80, 532-537.
Dwyer, J.H. (1983). Statistical models for the social and behavioral sciences. New York: Oxford
University Press.
Emery, F. E., & Thorsrud, E. (1969). Form and content in industrial democracy. London:
Tavistock.
Fay, D. (1998). Personal Initiative: Construct validation of a new concept of performance at work.
Doctoral Dissertation. Amsterdam: Faculty of Psychology, Univ. of Amsterdam.
Finkel, S.E. (1995). Causal analysis with panel data. Sage University series in Quantitative
Applications in the Social Sciences, 07-105. Thousand Oaks, Ca: Sage.
Fishbein, M. & Ajzen, I. (1975). Belief, attitude, intention and behavior: An introduction to theory
and research. Reading, MA: Addison-Wesley.
Folkman, S. (1984). Personal control and stress and coping processes: A theoretical analysis.
Journal of Personality and Social Psychology, 46, 839-852.
Ford, M.E. (1992). Motivating humans. Newbury Park, California: Sage
Frankenhaeuser, M., & Gardell, B. (1976). Underload and overload in working life: Outline of a
multidisciplinary approach. Journal of Human Stress, 35-46.
Frese, M. (1982). Occupational socialization and psychological development: An underemphasized
research perspective in industrial psychology. Journal of Occupational Psychology, 55, 209-224.
110
Frese, M. (1984). Do workers want control at work or don't they: Some results on denial and
adjustment. Berlin. Institut für Humanwissenschaft in Arbeit und Ausbildung der Technischen
Universitaet Berlin .
Frese, M. (1987). A theory of control and complexity: Implications for software design and
integration of computer system into the work place. In M. Frese, E. Ulich, & W. Dzida (Eds.),
Psychological issues of human-computer interaction at the work place (pp. 313-337). Amsterdam:
North-Holland.
Frese, M. (1989). The concept of personal initiative: Operationalization, reliability and validity in
two German samples. Journal of Occupational and Organizational Psychology, 70, 139-161.
Frese, M., Fay, D., Hilburger, T., Leng, K., & Tag, A. (1997). The concept of personal initiative:
Operationalization, reliability and validity in two German samples. Journal of Occupational and
Organizational Psychology, 70, 139-161.
Frese, M., Kring, W., Soose, A., & Zempel, J. (1996). Personal Initiative at work: Differences
between East and West Germany. Academy of Management Journal, 39, 37-63.
Frese, M., & Zapf, D. (1988). Methodological issues in the study of work stress: Objective vs
subjective measurement of work stress and the question of longitudinal studies. In C. L. Cooper &
R. Payne (Eds.), Causes, coping and consequences of stress at work (pp. 375-411). Chichester:
Wiley.
Frese, M., & Zapf, D. (1994). Action as the core of work psychology; A German approach. In H. C.
Triandis, M. D. Dunnette, & L. Hough (Eds.), Handbook of Industrial and Organizational
Psychology (pp. 271-340). Palo Alto: Consulting Psychologists Press.
Gardell, B. (1971). Alienation and mental health in the modern industrial environment. In L. Levi
(Ed.), Society, stress, and disease. vol. 1: The psychosocial environment and psychosomatic
diseases London: Oxford University Press.
Gerhart, B. (1988). Sources of variance in incumbent perceptions of job complexity. Journal of
Applied Psychology, 73, 154-162.
Gollwitzer, P. M. (1993). Goal achievement: The role of intentions. In W. Stroebe & M. Hewstone
(Eds.), European review of social psychology (pp. 141-185). London: Wiley.
111
Graham, J.W., & Donaldson, S.I. (1993). Evaluating interventions with differential attrition: the
importance of nonresponse mechanisms and use of follow-up data. Journal of Applied Psychology,
78, 119-128.
Greenberger, D. B., & Strasser, S. (1986). Development and application of a model of personal
control in organizations. Academy of Management Review, 11, 164-177.
Greenberger, D. B., & Strasser, S. (1991). The role of situational and dispositional factors in the
enhancement of personal control in organizations. In L. L. Cummings & B. M. Staw (Eds.),
Research in Organizational Behavior (pp. 111-146). Greenwich, Conn.: JAI Press.
Greenberger, D. B., Strasser, S., Cummings, L. L., & Dunham, R. B. (1989). The impact of
personal control on performance and satisfaction. Organizational Behavior and Human Decision
Processes, 43, 29-51.
Gulowsen, J. (1972). A measure of work-group autonomy. In L. E. Davis & J. C. Taylor (Eds.),
Design of jobs (pp. 374-390). Harmondsworth: Penguin.
Guzzo, R. A., Jette, R. D., & Katzell, R. A. (1985). The effects of psychologically based
intervention programs on work productivity: A meta-analysis. Personnel Psychology, 38, 275-291.
Hacker, W. (1986). Arbeitspsychologie. Bern: Huber.
Hacker, W. (1992). Expertenkönnen. Erkennen und Vermitteln. Göttingen: Hogrefe.
Hackman, J. R. (1970). Tasks and task performance in research on stress. In J. E. McGrath Ed.),
Social and psychological factors in stress pp. 202-237). New York: Holt, Rinehart & Winston.
Hackman, J. R., & Lawler, E. E. (1971). Employee reactions to job characteristics. Journal of
Applied Psychology, 55, 259-286.
Hackman, J. R., & Oldham, G. R. (1975). Development of the job diagnostic survey. Journal of
Applied Psychology, 60, 259-270.
Hayduk, L. A. (1987). Structural equation modeling with LISREL: Essentials and advances,
Baltimore: Johns Hopkins University Press.
Heckhausen, J., & Schulz, R. (1995). A life-span theory of control. Psychological Review, 102,
284-304.
112
Hertzog, C., & Nesselroade, J.R.(1987). Beyond autoregressive models: some implications of the
trait-state distinction of the structural modeling of developmental change. Child Development, 58,
93-109.
Hisrich, R. D. (1990). Entrepreneurship/intrapreneurship. American Psychologist, 45, 209-222.
Ilgen, D. R., & Hollenbeck, J. R. (1991). The structure of work: Job design and roles. In M. D.
Dunnette & L. M. Hough (Eds.), Handbook of industrial and organizational psychology (pp. 165-
208). Palo Alto, Calif.: Consulting Psychologists Press.
Imai, M. (1994). Kaizen. Berlin: Ullstein.
Jackson, P. R., Wall, T. D., Martin, R., & Davids, K. (1993). New measures of job control,
cognitive demand, and production responsibility. Journal of Applied Psychology, 78, 753-762.
James, L. R., & Brett, J. M. (1984). Mediators, moderators and tests for mediation. Journal of
Applied Psychology, 69, 307-321.
Jöreskog, K.G., & Sörbom, D. (1989). LISREL 7: A guide to the program and applications (2nd
ed.). Chicago:SPSS.
Jöreskog, K.G., & Sörbom, D. (1993a). LISREL8 user’s reference guide. Chicago: Scientific
Software International, Inc.
Jöreskog, K.G., & Sörbom, D. (1993b). LISREL8: Structural equation modeling with the SIMPLIS
command language. Hilldale, NJ: Lawrence Erlbaum Associates.
Kahn, R. L., & Byosiere, P. (1992). Stress in organizations. In M. D. Dunnette & L. Hough (Eds.),
Handbook of industrial and organizational psychology (pp. 571-650). Palo Alto, CA: Consulting
Psychologists Press.
Karasek, R. A. (1979). Job demands, job decision latitude and mental strain: Implications for job
redesign. Administrative Science Quarterly, 24, 385-408.
Karasek, R. A., & Theorell, T. (1990). Healthy work. Stress, productivity, and the reconstruction of
working life. New York: Basic Books.
Kenny D.A. & Campbell D.T. (1989). On the measurement of stability in over-time data. Journal of
Personality, 57, 445-481.
Kohn, M. L., & Schooler, C. (1978). The reciprocal effects of the substantive complexity of work
and intellectual flexibility: A longitudinal assessment. American Journal of Sociology, 84, 24-52.
113
Kohn, M. L., & Schooler, C. (1982). Job conditions and personality: A longitudinal assessment of
their reciprocal effects. American Journal of Sociology, 87, 1257-1286.
Kohn, M. L., Slomczynski, K. M., Janicka, K., Khmelko, V., Mach, B. W., Paniotto, V.,
Zaborowski, W., Gutierrez, R., & Heyman, C. (1997). Social structure and personality under
conditions of radical social change: A comparative analysis of Poland and Ukraine. American
Sociological Review, 62, 614-638.
Kornhauser, A. (1965). Mental health of the industrial worker. New York: Wiley.
Kuhl, J. (1992). A theory of self-regulation: Action versus state orientation, self-discrimination, and
some applications. Applied Psychology: An International Review, 41, 97-129.
Latham, G. P., & Saari, L. M. (1984). Do people do what they say? Further studies on the
situational interview. Journal of Applied Psychology, 69, 569-573.
Lawler, E. E., III (1992). The ultimate advantage: Creating the high involvement organization. San
Francisco: Jossey-Bass.
Lazarus, R. S., & Folkman, S. (1984). Stress, appraisal and coping. New York: Springer.
Lindsley, D.H., Brass, D.J. & Thomas, J.B. (1995). Efficacy-performance spirals: A multilevel
perspective. Academy of Management Review, 20, 645-678.
Locke, E. A., & Latham, G. P. (1990). A theory of goal setting and task performance. Englewood
Cliffs, NJ: Prentice-Hall.
Loher, B.T.,Noe, R.A.,Moeller, N.L. Fitzgerald, M.P.(1985). A meta-analysis of the relation of job
characteristics to job satisfaction. Journal of Applied Psychology, 70, 280-289
MacCallum, R.C. & Browne, M.C. (1993). The use of causal indicators in covariance structure
models: some practical issues. Psychological Bulletin, 114, 533-541.
Marsh, H.W. (1993). Stability of individual differences in multiwave panel studies: comparison of
simplex models and one factor models. Journal of Educational Measurement, 30, 157-183.
Marsh, H.W., Hau, K., Balla, J.R. & Grayson, D. (1998). Is more ever too much? The number of
indicators per factor in confirmatory factor analysis. Multivariate Behavior Behavioral Research,
33, 181-220.
McDonald, R.P.(1996). Path analysis with composite variables. Multivariate Behavioral Research,
31, 239-270.
114
Miller, G. A., Galanter, E., & Pribram, K. H. (1960). Plans and the structure of behavior. London:
Holt.
Mischel, W. & Shoda, Y. (1995). A cognitive-affective system theory of personality:
Reconceptualizing situations, dispositions, dynamics, and invariance in personality structure.
Psychological Review, 102, 246-268.
Morrison, E. W. (1993). Longitudinal study of the effects of information seeking on newcomer
socialization. Journal of Applied Psychology, 78, 173- 183.
Mortimer, J.T. & Lorence, J. (1997a). Work experience and occupational value socialization: A
longitudinal study. American Journal of Socioloy, 84, 1361-1387.
Mortimer, J.T. & Lorence, J. (1997b). Occupational experience and and the self-concept: A
longitudinal study. Social Psychology Quarterly, 42, 307-323.
Motowidlo, S. J., Borman, W. C., & Schmit, M. J. (1997). A theory of individual differences in task
and contextual performance. Human Performance, 10, 71-84.
Mueller, R.O. (1996. Basic principles of structural equation modeling. An introduction to LISREL
and EQS. New York: Springer-Verlag.
Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika. 54,
557-585.
Nickel, H. M., Kühl, J., & Schenk, S. (Eds.). (1994). Erwerbsarbeit und Beschäftigung im
Umbruch. Berlin: Akademie Verlag.
Organ, D. (1988). Organizational citizenship behavior: The good soldier syndrome. Lezington,
MA: Lexington Books.
Organ, D. W. (1997). Organizational Citizenship Behavior: It's construct clean-up time. Human
Performance, 10, 85-98.
Parker, S.K., Wall, T.D. & Jackson, P.R. (1997). “That’s not my job”: Developing flexible
employee work orientations. Academy of Management Journal, 40, 899-929.
Peters, T. J., & Waterman, R. H. (1982). In search of excellence. New York: Harper & Row.
Pentzt, M.A. & Chou C.P. (1994). Measurement invariance in longitudinal research assuming
change from development and intervention. Journal of Consulting and Clinical Psychology,62,
450-462.
115
Plewis, I. (1985). Analysing change. Chichester: Wiley.
Plewis, I. (1996). Statistical methods for understanding cognitive growth: a review, a synthesis and
an application. British Journal of Mathematical and Statistical Psychology, 49, 25–42.
Raffalovich, L.E. & Bohrnstedt,G.W. (1987). Common, specific, and error variance components of
factor models. Sociological Methods & Research.15, 385-405.
Remdisch, S. (1998). Gruppenarbeit in der Automobilindustrie: Die Rolle der Gruppensprecher
und Meister. PhD, Univ. of Giessen, Germany.
Roth, P.L. (1994). Missing data: a conceptual review for applied psychologists. Personnel
Psychology, 47, 537-560.
Rogosa, R. (1995). Myths and Methods: “Myths about Longitudinal research” plus Supplemental
Questions. In J.M. Gottmann (Ed). The analysis of change (pp.3-66). Mahwah, NJ: Erlbaum.
Rotter, J. B. (1972). An introduction to social learning theory. In J. B. Rotter, J. E. Chance, & E. J.
Phares (Eds.), Applications of a social learning theory of personality. New York: Holt.
Rothbaum, F. W., Weisz, J. R., & Snyder, S. S. (1982). Changing the world and changing the self:
A two-process model of perceived control. Journal of Personality and Social Psychology, 42, 5-37.
Rovine, J.M. & Molenaar, P.C.M. (1998). A LISREL model for the analysis of repeated measures
with a patterned covariance matrix. Structural Equation Modeling, 5, 318-384.
Schaie, K.W. (1973). Methodological problems in descriptive developmental research on adulthood
and aging. In J.R. Nesselroade & H.W. Reese (Eds.). Life-span development psychology:
methodological issues (pp. 253-280). New York: Academic.
Schallberger, U. (1988). Berufsausbildung und Intelligenz (occupational education and
intelligence). In K. Häfeli, U. Kraft & U. Schallberger (Eds.) Berufsausbildung und
Persönlichkeitsentwicklung: Eine Längsschnittuntersuchung (Occupational education and
personality development: A longitudinal study) (pp. 148-167). Bern: Huber.
Schwarzer, R., Baessler, J., Kwiatek, P., Schroeder, K., & Zhang, J. X. (1997). The assessment of
optimistic self-beliefs: Comparison of the German, Spanish, and Chinese versions of the General
Self-Efficacy Scale. Applied Psychology: An International Review, 46, 69-88.
Seligman, M. (1975). Helplessness: On depression, development and death. San Francisco:
Freeman.
116
Seligman, M. E. P., & Schulman, P. (1986). Explanatory style as a predictor of productivity and
quitting among life insurance sales agents. Journal of Personality and Social Psychology, 50, 432-
438.
Semmer, N. (1982). Stress at work, stress in private life and psychological well-being. In W.
Bachmann & I. Udris (Eds.), Mental load and stress in activity: European approaches (pp. 42-55).
Amsterdam: Elsevier.
Semmer, N. (1984). Streßbezogene Tätigkeitsanalyse: Psychologische Untersuchungen zur Analyse
von Streß am Arbeitsplatz. Weinheim: Beltz.
Semmer, N., & Schallberger, U. (1996). Selection, socialisation, and mutual adaptation: Resolving
discrepancies between people and work. Applied Psychology: An International Review, 263-288.
Spector, P. E. (1986). Perceived control by employees: A meta-analysis of studies concerning
autonomy and participation at work. Human Relations, 11, 1005-1016.
Spector, P. E. (1992). A consideration of the validity and meaning of self-report measures of job
conditions. In C. L. Cooper & I. T. Robertson (Eds.), International review of industrial and
organizational psychology 1992 (pp. 123-151). Chichester: Wiley.
Smith, C. A., Organ, D. W., & Near, J. P. (1983). Organizational citizenship behavior: its nature
and antecedents. Journal of Applied Psychology, 68, 653-663.
Speier, C., & Frese, M. (1997). Generalized self-efficacy as a mediator and moderator between
control and complexity at work and personal initiative: A longitudinal field study in East Germany.
Human Performance, 10, 171-192.
Spreitzer, G. M. (1995). Psychological empowerment in the workplace: Dimensions, measurement,
and validation. Academy of Management Journal, 38, 1442-1465.
Staw, B. M., & Boettger, R. D. (1990). Task revision: A neglected form of work performance.
Academy of Management Journal, 33, 534-559.
Stajkovic, A.D. & Luthans, F. (1998). Self-efficacy and work-related performance: A meta-analysis.
Psychological Bulletin, 124, 240-261.
Sternberg, R.J. & Wagner, R.K. (1986). Practical intelligence. Cambridge, England: Cambridge
Univ. Press.
117
Stoolmiller, M. (1995). Autoregressive effects in structural equation models: we see some
problems. In J.M. Gottmann (Ed). The analysis of change (pp. 261-276). Mahwah, NJ: Erlbaum.
Taira, K. (1996). Compatibility of human resource management, industrial relations, and
engineering under mass production and lean production: An exploration. Applied Psychology: An
International Review, 45, 97-117.
Van Maanen, J. (1976). Breaking in: Socialization to work. In R. Dubin (Ed.), Handbook of work,
organization, and society (pp. 67-130). Chicago: Rand McNally.
Volpert, W. (1977). Einleitung zum Neudruck von Grundsätze der wissenschaftlichen
Betriebsführung. In W. Volpert & R. Vahrenkamp (Eds.), Frederick W. Taylor: Grundsätze der
wissenschaftlichen Betriebsführung. Neuauflage Weinheim, Germany: Beltz.
Vonesh E.F., & Chinchilli V.M. (1997). Linear and nonlinear models for the analysis of repeated
measurements. New York: Marcel Dekker.
Wall, T. D., & Clegg, C. W. (1981). A longitudinal study of group work redesign. Journal of
Occupational Psychology, 2, 31-49.
Wall, T. D., Clegg, C. W., & Jackson, P. R. (1978). An evaluation of the Job Characteristics Model.
Journal of Occupational Psychology, 51, 183-196.
Wall, T. D., Jackson, P. R., Mullarkey, S., & Parker, S. (1996). The demands-control model of job
strain: A more specific test. Journal of Occupational and Organizational Psychology, 69, 153-166.
Wall, T. D., & Jackson, P. S. (1995). New manufacturing initiatives and shop floor job design. In
A. Howard (Ed.), The changing nature of work (pp. 139-174). San Francisco: Jossey-Bass.
West, M. A., & Farr, J. L. (Eds.. (1990). Innovation and creativity at work: Psychological and
organizational strategies. Chichester, England: Wiley.
White, R. (1959). Motivation reconsidered: The concept of competence. Psychological Review, 66,
267-333.
Wicklund, R. A. (1974). Freedom and reactance. Hillsdale: Lawrence Erlbaum.
Wilk, S. L., Desmarais, L. B., & Sackett, P. R. (1995). Gravitation to jobs commensurate with
ability: Longitudinal and cross-sectional tests. Journal of Applied Psychology, 80, 79-85.
Willett, J.B. Sayer, A.G. (1994). Using covariance structure analysis to detect correlates of
individual change over time. Psychological Bulletin, 116, 363–381.
118
Willett, J.B. Sayer, A.G. (1995). Cross-domain analysis of change over time: Combining growth
curve modeling and covariance structure analysis. In G.A. Marcoulides & R.E. Schumacker (Eds).
Advanced structural equation modeling: Issues and techniques (pp. 125-157). Mahwah, NJ:
Erlbaum.
Williams, L.J. &. Podsakoff, P.M. (1989). Longitudinal field methods for studying reciprocal
relationships in organizational behavior research: toward improved causal analysis. Research in
Organizational Behavior, 11, 247-292.
Womack, J. P., Jones, D. T., & Roos, D. (1990). The machine that changed the world. New York:
Rawson.
Wood, R. E. (1986). Task complexity: Definition of the construct. Organizational Behavior and
Human Decision Processes, 37, 60-82.
Wortman, C. B., & Brehm, J. W. (1975). Responses to uncontrollable outcomes: An integration of
reactance theory and the learned helplessness model. In L. Berkowitz (Ed.), Advances in
experimental social psychology. New York: Academic Press.
Zapf, D. (1989). Selbst-und Fremdbeobachtung in der psychologischen Arbeitsanalyse. Göttingen:
Hogrefe.
Zapf, D. (1993). Stress-oriented job analysis of computerized office work. The European Work and
Organizational Psychologist, 3, 85-100.
119
Chapter 4
The Temporal Factor of Change in Stressor-Strain Relationships:
A Growth Curve Model on a Longitudinal Study in East Germany
In this chapter we examine the stressor-strain relationships using longitudinal data (six
measurement points) in a radical change situation - the situation in East Germany after the collapse
of communism in 1990. This article contributes to the literature in the following ways: First, the
stress literature is vast, but there is a lack of longitudinal studies (Zapf, Dormann & Frese, 1996).
Many authors have called for longitudinal studies. Second, stress effects unfold in time. However,
stress research has not been explicit in discussing this process. In this article we shall discuss
alternative models on time lags necessary for stressors to have an effect on strain. Third, there has
been a call in stress research to look for intraindividual differences in these processes (Frese &
Zapf, 1988). In this chapter we make a first attempt to focus on the relationships between within-
person changes in stressors and within-person changes in strain. For example, some individuals may
react to a decrease of a stressor with an immediate decline in their strain level, whereas others take a
much longer time to react. Fourth, the focus on intraindividual changes over a long time frame
enabled us to decompose changes in slow moving trendlike changes and short-term statelike
fluctuations. Fifth, to do this, we had to use a methodological procedure not frequently applied in
stress research: the growth curve model. Sixth, Kasl (1978) argued that stress research should
capitalize on naturally occurring events that have an impact on stress. East German society and
workplaces changed completely from socialism to capitalism after the introduction of the West
German D-Mark in mid 1990. This is a natural starting point for stressor changes. Finally, this study
used a representative sampling procedure, so that the stress process in multiple worksites or
industries and the role of occupational self-selection and drift can be studied (recommended by
Murphy, Hurrell and Quick (1992)).
Stressor-Strain Models
The issue of how stressor-strain relationships unfold in time is of fundamental importance
for stress research although it has not been studied systematically. The theoretical framework for
our models was inspired by the stressor-strain models presented by Frese and Zapf (1988) and the
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interpretation of change by Nesselroade (1991). Nesselroade (1991, p. 96) distinguishes three kinds
of variability: (1) intraindividual variability (relatively rapid, more or less reversible changes, such
as states), (2) intraindividual change (relatively slow changes reflecting processes, such as
development, labeled as ‘trait change’) and (3) inter-individual changes (highly stable, even over
long periods, denoted as ‘traits’). The stressor-strain models of Frese & Zapf (1988) explain the
various ways exposure to stressors may lead to psychological and psychosomatic dysfunctioning in
the course of time.
From these two sources we distilled six theoretical models that were tested in this study;
they are summarized in Table 4. Table 4 also presents differences between the models with regard
to their predictions, time perspectives, and causal agents. The last column on statistical predictions
is described in more detail later. These predictions range from perfect stability to very short-term
effects of stressors on strain. An additional model is the Reverse Causation Model, which argues for
the opposite direction of strain effects on stressors.
1) Strain Stability Model. There are two types of stability. One relates to the stability of the
means of stressors and strains (mean stability). The other one is the stability of individual
differences. The stability of individual differences implies that the relative position of the subjects
scores does not change over time. For instance, all people can move in the same direction, which
implies a mean change, but the relative position of persons might remain unaltered. Theoretically, it
has been argued that strain is a function of negative affectivity and that negative affectivity is
genetically determined (Brief, Burke, George, Robinson & Webster, 1988; Burke, Brief & George,
1993; Spector, Zapf, Chen & Frese, in press). In its strong form, this hypothesis implies that strain
is completely stable both in terms of means and in terms of individual differences. This means that
a person’s psychological health is not affected by changes in the outside world; strain is
conceptualized as a stable trait despite changing circumstances.
On the stressor side, we hypothesized changes because East Germany is in a radical change
situation, which should translate into changes in the levels of stressors. This implies that there
should be clear changes in the means and probably in the individual differences, because not all
people are equally affected by the shifts in stressor levels.
2) Interindividual Differences Model. In contrast to the Strain Stability Model, the
Interindividual Difference Model predicts that stressors and strains should be related. Furthermore,
the Interindividual Difference Model does not expect the strains to be completely stable, although
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this model refers to the stable component in the strains. In addition, this model argues that there is
also a stable component in the stressors and that the stable parts of stressors and strains should be
related. We call it the Interindividual Differences Model, because the covariation between stressors
and strains in all measurement waves can be fully explained by differences between people. Two
processes may be responsible for the relationship between stressors and strains. First, there may be a
fit between personal characteristics (e.g., strain) and situational parameters (e.g., stressors) that are
constantly adjusting to each other. This leads to a highly stable, mutually reinforcing equilibrium
that would imply that relationships between variables do not change. Second, the model may also
come about because one underlying ultrastable personality trait causes both stressors and strains.
This could be a result of negative affectivity (Brief, et al., 1988; Burke et al., 1993). Negative
affectivity implies that a stable negative affectivity trait produces spurious correlations between
reports of stressors and strains (Brief et al., 1988). Thus, equilibrium processes or a stable third
variable could cause high stability of interindividual differences in both stressors and strains.
3) Stressor-Strain Trend Model. In contrast to the previous models this model does not
refer to the completely stable components, but instead to the relatively slow moving changes in
stressors and strains. The Stressor-Strain Trend Model implies that long-term changes in one
stressor lead to corresponding changes in the strain variables. Thus, the trends of stressors and strain
are related. This is, for example, the case when time pressures in the job gradually increases. People
do not react immediately to the accompanying daily fluctuations in time pressure, but instead
gradually develop visible psychosomatic symptoms. This model allows for a waxing and waning in
the symptoms as well, which might be related to the daily fluctuations in stress levels.
4) Reverse Causation Model. Most stress models focus on the effects of stressors, but
some models argue for a reverse causation: Initial strain levels may determine later exposure to
stressors. Two mechanisms can explain the impact on later stressors: selection and direct effects.
Selection effects can have benign or detrimental effects on later stressors. Kohn (1973) and Frese
(1985) have argued that one legitimate hypothesis is that people with a high degree of strain tend to
fall back to less desirable jobs or get assigned more stressful tasks within their jobs (drift model).
The reason is that they, either cannot cope well with the job and, therefore, do not receive more
desirable assignments, or because of a high degree of absenteeism are relegated to more stressful
tasks (or vice versa, those who can cope better get better tasks). However, initial strain levels may
also have opposite effects on later stressor levels: The selection mechanism with an opposite
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continuation Table 4
Reverse
Causation
long-term
influence of strains on stressors
lagged strains
correlation betw
een strain intercept factor and stressor slope factor
Sleeper-E
ffect M
odel long term
influences of stressors on strains
lagged stressors
positive correlation betw
een stressor intercept factors and strain slope factors
Short-Term
R
eaction M
odel
short-term
continuous effects of stressors on strains
synchronous stressors
significant
positive covariates
123
Table 4. C
haracteristics and Statistical Predictions for Theoretical M
odels T
ested in: M
odel Prediction
Tim
e perspective
Causal agent
Spurious m
odel L
atent Grow
th m
odel M
easurement
model
Hybrid m
odel
Strain S
tability M
odel a) m
ean stability b) stability of individual differences
stable means
of strains, but stressors m
eans change no change in the relative position of strain scores
long time
stability for strains
stable trait
equality constraints for m
eans low
stability coefficients
Interindivi-dual D
ifference M
odel
Stable parts of stressors and strains are related
long time-
period stable trait
one perfectly stable latent variable explains the covariances of all stressors and strains
Stressor-
Strain Trend
Model
continuous influence of stressors on strains
trends over a long tim
e-period
stressors
positive correlation betw
een stressor slopes factors and strain slope factors
124
outcome is the Refuge Model. Employees suffering from high strain may seek new jobs (or diffe-
rent tasks within the same job) so that they can reduce their stress level. This kind of selection effect
is called the Refuge Model, because employees retreat from the tough jobs and look for the less
stressful jobs (and the other way around, some people may look for challenges when their strain
level is low). The Drift Model and the Refuge Model differ in their prediction for the development
of later stressors. The Drift Model predicts a positive relationship between initial strain and later
stressors, because of the worsening of the working conditions, whereas a Refuge Model predicts a
negative relationship, because workers are successful in reducing the level of stress to which they
are exposed. Direct effects can also be either positive or negative. The extent to which coping
efforts are successful is crucial. Positive effects can be expected if problem-focused coping reduces
chronic stressors. An example of negative effects is the true strain-stressor10 hypothesis (Zapf,
Dormann & Frese, 1996). For instance, software designers who cannot cope with time pressure,
may become too anxious, resulting in reduced cognitive abilities, and this may result in more errors.
Correcting these errors increases the workload even further.
5) Sleeper Effect Model. A sleeper effect occurs when stressors do not have an immediate
effect but need some “incubation” time (Nesselroade, 1991, Frese & Zapf, 1988). An analogy is
post-traumatic stress disorder (DSM IV American Psychiatric Association, 1994) or burnout (Glass
& McKnight, 1996; Maslach, 1998). For our purposes, the question is whether there are long-term
lagged effects of stressors that appear much later. For example, social stressors may lead to a
cautious and even hostile attitude toward colleagues that contributes to later depression. In this case,
the hostile attitude acts like a slow-acting virus. An alternative mechanism for this effect is the
accumulation model with a threshold. Such a model has been argued for the results of night work
and shift work (Frese & Okonek, 1984). Only after a certain threshold (breaking point) is reached
do long-term effects of shift work appear. These effects do not disappear even with the cessation of
the shift work.
6) Short-Term Reaction Model. Stressors can have an immediate effect on strain (Frese &
Zapf, 1988, refer to this as an initial impact model). Thus, there is an immediate reaction to a
stressor that may subside shortly thereafter if there is no exposure to this stressor any longer. Thus,
10 In the context of negative affectivity a similar hypothesis is called the ‘stressor creation hypothesis’ by Spector, Chen,
Zapf & Frese (in press).
125
strain fluctuates directly with the level of stressors involved. Although this model sounds like a
simple stimulus-response model and, therefore, is reminiscent of the stress-strain models of the
stress research in the 50s and 60s, it is also possible to posit some intermediate coping processes
(Lazarus & Folkman, 1984). However, in contrast to the sleeper effect these processes should occur
relatively quickly.
In summary, the first two models (the Strain Stability Model and the Individual Differences
Model) can be regarded as personality models and therefore predict high stability in strains. The
difference between the Strain Stability Model and the Individual Differences Model is that the first
treats the measurement of the stressors as reflecting objective characteristics of the work
environment, which can change of course, although these changes do not affect the strains. In
contrast, the Individual Difference Model treats the stressor reports as strongly confounded with
personality and does not predict that the residual changes (thus, after the stable trait has been
partialled out) in stressors and strains are related to each other. The Reverse Causation Model and
the Sleeper Effect Model are both lagged models, but they differ in their causal direction: Initial
strain predicts later stressor levels or vice versa, earlier levels of stressors have a lagged effect on
strains. The Sleeper Effect Model, the Stressor-Strain Trend Model and the Short-Term Reaction
Model are traditional stress models in the sense that they consider stressors as the causal agents.
The last two models differ because they focus on different aspects of the data: The slow moving
systematic changes versus the rapid fluctuations. An analogy is the effects of trends of air pollution
on climate versus the short-term effects of air pollution on weather conditions.
The Situation in East Germany
Our approach in looking at growth curves is particularly interesting in a country that has
changed dramatically in terms of working conditions and social makeup. All East European
countries share this dramatic change. We concentrate on East Germany during the 5 years after
unification.
Table 5 shows a few dates to emphasize the historical context in which our study was done.
As the short description in Table 5 shows, the economic situation in East Germany changed most
radically in late 1990 - 1991. Democracy and capitalism came to East Germany mid 1990. Because
the workplaces did not become more democratic until late 1990 and in 1991, our T1 data were
collected at a time when socialist practices were still widespread in the state-run companies.
126
Although all respondents knew that changes were imminent, most did not anticipate the quality and
level of the impending changes.
Table 5 Historical context in East Germany
Time Historical events Study waves
October-November 1989 Mass demonstrations in Leipzig, Dresden and Berlin November 1989 The Berlin wall opens March 1990 First free election in East Germany July 1990 Economic unification; the DM (the West German
currency) is introduced in East Germany; the first changes appear at the work places; East German companies are start to be sold off, mainly to West German firms; workplaces are still very much like they were under socialism
T1
October 1990 Political unification November 1990 Workplaces start to be changed T2 December 1990 First general election in all of Germany 1991 Serious economic crisis in East Germany, many work
related education programs started by government
August-September 1991 Dramatic changes in workplaces; many people change jobs
T3
1992-1993 The economic crisis in East Germany deepens; wages increase to ca. 70 - 80% of Western level; many government programs to stimulate growth; more and more resentment toward West German managers among East Germans
August-September 1992 T4 August-September 1993 T5 1994-1995 The economic situation in East Germany stabilizes on a
low level; unemployment is high, in some towns approaching 50%; there are pockets of very high productivity in the East; however, average productivity of East German workers is about 70% of those in the West; most industrial jobs have been lost; West Germany slides into an economic recession with high unemployment
August-September 1995 T6
With regard to the stressors, the following hypotheses are plausible. Under socialism,
unemployment was virtually unknown. This was still the case in 1990, during the first wave of our
study (we only included employed people at T1 in our sample). People were aware that the
introduction of capitalism would mean layoffs. Moreover, they had few illusions about the
127
competitive strength of their companies. It was obvious to everyone how badly work was organized
and how many investments were needed to bring productivity and product quality up to modern
standards. Thus, they knew that many jobs would be lost and, therefore, job insecurity should be
high from the start. However, at the same time optimism with regard to the labor market prevailed.
People expected that even if they lost their jobs, it would be easy to find new ones. We
hypothesized that fear of unemployment would peak at T3 and then level off. Unemployment
increases were higher in the beginning years of economic change, particularly 1991, because the
firms had to lay off staff to trim their companies and make them ready for sale (nearly all state-
owned companies were sold until 1995). Although the rate of unemployment still continued to
increase, those who had a job in 1993 could feel much more secure than in 1991.
At T1, work life was still socialist, which implied that people could easily leave the
workplace to go shopping and that work was slow and comparatively nondemanding. However,
there were many organizational problems: obtaining needed supplies, trying to complete tasks with
inadequate tools, etc. In other words, time pressure was low and organizational problems were high.
It was our hypothesis that during the 5 years of our study, time pressure would increase because of
the work pressures of modern management systems. On the other hand, organizational problems
would decrease as the tools of production became more modern and the introduction of supplies
became better planned.
Socialist East Germany has been described as a "niche society" in which friendships were
very important and where comradeship at work was high. Newspaper reports and psychotherapists
(e.g., Maaz, 1992) have argued that with the introduction of capitalism the social climate has
become rougher because competition has increased (e.g., for workplaces, for better jobs, for a
career). This would suggest that in 1990, social stressors should be lower and that they should
increase linearly with time.
Work requirements were not clearly laid down in socialist times; thus, it was not quite clear
which job requirements one had to fulfill and which ones not (Pearce, Branyicki & Bukacsi, 1994).
It is reasonable to assume that this led to role ambiguity and role conflicts. We assume that the
modern management methods introduced in 1991 would gradually give the employees a clearer
sense of what was expected of them, thus reducing uncertainty (which is a conglomerate of role
ambiguity and conflict).
One could interpret the radical change situation as a stressful life event. Although many
changes were, of course, most welcome, others might be perceived to be negative. The social
128
atmosphere would become harder and more competitive - the niche society could not be upheld. On
the other hand the introduction of modern management would lead to the decrease of organizational
problems and uncertainty. Thus, we hypothesized that some of the work stressors would increase,
whereas others would decrease, and that the combined effects of all the work stressors would
produce a more or less constant level of strain during the period of our study.
Method
The data in this study were gathered in the AHUS project. AHUS is a German acronym for
“active actions in a radical change situation”. The goal of the project was to study the effects of the
drastic changes that took place after the unification of East and West Germany, and one of the
research questions was which people could cope better with the many stressors they encountered.
This study used all 6 waves over a five year time period. Other publications of this study
concentrated on personal initiative (Frese, Kring, Soose, & Zempel, 1996; Frese, Fay, Hilburger,
Leng, & Tag, 1997; Frese, Garst, & Fay, 1998) and social support as a moderator of stressors
(Dormann & Zapf, 1999). None of the data reported here have been published before.
Sample
A representative sample was drawn in Dresden, a large city in the south of East Germany; it
is the capital of Saxonia, houses a large technical university, and is relatively well-off (e.g.,
compared with cities in the north of East Germany). The sampling was done by randomly selecting
streets, then selecting every third house, and then in each house, every fourth apartment (in smaller
houses every third one). All people between the ages of 17 and 65 with full-time employment at T1
participated (thus, we sometimes had more than one participant per family). The refusal rate of 33%
was quite low for a study of this kind. Confidentiality was assured; if participants preferred
anonymity, they were assigned a personal code word.
At T1 (July 1990), 463 people participated in Dresden. At T2 (November and December,
1990) 202 additional people were asked to participate11. At T3 (September 1991), the N was 543, at
T4 (September 1992) the N was 506, at T5 (September 1993), N = 478, at T6 (September 1995), N
11 Additional people were added to ascertain whether repeated participation had an influence on the variables of the
questionnaire. This was not the case.
129
= 489. Experimental mortality did not change the makeup of the sample. There were no significant
differences in the stressor variables between dropouts from T1 to T3 and full participants. The
sample is representative of the Dresden population on the relevant parameters (e.g., for age, social
class, male and female percentage at work). Fifty-three percent of the participants were male and
47% were female. At T3 ages ranged from 17 to 65 years (M = 39, SD = 11.4). Most participants
worked in public or private services (35,9%), followed by those who were employed in trade or
manufacturing enterprises (30.9%). Of the office workers in the study 18.9% had jobs that required
minimal qualifications, whereas 27.4% were either managers or professionals positions calling for
higher qualifications. Higher level public servants, mostly employed in schools and universities
made up 12,5% of the participants. The study also contained skilled (16.5%) and unskilled blue-
collar workers (14.9%). At the start of the study none of the participants were unemployed, but the
unemployment figures for the subsequent waves were n = 42 (7%) at T2, n = 59 (11%) at T3, n = 38
(7.8%) at T4, n = 35 (7.5%) at T5 and n = 37 (8.1%) at T6. After the first wave, some of the
participants had no job for reasons other than involuntary unemployment (e.g., retirement,
schooling, parental leave). The items on the stressor scales were not administered to those people
who did not have a job at the time of the assessment.
Measures
All stressor and strain measures were ascertained with a questionnaire.
Strain Variables. The strain variables, depression, psychosomatic complaints, irritation and
worrying, are adaptations of Mohr’s (1986) scales – a group of well-validated scales that are used
frequently in Germany.
Depression (four items) was originally adapted from Zung (1965), and all of those items that
referred to physical problems (e.g., not being able to sleep) were excluded to reduce the overlap
with psychosomatic complaints. Items were “A good deal seems senseless to me” and “I have sad
moods”. A 7-point Likert scale was used and the extreme response categories were described as
“almost always” and “never”.
Psychosomatic complaints (eight items) was originally adapted from Fahrenberg (1975) and
related to aches and other negative bodily sensations, that are commonly regarded as strain
symptoms. The respondents can easily detect the symptoms and no medical assistance is needed for
its diagnosis. The contents of some items were: “Do you feel pain in your shoulders?” and “Do you
130
have feelings of dizziness?”. A 5-point Likert scale was used with response categories ranging
from ‘almost daily’ to ‘never’.
Irritation (five items) and Worrying (three items) were both derivatives of the scale of
irritation and strain developed by Mohr (1986), because preliminary analysis indicated that two
(only moderately correlated) factors could be distinguished.
Worrying referred to the preoccupation of work-related problems in one’s spare time (“Even
during holidays I think a lot about problems at my work”). The scope of the original irritation scale
was narrowed down to feelings of irritation and nervousness (“I’m easily agitated”). A 7-point
Likert scale was used.
Stressors. The stressors used a 5-point Likert-type answer scale and have all been adapted from
Semmer (1982; 1984) and Zapf (1991) with the exception of social stressors (Frese & Zapf, 1987).
The scale development of the stressors was influenced by Caplan, Cobb, French, van Harrison and
Pinneau (1975). All of these scales are frequently used in German studies and have been well
validated.
Job insecurity (four items) asked about how secure the job was. Questions referred to the
probability of becoming unemployed or of the chance of finding a new job in case one became
unemployed.
Time pressure (five items) included several aspects of mental efforts (concentration,
vigilance, long working hours and time-pressure) (e.g., “How often do you experience time
pressure?”).
Organizational problems (eight items) was longer than the original Semmer scale, because
we wanted to include more East-German-specific items. It measured whether the material, the
supplies, and the tools were adequate so that work could be done without interruptions. In a prior
study it had been shown to be one of the stressors most strongly related to psychosomatic
complaints (Semmer, 1984). The construct is similar to the organizational constraints described in
Peters, O’Connor, and Rudolf (1980). They defined the construct as ‘facilitating and inhibiting
conditions not under the control of the individual’, and they found a relation not only with
performance but also with affective responses.
Social stressors (six items) referred to several aspects of work relationships e.g., a negative
group climate, conflicts with coworkers and supervisors, and social animosities.
Uncertainty (five items) combined role conflict and role ambiguity by asking for unclear and
conflicting commands and the problem that a mistake may lead to damages.
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Modeling Strategy
Our modeling strategy consisted of two steps. In the first step we tested the measurement
models. The second step was used to test the structural models (Anderson & Gerbing, 1988).
Measurement Models
Strain variables. The strategy of the measurement modeling involved three basic steps. In
the first step (Model 1) a longitudinal measurement model was tested.
The assumption that the same construct was measured across all time points is crucial
(Plewis 1996; Kenny & Campbell 1989). Therefore, steps two and three tested measurement
invariance (Little 1997; Meredith, 1993). The second step (Model 2) tested for equality of factor
loadings over time. Changes in relationships of the latent construct and the items over time is an
indication of a gamma change (Golembiewski, Billingsley & Yeager, 1976), which implies a
change in the respondent’s interpretation of the item content (Oort, 1996). If there is a sizeable
gamma change, comparisons of the relevant constructs over time are impossible. In a third step
(Model 3), the equivalence of item intercepts over time was tested. If all factor loadings are equal, a
change in the item intercepts indicates a general change in the level of the item response. This
implies that the item is more or less attractive and, that this shift cannot be explained by a change in
the latent trait. This phenomenon is called beta change (also called a response shift) and occurs if a
respondent changes his or her meaning of the item response scale’s value (Oort, 1996). Some
authors (Byrne, Shavelson & Muthén, 1989; Pentz & Chou, 1994) have argued that in practice a
few violations can be tolerated and that partial measurement invariance is a more realistic goal.
Stressors. The stressor variables were not fitted with a confirmatory factor analysis, and
internal consistencies were not calculated. The reason for this is that we prefer to see the stressor
items as a mixture of causal and effect indicators12 (Bollen & Lennox, 1991; Cohen, Cohen, Teresi,
Marchi & Velez 1990; MacCallum & Browne, 1993; Spector & Jex, 1998). In general, variables
can be conceived either as causes or as effects of a latent construct (Blalock, 1967, pp. 163-164). In
a factor model, the latent construct is conceived as the cause for the observed variables (e.g.,
12 Causal indicators are also known as ‘formative’ indicators, while effect indicators are often called ‘reflective’
indicators.
132
responses to the items of a questionnaire) that are called effect indicators. In contrast, a causal
indicator model assumes that the observed variables determine the latent construct. However,
sometimes both models seem to be at least partly valid, and this poses a problem for constructing a
measurement model. This was the case in our study, where the stressor variables were based upon a
questionnaire, in which the items focused on external events the respondent encountered. Semmer,
Zapf, and Greif (1996) showed that our measures of the stressors were at least partly related to the
“objective” work situation. Therefore, it is best to consider the stressor variables as representing
both subjective and objective features of the work situation (Ilgen & Hollenback, 1992, Spector,
1998, p.161). However, the subjective and the objective interpretations have different implications
for both the direction of the paths between the latent construct and the indicators, as well as the
form of the covariance matrix of the indicators of the stressor scales. For practical purposes a
reasonable solution is the use of an equal weighting scheme for the items, because no information is
available about more appropriate weighting (McDonald, 1996).
One could argue that the same reasoning would also apply to some of the strain measures,
for example, for psychosomatic complaints. Although there are pros and cons for both views, we
preferred the effect indicator model because we did not want to measure psychosomatic symptoms
per se, but the underlying strain which manifests itself in various forms of bodily discomfort. We
acknowledge that for each single complaint there are manifold causes, but one common cause is the
strain level of the person.
The measurement models were also used to test the Strain Stability Model (cf. Table 4). As
described in Table 4, mean stability required that the latent means of the strain variables were
restricted to be equal in the measurement models. This can be tested with a difference chi-square
test, because this is a nested model (Bollen, 1989). The stressors were not modeled as latent
variables, and hence we used paired t-tests to test for the equality of means. The stability of the
individual differences model is correct, if the correlations of the latent constructs are very high and
are equally high across two adjacent time points and 5 time points (for example, T1-T2 stability
should be similarly as high as the T1-T6 stability); (again, for the strain variables we used the latent
constructs, for the stressors variables, the observed constructs).
Structural models
To test the structural models, it was necessary to fit separate models for each combination of
a strain and a stressor variable. Both restrictions of the software and the limited sample size
133
(Bentler & Chou, 1987) forced us to use this modeling strategy. Table 4 explains the relationship
between the theoretical models and the statistical tests. As previously described, the Strain Stability
Model was tested by imposing constraints on the measurement models.
The Interindividual Differences model was tested with the spurious model. This is a one-
factor model for all the stressor and strain variables. This factor represents a stable construct that
explains all the covariation between all the stressor and the strain variables (see Figure 22).
Figure 22. Spurious Model: one perfectly stable construct explains all the covariation between stressors and strain variables.
To test all the other models in Table 4, we needed to use growth curve models (compare the
Appendix for a short introduction to the growth curve modeling), although they are not typically
used in the stress literature. Briefly, growth curve models focus on intraindividual changes and
interindividual differences in change patterns. Therefore, they allow us to test (stressor) trend –
(strain) trend correlations (slope-slope correlations) and correlations between initial values
(intercepts) and change patterns (slopes). In addition, we also used one hybrid model (to be
explained later).
The next model in Table 4 – the Stressor-Strain Trend Model – was tested within a specific
growth curve model. This growth curve model can either be linear or nonlinear (depending upon
which one has the best fit). If growth cannot be considered as linear over time, some of the slope
factor loadings can be estimated (more on this in the Appendix). This can be done for both the
stressors and the strain variables. A convenient strategy (Meredith & Tisak, 1990; McArdle, 1988)
T1 T2 T3 T4 T5 T6
T6T5T4T3T2T1
Stressor Variables
Strain Variables
134
is to fix the slope factor loading for the first measurement wave to the value 0 and for the second
measurement wave to the value of 1. The other factor loadings are then estimated. From these
growth models, we derived the slope-slope correlations. Figure 23 explains this. There are two
factors for both strains and stressors: Slope and Intercept. The slope factor S is a latent construct
that represents the slope coefficients for each individual (as deviations from the mean slope). A
high factor score for S means that the slope for that individual deviates strongly from the mean
slope. If the mean slope is zero (no mean changes over time), a high positive (negative) factor score
implies a strong positive (negative) change for that person and a low positive (negative) value
means that there is little positive (negative) change. Thus, S tells us something about the
interindividual differences in change processes (more on this in the Appendix). The correlation
between the two slopes of stressors and strain tells us something about how individual differences
in the stressor trajectories are related to individual differences in strain trajectories. It is convenient
to fix the slope factor loading for the first measurement occasion to zero. In that case, the intercept
factor can be interpreted as representing the expected values for the first measurement wave (initial
status; see Appendix). A high positive (negative) factor score on the intercept factor (denoted as I in
Figure 2) means that the growth curve starts at a higher (lower) initial value than the average growth
curve. A positive intercept-intercept correlation means that people with higher (lower) initial values
on one variable also tend to have higher (lower) initial values on the other variable.
The fourth model in Table 4 – Reverse Causation Model – was be tested by looking at how
strongly earlier levels of strains were predictive of later developmental trajectories of stressors. We
fixed the slope factor loading for the first measurement wave to the value 0 (cf. Figure 23) and now
we could then interpret the intercept factor score as the expected initial value (T1) for a particular
subject. The Reverse Causation Model was tested by the intercept-slope correlation of strain and
stressors within the linear or nonlinear growth curve model (depending upon which one had the best
fit).
The Sleeper Effect Model was tested with the same statistical procedure as the Reverse
Causation Model (cf. Figure 23); however, this time we looked for the relationship between earlier
levels of stressor on later strain developments. Technically, this means that the stressor intercept
factor is correlated with the strain slope factor.
The final model in Table 4 – the Short-Term Reaction Model – was be tested with a hybrid
135
Figure 23. (Non)linear grow
th curve model of stressors and strain w
ith a measurem
ent model included for the strain variables.
Note: I = intercept; S
= slope; not shown autocorrelations betw
een unique factors of strain items.
1
11
11
1
IS
T1
T2
T3
T4
T5
T6
IS
T1
T2
T3
T4
T5
T6
11
1
1
11
11
11
11
Stressors
Strains
‘slope stressor-slope strain’correlation tested inStressor-S
train Trend Model
‘intercept strain-slope stressor’correlation tested inR
everse-Causal M
odel
‘intercept stressor-slope strain’correlation tested inSleeper E
ffect Model
136
model that is a combination of a latent growth curve model and an autoregressive model10. (The
autoregressive model assumes that the immediately preceding variable has a path on the next
without regard to time. This means that stressors at the first measurement point predict the stressors
at the next measure). This combination is more appropriate for the short-term reaction effect
because it allows synchronous effects from stressors on strain (unlike a combination of two growth
curve models). Figure 24 describes this model. The introduction of time-varying covariates will
change the interpretation of the growth curve itself: the growth curve describes the adjusted values
after the influence of the covariates (the stressors) is taken into account. Or, equivalently, the
stressor explains the state variance in the strain, because the trendlike changes are already partialled
out. In the hybrid model, the covariates are unrelated to the intercept and slope factor and the time-
specific residual (cf. Figure 24). Thus, the variance of each strain variable can be partitioned into
three nonoverlapping components: explained variance by the growth curve, the covariate, and a
time-specific residual.
All of the described models were tested against a maximal model that did not place any
constraints on the structural relations of the variables; this is called the correlated model, and is
used as a baseline model.
To evaluate all the models, covariance matrices and means were estimated with the
computer program NORMS (Schafer, 1997), and these matrices and mean vectors were used as
input for LISREL (Version 8.14, Jöreskog & Sörbom, 1993). The NORMS program is specifically
designed for handling missing data problems. We used the EM algorithm of NORMS. The EM
algorithm (Dempster, Laird & Rubin, 1977) is a general technique for finding maximum-likelihood
estimates for models with partial missingness. It is based upon the assumption that data are
"missing at random" (MAR), which is a much milder assumption than the assumption that
"missingness occurs completely at random" (MCAR). MAR only requires that the missing values
behave like a random sample of all values within subclasses defined by observed data (Schafer,
1997, p. 11). The sample size used for a particular LISREL analysis was calculated by the mean of
the different sample sizes of the input matrix (N = 448 for depression; N = 445 for psychosomatic
complaints; N = 447 for irritation; N = 447 for worrying).
10 Actually, we also did an extensive comparison of the autoregressive and the growth curve model for all of the models
described in this study. For space constraints this part was left out.
137
Figure 24. Hybrid m
odel: combination of (non)linear grow
th curve model (above) for the strain variables
(measurem
ent model included) and a first order autoregressive m
odel (below) for the stressor variables.
Note: I = intercept; S
= slope; not shown autocorrelations betw
een unique factors of strain items.
1
11
11
1
IS
T1
T2
T3
T4
T5
T6
T6
T5
T4
T3
T2
T1
Strains
Stressors
regression coefficientstested inShort-T
erm R
eactionM
odel
138
To evaluate the overall fit of the models, we report the chi-square statistic, the Akaike
Information Criterion (AIC; Akaike, 1987) and the comparative fit index (CFI; Bentler, 1990). One
disadvantage with the chi-square statistic in comparative model fitting is that it always decreases
when parameters are added to the model. Therefore, we also report the AIC index, because it takes
parsimony (in the sense of as few parameters as possible) as well as fit into account (Jöreskog &
Sörbom, 1993). However, if two models were nested, we report the chi-square difference test
(Bollen, 1989). The CFI is based on a comparison of the fit of the hypothesized model to the fit of
the null baseline model and most researchers consider values greater than .90 as an indication for a
good fit, although recent research suggests a cutoff value close to .95 (Hu & Bentler, 1999).
To evaluate effect sizes, we report the parameters of interest, the standard errors, and the z
values. Unfortunately, in the multivariate nonlinear latent growth curve models (with freely
estimated factor loadings), we could not test the significance of several growth curve parameter
estimates. The reason is that the z values for those estimates are not invariant under different
fixation schemes (more about this in the Appendix E).
Results
Descriptive Data
In Table 6 to 11 the means, standard deviations, and cross-sectional intercorrelations of the
summated scores of the stressor and strain scales for each measurement wave are presented
separately.
In Table 12, the zero-order intercorrelations of the strains and stressors scale scores for all
time periods are shown. Many of the correlations between stressors and strains are small to
moderate in size.
139
Table 6
Means, Standard D
eviations, and Intercorrelations at T1
Subscale M
S
D
1 2
3 4
5 6
7 8
9 S
tressors
1. Job insecurity 2.80
.73
2. T
ime pressure
3.10 .86
.07
3. Organizational constraints
2.80 .77
-.04 .11
4. Social stressors 2.05
.65 .16*
.22** .27**
5. U
ncertainty 2.42
.77 .00
.36** .40**
.41**
S
trains
6. Depression
2.70 .90
.31** .01
.15* .26**
.15*
7. Psychosomatic com
plaints 2.03
.84 .17*
.24** .11
.23** .12
.35**
8. Irritation
3.22 1.29
.20** .15*
.10 .34**
.23** .47**
.37**
9. Worrying
3.29 1.48
.16* .28**
.00 .22**
.18* .29**
.32** .51**
Note. N
= 179 (listw
ise deletion); * p < .05. ** p <
.01. T
able 7 M
eans, Standard Deviations, and Intercorrelations at T
2 Subscale
M
SD
1
2 3
4 5
6 7
8 9
Stressors
1. Job insecurity 3.06
.78
2. T
ime pressure
3.28 .77
-.08
3. Organizational constraints
2.34 .73
.03 .09
4. Social stressors 2.00
.70 .10*
.12* .32**
5. U
ncertainty 2.27
.68 -.02
.29** .36**
.40**
S
trains
6. Depression
2.73 .90
.17** -.09
.15** .21**
.11*
7. Psychosomatic com
plaints 2.10
.77 .09*
.10* .08
.12** .17**
.46**
8. Irritation
3.19 1.18
.10* .03
.09 .20**
.16** .48**
.49**
9. Worrying
3.56 1.50
.13** .25**
.00 .08
.10* .22**
.26** .40**
Note. N
= 440 (listw
ise deletion); * p < .05. ** p <
.01.
140
Table 8
Means, Standard D
eviations, and Intercorrelations at T3
Subscale M
S
D
1 2
3 4
5 6
7 8
9 Stressors
1. Job insecurity
2.77 .72
2. Tim
e pressure 3.36
.74 -.09
3. O
rganizational constraints 2.03
.69 .14**
-.05
4. Social stressors
1.98 .69
.08 .04
.29**
5. Uncertainty
2.26 .67
-.04 .17**
.26** .49**
Strains
6. D
epression 2.68
.93 .22**
-.05 .15**
.27** .11*
7. Psychosom
atic complaints
2.15 .78
.12* .13*
.11* .09
.10 .40**
8. Irritation 3.28
1.12 .11*
.08 .16**
.25** .23**
.46** .49**
9. W
orrying 3.77
1.41 .15**
.27** .01
.07 .09
.24** .26**
.41**
N
ote. N =
362 (listwise deletion); * p <
.05. ** p < .01.
Table 9
Means, Standard D
eviations, and Intercorrelations at T4
Subscale
M
SD
1
2 3
4 5
6 7
8 9
Stressors
1. Job insecurity 2.71
.73
2. T
ime pressure
3.47 .75
-.16**
3. Organizational constraints
1.92 .67
.18** -.02
4. Social stressors 1.97
.72 .19**
.10 .37**
5. U
ncertainty 2.19
.64 -.02
.13* .34**
.43**
S
trains
6. Depression
2.67 .98
.30** -.15**
.23** .30**
.14*
7. Psychosomatic com
plaints 2.21
.80 .24**
.09 .10
.13* .06
.36**
8. Irritation
3.23 1.16
.21** .05
.22** .24**
.12* .50**
.48**
9. Worrying
3.84 1.46
.13* .31**
.01 .12*
.06 .21**
.29** .41**
Note. N
= 332 (listw
ise deletion); * p < .05. ** p <
.01.
141
Table 10
Means, Standard D
eviations, and Intercorrelations at T5
Subscale
M
SD
1
2 3
4 5
6 7
8 9
Stressors
1. Job insecurity 2.71
.67
2. T
ime pressure
3.49 .69
-.05
3. Organizational constraints
1.81 .66
.15** -.04
4. Social stressors 2.00
.70 .22**
.14* .36**
5. U
ncertainty 2.18
.62 .07
.23** .40**
.39**
S
trains
6. Depression
2.60 .94
.22** -.07
.26** .34**
.23**
7. Psychosomatic com
plaints 2.23
.80 .17**
.13* .09
.15** .13*
.42**
8. Irritation
3.17 1.12
.15** .07
.19** .27**
.13* .52**
.48**
9. Worrying
3.87 1.44
.08 .25**
.07 .15*
.10 .23**
.32** .41**
Note. N
= 304 (listw
ise deletion); * p < .05. ** p <
.01. T
able 11 M
eans, Standard Deviations, and Intercorrelations at T
6 S
ubscale M
S
D
1 2
3 4
5 6
7 8
9 Stressors
1. Job insecurity
2.74 .67
2. Tim
e pressure 3.50
.68 -.02
3. O
rganizational constraints 1.77
.62 .11*
.09
4. Social stressors
2.02 .72
.16** .19**
.33**
5. Uncertainty
2.21 .64
.05 .33**
.34** .51**
Strains
6. D
epression 2.59
.92 .25**
-.03 .24**
.29** .25**
7. Psychosom
atic complaints
2.19 .77
.14* .11
.08 .20**
.15** .42**
8. Irritation 3.16
1.09 .10
.11* .25**
.27** .19**
.42** .36**
9. W
orrying 3.86
1.41 .12*
.24** .07
.20** .19**
.28** .28**
.46**
N
ote. N =
316 (listwise deletion); * p <
.05. ** p < .01.
142
Table 12
Correlation M
atrix of Strain with Stressor V
ariables
D
epression
Psychosom
atic complaints
Irritation
Worrying
Stressors
T1
T2
T3
T4
T5
T6
T
1 T
2 T
3 T
4 T
5 T
6
T1
T2
T3
T4
T5
T6
T1
T2
T3
T4
T5
T6
Job insecurity T
1 .22*
.15* .16* .25* .26*
.21* .11* .10
.11 .11
.11 .05
.17* .08
.10 .07
.12 .09
.13* .12*
.15* .10 .08
.11
T2
.22* .19* .19*
.22* .22* .17*
.16* .12* .13* .18*
.14* .08
.14* .11* .17* .13*
.14* .08
.14* .11* .15* .10
.08 .09
T
3 .20*
.21* .24* .30* .29*
.22* .16* .16*
.14* .18* .11* .08
.17* .09
.12* .14* .14* .04
.09
.14* .13* .08
.03 .06
T
4 .24*
.17* .15* .28* .23*
.17* .15* .15*
.13* .22* .18* .13*
.13* .12* .14* .17*
.14* .08
.09 .10*
.07 .09
.04 .09
T
5 .29*
.16* .16* .25* .24*
.19* .19* .13*
.15* .21* .17* .18*
.19* .06 .15* .18*
.15* .12*
.13* .07 .07
.07 .04
.08
T6
.23* .19* .22*
.26* .25* .28*
.14* .11* .13* .18*
.11* .16* .12* .03
.15* .17* .12* .13*
.19* .04
.08 .08
.02 .07
Tim
e pressure T
1 .00
-.01 -.08
-.12* -.10 -.07
.15* .08
.10 .03
.09 -.08
.15* .08
.05 .07
.08 .08
.31* .27*
.20* .23* .26* .14*
T
2 -.02
-.10* -.07 -.09
-.04 .00
.15* .10*
.14* .14* .16* .09
.12* .06
.02 .07
.09 .02
.31* .28*
.27* .34* .24* .18*
T
3 -.02
-.11* -.09 -.09
-.04 -.06
.10
.06 .10* .12*
.11* .09
.10* .05 .07
.06 .08
.05
.27* .26* .28* .31*
.24* .15*
T4
-.07 -.14* -.10* -.13* -.09
-.07
.07 .07
.06 .08
.09 .04
.04
.02 .02
.08 .05
.03
.20* .18* .19* .31*
.23* .18*
T5
-.06 -.14* -.12* -.15* -.08
-.12* .08
.04 .06
.08 .10
.06
.02 -.01
-.05 .01
.05 .00
.17* .17*
.14* .24* .25* .20*
T
6 -.07
-.15* -.13* -.15* -.15* -.05
.06 -.02
.02 .04
.06 .07
.01
-.04 -.03
.01 .01
.10
.12* .13* .10* .19*
.14* .27* O
rganizational T
1 .17*
.11 .18*
.05 .20*
.18*
.11 .00
.05 -.06
-.04 -.08
.09
.10 .09
.08 .11
.18*
.02 .01
.10 -.04
.05 .04
problems
T2
.13 .15* .15*
.15* .20* .19*
.13
.08 .11* .10
.05 .04
.11
.09* .10
.15* .11* .13*
.04
.00 .00
.00 .09
.04
T3
.08 .11* .18*
.18* .20* .19*
.06
.08 .13* .08
.11* .06
.12 .11*
.18* .19* .22* .18*
.11
-.02 .03
.00 .07
.02
T4
.08 .11* .19*
.23* .22* .22*
.08
.08 .08
.08 .07
.06
.10 .08
.17* .21* .19* .17*
-.03 -.05
.01 .01
.05 .03
T
5 .06
.10* .16* .17* .25*
.25*
.11 .06
.09 .05
.09 .07
.09
.12* .15* .15*
.18* .22* -.08
-.07 -.08
-.06 .04
.01
T6
.04 .07
.14* .15* .19*
.26*
.08 .01
.10 .09
.03 .08
.14
.07 .14* .17*
.14* .25*
.07 .04
.09 .03
.06 .06
Social stressors T
1 .21*
.12* .17* .19* .20*
.07
.21* .03 .06
-.02 .09
.07
.27* .16* .19* .20*
.14* .21*
.17* .10 .09
.14* .05
.14*
T2
.20* .19* .18*
.16* .18* .12*
.18* .10*
.09 .05
.07 .08
.23* .21*
.19* .11* .09
.11*
.14* .07 .06
.05 .05
.04
T3
.20* .16* .25*
.22* .20* .12*
.18* .05
.10* .06 .08
.08
.24* .17* .24* .19*
.16* .20*
.09 -.03
.06 .07
.04 .05
T
4 .19*
.11* .25* .29* .21*
.19*
.11 .10*
.11* .11* .13* .08
.16* .12*
.20* .24* .17* .17*
.03
.02 .05
.11* .05
.07
T5
.23* .16* .27*
.25* .30* .23*
.15* .06
.14* .11 .15* .13*
.18* .14*
.22* .24* .27* .24*
.14* .02
.08 .08
.14* .12*
T6
.25* .15* .24*
.25* .18* .29*
.18* .05
.10* .12* .13* .22*
.23* .15*
.24* .26* .17* .29*
.14* .10
.15* .16* .11
.20* U
ncertainty T
1 .11*
.04 .08
.07 .17*
.14*
.11* .11* .08
.03 .10
.08
.21* .20* .16* .17*
.19* .18*
.23* .11* .13* .08
.14* .10
T2
.15* .08
.09 .09
.14* .15*
.10
.15* .12* .09
.11* .13*
.18* .16* .12* .05
.06 .10
.21* .10*
.05 -.01
.01 .06
T
3 .12*
.04 .10*
.11* .17* .16*
.09
.11* .11* .09
.10 .11*
.19* .14*
.23* .16* .13* .20*
.12* .05
.10* .02 .06
.14*
T4
.12* .01
.13* .13* .17*
.21*
.08 .10*
.09 .07
.04 .10
.16* .06
.12* .15* .10
.13*
.12 .02
.02 .09
.11* .15*
T5
.10 .05
.15* .07
.20* .19*
.10
.08 .17* .07
.10 .12*
.08
.08 .19* .07
.12* .13*
.14* .02 .09
.03 .09
.11*
T6
.12* .07
.09 .12* .16*
.24*
.14* .03 .14* .07
.10 .15*
.18* .13*
.18* .16* .12* .19*
.18* .07
.13* .03
.09 .19*
Note. * p <
.05. N varies because of m
issing data (range N: 159-526, m
ean N =
345).
143
Strain Measurement Models
The goodness-of-fit measures of the measurement models are shown in Table 13. The Null -
Model assumes complete independence between the items. The unconstrained model (Model 1) is a
longitudinal measurement model that is unconstrained, allowing different factor loadings and item
intercepts over time. Model 2 is a restricted model, with equal factor loadings over time. Model 3 is
more restrictive and additionally assumes equal item intercepts over time. Model 4 will be
discussed later and tests for equal means of the latent constructs over time. Measurement invariance
across time is one prerequisite interpreting the constructs to be comparable over time. Measurement
invariance can be assumed to exist if equal factor loadings and item intercepts do not lead to a
significantly worse fit of the model. Only a few parameters needed to be freed for depression and
psychosomatic complaints. Although, after these modifications, the results of the chi-square
difference tests of irritation and psychosomatic complaints remained significant, further freeing of
parameters led to estimates which were only trivially different from the restricted ones.
Thus, for irritation and worrying we found full measurement invariance, and for depression
and psychosomatic complaints we found partial measurement invariance. This is not a problem
because partial measurement invariance is sufficient (Byrne et al., 1989; Muthén & Muthén, 1998;
Pentz & Chou, 1994). We note that for the modified constrained measurement models all values of
the CFI were above .94, which can be considered a good fit.
Structural Models
The goodness-of-fit measures of our model tests are shown in Table 14. The first model
(“correlated”) is an unconstrained structural model that can be used as a baseline for the growth
curve models. The second model is the Interindividual Difference Model (“spurious model”) in
which the correlations of all the stressor and strain variables can be explained by one common,
unmeasured factor, which is assumed to be perfectly stable over time.
The next two models are latent growth curve models (linear and nonlinear) to test for the
relevant parameters for the Stressor-Strain Trend Model, the Reverse Causation Model and Sleeper-
Effect Model. The last model is a hybrid model (to test for the Short-Term Reaction Model), which
combines a latent growth curve model for the strain variables and a first-order autoregressive model
for the stressor variables that act as synchronous covariates for the strain variables.
144
Table 13
Goodness of Fit M
easures for Measurem
ent Models and M
ean Stability M
odel
D
epression P
sychosomatic com
plaints Irritation
Worrying
Model
χ2
df. A
IC
CF
I χ
2 df.
AIC
C
FI
χ2
df. A
IC
CF
I χ
2 df.
AIC
C
FI
Null 6 908.50
276 7079.00
16485.87 1128 16581.97
9656.21
435 9716.21
6053.92
153 6089.92
1. Unconstrained
298.75 177
544.75 .982
1369.00 699
1777.00 .944
628.64 315
928.64 .966
125.07 75
317.07 .992
2. Equal factor loadings 311.00
190 531.00
.982 1409.87
729 1757.87
.943 652.30
335 912.30
.966 139.78
85 311.78
.991
Difference of 2 and 1
30.28* 17
40.87
30
23.66
20
14.71
10
3. Equal loadings and
intercepts
383.07 203
625.07 .973
1469.29 758
1843.29 .941
686.55 355
966.55 .964
161.71 95
349.71 .989
Difference of 3 and 2
72.07* 13
59.42* 29
34.25 20
21.93 10
Mean stability
4. Equal latent m
eans 391.87
208 623.87
.972 1494.44
763 1858.44
.939 695.79
360 965.79
.964 178.33
100 356.33
.987
Difference of 4 and 3
8.80 5
25.15* 5
9.24
5
16.62* 5
Note.
* Chi-square difference test w
as significant (α =
0.01)
N =
448 for depression; N =
445 for psychosomatic com
plaints; N =
447 for irritation; N =
447 for worrying
145
Table 14
Goodness of Fit M
easures for Structural Models
D
epression Psychosom
atic complaints
Irritation W
orrying
χ2
df A
IC
CF
I χ
2 df
AIC
C
FI
χ2
df A
IC
CF
I χ
2 df
AIC
C
FI
Job insecurity
correlated 669.54
315 1029.54
.959 1863.66
974 2363.66
.936 1007.06
499 1413.06
.955 305.68
167 619.68
.982 spurious
1413.06 354
1635.06 .876
3145.69 999
3499.69 .846
2352.33 533
2618.33 .837
1438.00 211
1616.00 .840
linear 1005.07
373 1249.07
.927 2238.52
1032 2622.52
.914 1333.55
557 1623.55
.931 648.08
225 846.08
.945 nonlinear
811.64 365
1071.64 .948
1992.74 1024
2392.74 .931
1134.91 549
1440.91 .948
431.82 217
645.82 .972
hybrid 765.11
363 1029.11
.953 1937.16
1022 2341.16
.935 1066.38
547 1376.38
.954 362.41
215 580.41
.981 T
ime pressure
correlated
666.55 315
1026.55 .958
1947.28 974
2447.28 .930
973.35 499
1379.35 .957
268.49 167
582.49 .987
spurious 1675.44
367 1871.44
.843 3258.62
999 3612.62
.837 2328.94
533 2594.94
.837 1351.46
211 1529.46
.851 linear
837.13 373
1081.13 .945
2136.97 1032
2520.97 .921
1154.15 557
1444.15 .946
472.38 225
670.38 .968
nonlinear 770.34
365 1030.34
.952 2052.54
1024 2452.54
.926 1059.39
549 1365.39
.954 367.75
217 581.75
.980 hybrid
753.00 363
1017.00 .954
2029.58 1022
2433.58 .927
1035.88 547
1345.88 .956
356.53 215
574.53 .982
Organizational problem
s
correlated 676.63
315 1036.63
.956 2052.97
974 2552.97
.921 987.52
499 1393.52
.955 322.68
167 636.68
.979 spurious
1441.52 367
1637.52 .868
3357.89 999
3711.89 .827
2239.29 533
2505.29 .841
1463.29 211
1641.29 .828
linear 1172.26
373 1416.26
.905 2604.77
1032 2988.77
.887 1461.40
557 1751.40
.917 835.17
225 1033.17
.919 nonlinear
796.22 365
1056.22 .947
2209.21 1024
2609.21 .913
1107.25 549
1413.25 .948
472.86 217
686.86 .965
hybrid 745.74
363 1009.74
.953 2179.29
1022 2583.29
.915 1085.47
547 1395.47
.950 438.21
215 656.21
.969 Social stressors
correlate 663.27
315 1023.27
.957 1819.21
974 2319.21
.937 927.77
499 1333.77
.960 321.97
167 635.97
.979 spurious
1600.02 367
1796.02 .847
3089.33 999
3443.33 .844
2081.75 533
2347.75 .854
1462.15 211
1640.15 .827
linear 838.80
373 1082.80
.943 1979.97
1032 2363.97
.929 1071.41
557 1361.41
.952 514.91
225 712.91
.960 nonlinear
748.51 365
1008.51 .953
1880.50 1024
2280.50 .936
982.49 549
1288.49 .959
409.80 217
623.80 .973
hybrid 795.27
363 1059.27
.947 1882.60
1022 2286.60
.936 1000.63
547 1310.63
.957 439.00
215 657.00
.969 U
ncertainty
correlate 648.18
315 1008.18
.958 1893.29
974 2393.29
.932 983.17
499 1389.17
.955 318.14
167 632.14
.979 spurious
1474.49 367
1670.49 .860
3102.29 999
3456.29 .843
2198.82 533
2464.82 .844
1405.80 211
1583.80 .835
linear 790.75
373 1034.75
.948 2051.73
1032 2435.73
.924 1137.93
557 1427.93
.946 506.00
225 704.00
.961 nonlinear
743.73 365
1003.73 .952
1980.67 1024
2380.67 .929
1082.57 549
1388.57 .950
437.47 217
651.47 .970
hybrid 742.52
363 1006.52
.952 1974.50
1022 2378.50
.929 1081.33
547 1391.33
.950 444.38
215 662.38
.968 N
OT
E. N
= 448 for depression; N
= 445 for psychosom
atic complaints; N
= 447 for irritation; N
= 447 for w
orrying correlated =
all constructs were allow
ed to correlate without further restrictions im
posed spurious =
one factor model for all stressor and strain variables
linear = linear grow
th model for stressor and strain variables
nonlinear = nonlinear grow
th model for stressor and strain variables
hybrid = nonlinear grow
th curve for strains with stressors as tim
e-varying covariates with a first order autoregressive structure
146
The AIC values displayed in Table 14 show that for the combination of strains with the
stressors, job insecurity, time pressure, and organizational problems were better (i.e. lowest) for the
hybrid than for the latent growth curve models, although the differences were not very high. For
social stressors and uncertainty, the nonlinear latent growth curve model yielded the lowest AIC
values. There was only one exception: The combination of psychosomatic complaints and
uncertainty gave a slightly lower AIC value for the hybrid model, although the difference in AIC
with the nonlinear latent growth curve model was negligible. Again, we note that AIC value
differences between alternative models were sometimes quite small. In those cases, in which the
differences between the growth curve and the hybrid models were relatively small, we could
continue to test hypotheses with either of those models.
Testing of the Theoretical Models
We now describe how the results bear on the theoretical models that are described in Table
4.
The Strain Stability Model.
This model argues that there is no change over time for strains, despite changes in the
stressors. The answer to this model can be split into questions of mean and individual differences
stabilities.
Mean stability for strain variables. The strain means were rather stable, as one can see in
Table 15. However, there were statistical differences for psychosomatic complaints, (∆χ2 = 25.15,
∆df = 5, p < 0.001; N = 445) and worrying, (∆χ2 = 16.62, ∆ df = 5, p = 0.005; N = 447), but not for
irritation, (∆χ2 = 9.24, ∆ df = 5, p = 0.10; N = 445) and depression, (∆χ2 = 8.8, ∆ df = 5, p = 0.12; N
= 448). From a practical perspective the differences in means for psychosomatic complaints and
worrying were not high.
Mean stability for stressor variables. The stressor variables were measured by the
unweighted summated scores, and the hypothesis of the stability of the means were tested by series
of paired t-tests. The results are shown in Table 16. There were no significant differences for social
stressors only. For uncertainty, there was only a significant result for the first waves, but if we apply
a Bonferroni adjustment to correct for multiple testing, we can conclude that no significant
differences could be detected. The most drastic changes were shown in the consistent decrease of
organizational problems (see Table 16). It seems there was a leveling off, noting the consistent
147
Table 15 Means of Latent Strains for all Measurement Waves
T1 T2 T3 T4 T5 T6 Depression 2.75
(0.053) 2.83
(0.054) 2.87
(0.052) 2.85
(0.053) 2.81
(0.052) 2.80
(0.054) Psychosomatic
complaints 1.57
(0.097) 1.62
(0.098) 1.67
(0.100) 1.70
(0.101) 1.67
(0.099) 1.69
(0.100) Irritation 3.09
(0.055) 3.11
(0.053) 3.14
(0.051) 3.11
(0.052) 3.04
(0.051) 3.05
(0.052) Worrying 3.70
(0.080) 3.74
(0.080) 3.92
(0.075) 3.93
(0.075) 3.90
(0.075) 3.92
(0.075) Note. Standard errors between parentheses Table 16 Means, Mean Differences and t-Tests for all Measurement Waves M ti M ti+1 M difference SE of M t df p
Job insecurity T1- T2 2.855 3.000 -.140 .039 -4.127 300 .000 T2- T3 3.018 2.746 .273 .032 8.626 380 .000 T3- T4 2.729 2.668 .061 .031 1.987 334 .048 T4- T5 2.644 2.653 -.008 .027 -.297 316 .766 T5- T6 2.635 2.684 -.049 .028 -1.778 305 .076
Time pressure T1-T2 3.215 3.225 -.010 .0304 -.343 335 .732 T2-T3 3.310 3.385 -.075 .0306 -2.451 394 .015 T3-T4 3.416 3.508 -.092 .0305 -3.021 332 .003 T4-T5 3.534 3.512 .022 .0327 .668 319 .505 T5-T6 3.526 3.545 -.019 .0312 -.608 307 .543
Organizational problems
T1-T2 2.792 2.480 .3121 .0480 6.492 169 .000 T2-T3 2.319 2.012 .3071 .0312 9.837 357 .000 T3-T4 2.016 1.889 .1275 .0328 3.887 297 .000 T4-T5 1.883 1.794 .0881 .0300 2.939 289 .004 T5-T6 1.806 1.750 .0561 .0301 1.868 285 .063
Social stressors T1-T2 1.935 1.925 .0104 .0318 .315 296 .753 T2-T3 2.000 1.986 .0141 .0328 .429 365 .668 T3-T4 1.979 1.971 .0075 .0369 .204 303 .839 T4-T5 1.945 1.969 -.0238 .0340 -.702 295 .483 T5-T6 1.972 2.022 -.0501 .0379 -1.319 277 .188
Uncertainty T1-T2 2.357 2.279 .0787 .0356 2.211 293 .028 T2-T3 2.254 2.248 .0564 .0301 .187 369 .852 T3-T4 2.263 2.223 .0406 .0373 1.087 301 .278 T4-T5 2.223 2.182 .0434 .0345 1.257 295 .210 T5-T6 2.197 2.222 -.0250 .0342 -.731 272 .466
148
decrease in mean differences, although the difference between T5 and T6 was not significant any
longer. The means of time pressure increased after the second wave, but after the fourth wave
stopped to change significantly. The mean of job insecurity increased in T2, which took place 3
months after the start of the study. After this increase there was a downward trend.
Stability of individual differences. The correlations of the latent constructs in Table 17 show
that the hypothesis of stability of individual differences is to be rejected. If one compares the last
column of Table 17 with all the other columns, it becomes clear that the stabilities across the 6
waves (a five year period) were much lower than the stabilities across adjacent waves.
The stabilities of the stressors are also shown in Table 17. Again, a comparison of the one-
wave lag with the six-wave lagged stabilities revealed a low degree of stabilities for the stressor
variables. In line with our expectation, more changes in organizational problems were present in the
first half of our study: In the last three years the scores were more stable than in the first two years.
Changes in social stressors took place in the period from T2 to T4, and again it stabilized in the last
years.
Thus, these results imply that the mean stability for the stressors was not really low (see
Table 17), but rather was lower than the stability for the strains, and that there was little stability in
individual differences across a long time frame.
Table 17 Stability Coefficients of Strains and Stressors
T1-T2 T2-T3 T3-T4 T4-T5 T5-T6 T1-T6 Strains
Depression .82 .78 .74 .77 .73 .56 Psychosomatic
complaints .87 .85 .80 .83 .82 .67
Irritation .70 .72 .76 .70 .74 .59 Worrying .73 .74 .73 .75 .68 .50
Stressors Job insecurity .82 .75 .87 .94 .88 .44 Time pressure .97 .88 .86 .87 .90 .58
Organizational problems
.73 .85 83 .92 .95 .45
Social Stressors .95 .84 .78 .93 .89 .51 Uncertainty .88 .93 .82 .97 .93 .60
NOTE. All time lags are 1 year, except T1-T2 lag (4 months) and T5-T6 lag (2 years)
149
Interindividual Differences Model
The Interindividual Differences Model was tested by the spurious model. In Table 14 the
goodness-of-fit measures for the spurious models are shown. In all cases the fit measures were poor.
The hypothesis that all the relationships between stressors and strains can fully be explained by one
stable construct has to be rejected.
Stressor-Strain Trend Model
The stressor-strain trend model was tested by the correlation of the stressor slope factor with
the strain slope factor in the nonlinear growth model (see again Figure 23). These correlations are
displayed in the first column of Table 18. If we concentrate on the combinations of social stressors
and uncertainty with all the strain variables, we notice that there were sizeable Slope Stressor-
Slope Strain correlations. Out of the eight correlations, 6 were higher than .20 and two were higher
than .30. This means that long-term changes in social stressors and uncertainty were accompanied
with corresponding changes in the strain variables. Remarkably, job insecurity slope factor had no
sizeable correlation with any of the strain variable slope factors. The slope factors of the other
stressors - time pressure and organizational problems - showed meaningful relationships with most
strain variables slopes.
Reverse Causation Model
This model was tested by the correlation of the Intercept Strain with Slope Stressor in the
nonlinear growth model (see again Figure 23). The correlations were by and large rather low (see
the second column in Table 15); however, almost all were negative, which is directly counter to the
drift model or the true strain hypothesis and in line with the Refuge Model or models with direct
positive effects due to successful problem-focused coping.
Sleeper Effect Model
This model was tested with the correlations of the intercept of the stressor with the slope of
strain in the nonlinear growth model (see, again, Figure 23), and the correlations are shown in the
third column of Table 15. There is little evidence for sleeper effects because nearly all correlations
were below .20, and instead of being positive, they were almost all negative.
150
Table 18
Correlations between Intercept Factors and Slope Factors of Strains and Stressors
Slope Stressor
–
Slope Strain
Intercept Strain
–
Slope Stressor
Intercept Stressor
–
Slope Strain
Depression
Job insecurity 0.122 -0.007 0.058
Time pressure -0.126 0.051 -0.064
Organizational problems 0.267 -0.026 -0.101
Social stressors 0.179 -0.021 0.065
Uncertainty 0.250 -0.033 -0.067
Psychosomatic Complaints
Job insecurity 0.118 -0.066 0.075
Time pressure 0.247 -0.124 -0.083
Organizational problems 0.154 -0.247 -0.020
Social stressors 0.335 -0.265 -0.059
Uncertainty 0.219 -0.147 -0.069
Irritation
Job insecurity 0.115 -0.121 -0.033
Time pressure 0.143 -0.041 -0.125
Organizational problems 0.207 -0.005 -0.126
Social stressors 0.250 -0.133 -0.087
Uncertainty 0.206 -0.163 -0.161
Worrying
Job insecurity -0.086 -0.053 -0.058
Time pressure 0.343 -0.180 -0.293
Organizational problems 0.080 0.098 -0.107
Social stressors 0.158 -0.079 -0.058
Uncertainty 0.493 -0.194 -0.229
NOTE.
Estimates are taken from the nonlinear latent growth models with correlated residuals
151
Short-Term Reaction Model
The Short-Term Reaction Model could be well modeled as a hybrid model and could be
tested by looking at the synchronous paths from stressors to strain variables. Table 19 shows the
standardized regression coefficients of the solution presented in Table 14; many of them were
significant. The strongest paths occurred for time pressure and worrying. Social stressors and
uncertainty were related to all strain variables with similar magnitude. Organizational problems
were related to the strain variables except to worrying.
Discussion
We tested several stressor-strain models. First, the Strain Stability Model has been shown to
be wrong for the stability of individual differences of strains, but there was a high degree of stability
of the means of strain variables. As predicted, meaningful differences in stressors could be detected
across the five-year period. Job insecurity peaked somewhat earlier than we predicted (at T2 and not
at T3), but we anticipated the leveling off: after T2 job insecurity decreased, to remain at a more or
less constant level. One has to keep in mind that job insecurity measured the fear of becoming
unemployed and should not be equated with the stressor of being unemployed itself. For a particular
wave, the people who had lost their jobs, the items of this scale were not included. It might be that
for some respondents with initial high scores on job insecurity their fears turned out to be realistic
and they indeed lost their jobs, which resulted in missing values for subsequent waves. Thus,
selection effects can partly explain the changes in the means of job insecurity. The means of time
pressure increased after T2 as expected, because Western production norms soon pervaded job
requirements and set the pace at higher standards. The monotonic decrease of the means of
organizational problems was also in line with our expectations. Although any transitional period
will create its own organizational troubles, apparently the new work systems run more smoothly,
and in the first year a decrease in organizational problems can already be detected.
The stability of the means for social stressors was unexpected, because we had originally
thought that social cohesion at the workplace would be reduced and competition would increase.
The stressor uncertainty showed a small decrease. This was in line with our expectations, because
more efficient organizations describe work requirements unambiguously, and this reduces role
conflicts and uncertainty.
152
Table 19
Regression C
oefficients for the Regression of the Strain V
ariables on the Stressors in the Hybrid M
odels
D
epression Psychosom
atic complaints
Irritation
Worrying
T
1 T
2 T
3 T
4 T
5 T
6 T
1 T
2 T
3 T
4 T
5 T
6 T
1 T
2 T
3 T
4 T
5 T
6 T
1 T
2 T
3 T
4 T
5 T
6
Job insecurity .14* .15* .18* .19*
.21* .21* .04
.08* .12* .14* .17* .15* .06 .08* .09* .09* .09* .09* .04
.06 .05
.01 -.01
-.01
Tim
e pressure -.01
.01 -.02
-.05 -.06
-.07 .11* .11* .10* .09* .06
.07* .12* .12* .13* .11* .08 .09* .37* .35* .37* .33*
.29* .29*
Organizational probl.
.17* .20* .22* .25* .24* .23*
.10* .12* .15* .16* .14* .14* .10* .13* .15* .17* .17* .15* .04 .05
.07 .05
.03 .04
Social stressors .17* .20* .23* .28*
.30* .31* .16* .19* .22* .24* .24* .25* .18* .24* .25* .26* .30* .30* .13* .13* .17* .18*
.17* .18*
Uncertainty
.15* .15* .15* .16* .18* .19*
.12* .14* .16* .15* .16* .16* .21* .20* .21* .17* .16* .18* .25* .23* .25* .22* .23*
.24*
NO
TE
. * z > 1.96 (based on unstandardized solution).
Regression coefficients taken from
LISR
EL
’s completely standardized solution.
N =
448 for depression; N =
445 for psychosomatic com
plaints; N =
447 for irritation; N =
447 for worrying.
153
The mean changes in stressors suggest that East Germany gradually moved in the direction
of a Western economy. There were higher work requirements, as indicated by more time pressure,
and smoother and more efficient organization and task design, as reflected by lower organizational
problems and lower levels of uncertainty. However, there were no signs of higher costs in the sense
of higher levels of strains.
The means of the strain variables remained almost stable, but there was no stability of
interindividual differences. This means that there were considerable changes in the relative
positions of people (as indicated by moderate stability coefficients). Thus, people changed in
different ways, with some people improving and some deteriorating (winners and losers of German
unification).
The fact that there were mean changes in stressors but not in strain should not be interpreted
to mean that there were no causal effects of stressors on strain. Because some stressors increased
over time (e.g., time pressure) and others decreased (e.g., organizational problems), the net effect on
strain may be the same.
Second, the Interindividual Differences Model could be clearly rejected. There was no stable
factor, be it negative affectivity or some other nonmeasured factor, that could explain all common
variance between stressors and strains. Because we only tested for a complete Interindividual
Differences model, there may still be some partial impact (e.g., of negative affectivity), that was not
captured in this model (Spector et al, in press).
Third, the Stressor – Strain Trend Model was supported by half of the possible combinations
of stressors and strains (see Table 18, first column): Uncertainty was related to all the strains
(depression, psychosomatic complaints, irritation, and worrying). Uncertainty seems to be one of
the most consistent and important stressors; this replicates other reports on the importance of role
ambiguity and conflict (Kahn & Byosiere, 1992).
Social stressors showed slope-slope correlations above .20 with psychosomatic complaints
and irritation. Time pressure was related to psychosomatic complaints and to worrying, and
organizational problems were related to irritation and depression. Interestingly, job insecurity was
not related to any of the strains within the constraints of this model.
Some of the slope-slope correlations were quite sizeable, such as social stressors with
psychosomatic complaints (.34) and time pressure (.34) and uncertainty (.49) with worrying. More
specifically, one can see a fit in the content of stressor and strain relationships. Worrying refers to
worrying about work after working time (mood spillover); thus, there is a delayed effect of time
154
pressure and uncertainty. One potential mechanism is that, with time pressure, a person does not
have time to worry about things during working hours and, therefore, does it outside of work.
Uncertainty was most highly related to worrying. Uncertainty leads to confusion and internal
conflict that takes a long time to be resolved and, therefore, carries over into nonwork time.
It is important to note that these correlations cannot be interpreted to be due to some stable
third variable (such as negative affectivity), because only the change part of stressors and strains is
related in the slope-slope correlation and the constant part is statistically held constant. From this
perspective, the size of the correlations is quite high.
An alternative explanation for stressor – strain relations is an overlap in the item content of
stressor and strain scales (cf. ‘the triviality trap’; Kasl, 1978). But an inspection of the items of
these scales led to the conclusion that this was not the case.
Fourth, the models that assume reverse causation were tested as latent growth curve and not
as hybrid models. The hybrid model, the best-fitting model for most stressor-strain combinations,
did not allow to test for lagged effects of the intercept parameter of the strain growth curve on the
stressor covariates. The Drift Model was not supported. Reverse Causation Models, which
hypothesized reduced stressors as a result of prior strain levels, were in line with the results. Both
positive selection mechanisms as well as positive direct effects can explain this result. Thus the
Refuge Model was supported. Since there was a radical change situation, many job movements
could occur within a short time. Therefore, people with high strain found jobs with less stressors,
and people with low strain found jobs with more challenges. Thus, a person with a high degree of
psychosomatic complaints attempted to find a job with less social and organizational stressors.
However, the effects were quite small and should not be overinterpreted. Additionally, several
Reverse Causation mechanisms might be valid only for subgroups, and this contributes to only
small correlations.
Fifth, the Sleeper-Effect Model was not supported. A methodological problem in detecting
lagged effects is that the presumed causal agents are constantly changing as well. Determining the
exact time length of the lagged effects is an unresolved methodological problem in longitudinal
research, especially if both short-term and long-term effects are present.
Sixth, the Short-Term Reaction Model is well supported by the results of the hybrid models.
In nearly every case, there were significant relationships between stressors and strains (the only real
exceptions being relationships of time pressure with depression and organizational problems and
job insecurity with worrying). For some stressors, the effects were quite high and suggest a
155
specificity effect. For instance, the strongest synchronous effects were detected for the relationship
of the stressor time pressure with worrying (with correlations around .33), but time pressure was
unrelated to depression. Time pressure does not depress people, but makes them active at work.
However, they worry about the job after working hours. General effects on strains were noticeable
for social stressors, and uncertainty. Note that the latent growth curve was partialled from the strain
variables. Thus, the results of Table 19 really present the immediate strain reactions to the stressors,
holding the slow moving trait change (the overall trend) for each individual constant.
The overall results can be interpreted in this way: There are two effects side by side. One is
the overall relationships between individual trends in stressors and strains (Stressor-Strain Trend
Model). In a way, this reflects the overall long-term effect of stressors on the slowly changing
component of strain (this has been called trait component by Nesselroade, 1991). The other effect is
the Short-Term Reaction effect, which means that there is a direct and immediate effect of stressors
on strains (synchronous). This is unrelated to the general trend and, therefore, is to be interpreted as
a clear state effect. This means that both components of strain - in Nesselroade’s terminology, state
and trait - are affected by the stressors.
As with any study, our research also has some limitations. One relates to the issue of
causality. Although we used a longitudinal study, the Stressor-Strains Trend Model cannot be
convincingly interpreted causally. One prerequisite for interpreting something as causal is the time
order effect. However, for example, the slope-slope correlations give up the time order because they
look at the general trends of stressors and strain over the full time range. Thus, these correlations
can also be the result of a causal effect of strain on stressors or a third variable explaining the
variance in both slope factors. The causal argument can be maintained more strongly for the hybrid
model that we used to test the Short-Term Reaction Model. Here the intercept and the slope factor
of the dependent variable strain were partialled out which means that there is some indication for a
causal influence of the stressor on strain even though the effect was synchronous.
A second limitation is that we could not discriminate between subgroups for which
differential models may hold (Frese & Zapf, 1988). Although this is true of most studies in the
field, it is potentially possible to use growth curve models for multiple groups. However, both
sample size limitations and software restrictions forbade using this procedure in this study.
Promising software developments have been announced, making it possible to integrate latent class
analysis and structural equation modeling (Muthén, in press).
156
The strengths of this study should not be overlooked. There are very few stressor-strain
studies with more than three waves in the literature (Zapf et al., 1996). There is no doubt that this is
a unique study in this regard. Another feature is that it took place in a unique historical period.
From one perspective this may be a limitation, because it may imply that one cannot generalize the
results. But from another perspective it means that one can model complex relationships in a radical
change situation more easily because more changes happen overall, therefore speeding up the
processes. Thus, similar to the laboratory situation, the “manipulation” is strong and compressed in
time (Moeller & Strauss, 1997).
Another design feature is that we used multiple measures of stressors and strains. This was
particularly important for the description of the mean changes of stressors in East Germany, because
we could show that there was a characteristic picture of some stressors increasing during the time of
the study, some stressors decreasing, and one not changing at all.
Another strength relates to our use of the growth curve models. There are two advantages.
We could look at the long-term changes from an overall trend point of view (trait perspective).
Moreover, it was possible to differentiate the trait and the state perspective on strain, because we
could look at the immediate effects of stressors on strain and at the long-term trends of the
relationships between stressors and strains. We found that there were stressor – strain relationships
appearing for different time frames side by side. This would have gone undetected with alternative
approaches (e.g., with an autoregressive model approach).
Another advantage of the growth curve analysis is that some of the relationships are much
stronger than the relationships shown by the zero-order relationships of the stressor and strain
variables (although even these relationships were already disattenuated, because the strain variables
were latent; cf. Table 12).
One important contribution of this article is its analysis strategy. To our knowledge, both
factor models within a growth curve approach and hybrid models are infrequently or never used in
the literature. The use of the factor models made it possible to test for measurement equivalence
over time, to ensure that the meaning of the latent constructs remained the same. The advantage of
the hybrid model was that we could adjust the growth curves for nontrendlike influences.
Introducing time-specific determinants into the model makes latent growth curve modeling a more
flexible strategy and partly compensates for the lack of stochastical variation which presumably is a
part of many psychological developmental processes (cf. Bock, 1991 p. 127).
157
References
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders
(4th ed.). Washington, DC: Author.
Anderson, J.C., & Gerbing, D.W. (1988). Structural equation modeling in practice: A review and
recommended two step approach. Psychological Bulletin, 103, 411-423.
Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107,
238-246.
Bentler, P.M., & Chou, C. (1987). Practical issues in structural modeling. Sociological Methods and
Research, 16, 78-117.
Blalock, H.M., Jr. (1967). Causal inferences in nonexperimental research. Chapel Hill, North
Carolina: University of North Carolina Press
Bock, R.D. (1991). Prediction of growth. In L. M. Collins & J.L. Horn (Eds.), Best methods for the
analysis of change: recent advances, unanswered questions, future directions (pp. 126 -136).
Washington, DC: American Psychological.Association.
Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.
Bollen, K., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation
approach. Psychological Bulletin, 110, 305-314.
Brief, A.P., Burke, M.J., George, J.M., Robinson, B., & Webster, J. (1988). Should negative
affectivity remain an unmeasured variable in the study of job stress? Journal of Applied
Psychology, 73, 193-198.
Burke, M.J., Brief, A.P., & George, J.M. (1993). The role of negative affectivity in understanding
relations between self-reports of stressors and strains: A comment on the applied psychology
literature. Journal of Applied Psychology, 78, 402-412.
Byrne, B.M., Shavelson, R.J., & Muthén, B. (1989). Testing for the equivalence of factor
covariance and mean structures: The issue of partial measurement invariance. Psychological
Bulletin, 105, 456-466.
Caplan, R. D., Cobb, S., French, J. R. P. Jr., van Harrison, R., & Pinneau, S. R., Jr. (1975). Job
demands and worker health. Washington DC: National Institute of Occupational Safety and
Health.
158
Cohen, P., Cohen, J., Teresi, J., Marchi, M., & Velez, C.N. (1990). Problems in the measurement of
latent variables in structural equations causal models. Applied Psychological Measurement, 14,
183-196.
Curran, P.J. (in press). A latent curve framework for the study of developmental trajectories in
adolescent substance use. In J. Rose, L. Chassin, C. Presson, & J. Sherman (Eds.), Multivariate
applications in substance use research. Hillsdale, NJ: Erlbaum.
Dormann, C., Zapf, D. (1999). Social support, social stressors at work and depressive symptoms:
testing for moderating effects with structural equations in a 3-wave longitudinal study. Journal of
Applied Psychology, 84, 874-884.
Dempster, A.P., Laird, N.M., & Rubin, D.B.(1977). Maximum likelihood estimation from
incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
Fahrenberg, J. (1975). Die Freiburger Beschwerdeliste (FBL) [The Freiburg Complaints List].
Zeitschrift für Klinische Psychologie, 4, 79-100.
Frese, M. (1985). Stress at work and psychosomatic complaints: A causal interpretation. Journal of
Applied Psychology, 70, 314-328.
Frese, M., Fay, D., Hilburger, T., Leng, K., & Tag, A. (1997). The concept of personal initiative:
Operationalization, reliability and validity in two German samples. Journal of Occupational and
Organizational Psychology, 70, 139-161.
Frese, M., Garst, H., Fay, D. (1998). Control and complexity in work and the development of
personal initiative (PI): A 5-wave longitudinal structural equation model of occupational
socialization. Manuscript submitted for publication.
Frese, M., Kring, W., Soose, A., & Zempel, J. (1996). Personal Initiative at work: Differences
between East and West Germany. Academy of Management Journal, 39, 37-63.
Frese, M., & Okonek, K. (1984). Reasons to leave shiftwork and psychological and psychosomatic
complaints of former shiftworkers. Journal of Applied Psychology, 69, 500-514.
Frese, M., & Zapf, D. (1988) Methodological issues in the study of work stress: Objective vs.
subjective measurement of work stress and the question of longitudinal studies. In C.L. Cooper &
R. Payne (Eds.), Causes, coping and consequences of stress at work (pp. 375-411). Chichester,
England: Wiley.
Frese, M., & Zapf, D. (1987). Eine Skala zur Erfassung von sozialen Stressoren am Arbeitsplatz [A
scale to assess social stressors at work]. Zeitschrift für Arbeitswissenschaft, 41, 134-142.
159
Glass, D.C., & McKnight, J.D. (1996). Perceived control, depressive symptomatology, and
professional burnout: A review of the evidence. Psychology and Health, 11, 23-48.
Golembiewski, R.T., Billingsley, K., & Yeager, S. (1976). Measuring change and persistence in
human affairs: Types of change generated by OD designs. Journal of Applied Behavioral Science,
12, 133-157.
Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis:
Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
Ilgen, D. R., & Hollenbeck, J. R. (1992). The structure of work: Job design and roles. In M. D.
Dunnette & L. M. Hough (Eds.), Handbook of industrial and organizational psychology (pp. 165-
208). Palo Alto, Ca.: Consulting Psychologists Press.
Jöreskog, K.G., & Sörbom, D. (1993). LISREL8 user’s reference guide. Chicago: Scientific
Software International.
Kahn, R. L., & Byosiere, P. (1992). Stress in organizations. In M. D. Dunnette
& L. Hough (Eds.), Handbook of industrial and organizational psychology, Vol. 3, (pp. 571-650).
Palo Alto, CA: Consulting Psychologists Press.
Kasl, S.V. (1978). Epidemiological contributions to the study of work stress. In C.L. Cooper & R.
Payne (Eds.), Stress at work (pp. 3-48). Chicester, England: Wiley.
Kenny, D.A., & Campbell, D.T. (1989). On the measurement of stability in over-time data. Journal
of Personality, 57, 445-481.
Kohn, M.L. (1973). Social class and schizophrenia: A critical review and a reformulation.
Schizophrenia Bulletin, 7, 60-79.
Lazarus, R.S., & Folkman, S. (1984). Stress, appraisal, and coping, New York: Springer.
Little, T.D. (1997). Mean and covariance structures (MACS) analysis of cross-cultural data:
Practical and theoretical issues. Multivariate Behavior Research, 32, 53-76.
Maaz, H.J. (1992). Interview of the Frankfurter Rundschau of July 6, 1992.
MacCallum, R.C., & Browne, M.W. (1993). The use of causal indicators in covariance structure
models: Some practical issues. Psychological Bulletin, 114, 533-541.
MacCallum, R.C., Kim, C., Malarkey, W.B., & Kiecolt-Glaser, J.K. (1997). Studying multivariate
change using multilevel models and latent curve models. Multivariate Behavioral Research, 32,
215-253.
Maslach, C. (1998). A multidimensional theory of burnout. In G.J.Cooper (Ed.), Theories of
organizational stress. New York: Oxford University Press.
160
McArdle, J.J. (1988). Dynamic but structural equation modeling of repeated measures data. In J.R.
Nesselroade & R.B. Cattell (Eds.), Handbook of multivariate experimental psychology (pp. 561-
614). New York: Plenum.
McArdle, J.J., & Woodcock, R.W. (1997). Expanding test-retest designs to include developmental
time-lag components. Psychological Methods, 2, 403-435.
McDonald, R.P. (1996). Path analysis with composite variables. Multivariate Behavior Research,
31, 239-270.
Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance.
Psychometrika, 58, 525-543.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
Moeller, J., & Strauss, B. (1997). Before and after the German reunification: Changes in observers'
commentaries on achievements in a natural experiment. Journal of Applied Social Psychology, 27,
75-93.
Mohr, G. (1986). Die Erfassung psychischer Befindensbeeinträchtigungen bei Industriearbeitern
[Measuring disturbances of psychological well-being in industrial blue collar workers]. Frankfurt
Germany: Peter Lang.
Murphy, L.R., Hurrell, J.J., Jr, Quick, J.C (1992). Work and well-being: Where do we go from
here? In J.C. Quick, L.R. Murphy & J.J. Hurrell, Jr. (Eds.) Stress & well-being at work. Washington
DC.: American Psychological Association.
Muthén, B. (in press). Second-generation structural equation modeling with a combination of
categorical and continuous latent variables: New opportunities for latent class/latent growth
modeling. In A. Sayer & L. Collins (Eds.), New methods for the analysis of change. Washinton
D.C.: American Psychological Association.
Muthén, B. (1997). Latent variable modeling with longitudinal and multilevel data. In A. Raftery
(Ed.), Sociological Methodology (pp. 453-480). Boston: Blackwell Publishers.
Muthén, B. & Muthén, L. (1998). Training session Stockholm August 1998 on: Analysis of
longitudinal data: Growth modeling using latent variables.
Muthén, B.O., & Curran, P.J. (1997). General longitudinal modeling of individual differences in
experimental designs: A latent variable framework for analysis and power estimation.
Psychological Methods, 2, 371-402.
161
Nesselroade, J.R. (1991). Interindividual differences in intraindividual change. In L. M. Collins &
J.L. Horn (Eds.), Best methods for the analysis change: Recent advances, unanswered questions,
future directions (pp. 92-105). Washington, DC.: American Psychological Association.
Oort, F.J.O. (1996). Using restricted factor analysis in test construction. Unpublished Dissertation
University of Amsterdam, the Netherlands.
Pearce, J., Branyicki, I., & Bukacsi, G. (1994). Person-based reward systems: A theory of
organizational reward practices in reform-communist organizations. Journal of Organizational
Behavior, 15, 261-282.
Pentz, M.A., & Chou, C.P. (1994). Measurement invariance in longitudinal clinical research
assuming change from development and intervention. Journal of Consulting and Clinical
Psychology, 62, 450-462.
Peters, L.H., O’Connor, E.J., & Rudolf, C.J. (1980). The behavioral and affective consequences of
performance-relevant situational variables. Organizational Behavior and Human Performance, 25,
79-96.
Plewis, I. (1996). Statistical methods for understanding cognitive growth: A review, a synthesis and
an application. British Journal of Mathematical and Statistical Psychology, 49, 25–42.
Rovine, M.J. & Molenaar, P.C.M. (1998). The covariance between level and shape in the latent
growth curve model with estimated basis vector coefficients. Methods of Psychological Research,
3, 95-107
Schafer, J.L. (1997). Analysis of incomplete multivariate data, London: Chapman & Hall.
Semmer, N. (1982). Stress at work, stress in private life and psychological well-being. In W.
Bachmann & I. Udris (Eds.), Mental load and stress in activity: European approaches (pp. 42-55).
Amsterdam: Elsevier.
Semmer, N. (1984). Stressbezogene Tätigkeitsanalyse: Psychologische Untersuchungen zur
Analyse von Stress am Arbeitsplatz [Stress oriented analysis of work: Psychological studies on the
analysis of stress at work]. Weinheim, Germany: Beltz.
Semmer, N., Zapf, D., & Greif, S. (1996). ‘Shared job strain’: A new approach for assessing the
validity of job stress measurements. Journal of Occupational and Organizational Psychology, 69,
293-310.
Spector, P.E. (1998). A control theory of the job stress process. In G.J. Cooper (Ed.), Theories of
organizational stress. New York: Oxford University Press.
162
Spector, P.E., & Jex, S.M. (1998). Development of four self-report measures of job stressors and
strain: Interpersonal Conflicts at Work Scale, Organizational Constraints Scale, Quantitative
Workload Inventory, and Physical Symptoms Inventory. Journal of Occupational Health
Psychology, 3, 356-367.
Spector, P.E., Zapf, D., Chen, P.Y., & Frese, M. (in press). Don’t throw out the baby with the bath
water: The role of negative affectivity in reports of job stressors and strains. Journal of
Organizational Behavior.
Willett, J.B. (1989). Some results on reliability for the longitudinal measurement of change:
Implications for the design of studies of individual growth. Educational and Psychological
Measurement, 49, 587-602.
Willett, J.B., & Sayer, A.G. (1994). Using covariance structure analysis to detect correlates and
predictors of individual change over time. Psychological Bulletin, 116, 363-381.
Willett, J.B., & Sayer, A.G. (1995). Cross-domain analysis of change over time: Combining growth
curve modeling and covariance structure analysis. In G.A. Marcoulides & R.E. Schumacker (Eds.),
Advanced structural equation modeling: Issues and techniques (pp. 125-157). Mahwah, NJ:
Erlbaum.
Zapf, D. (1991). Stressbezogene Arbeitsanalyse bei der Arbeit mit unterschiedlichen Bü-
rosoftwaresystemen. [Stress-related job-analysis for various office software-systems]. Zeitschrift für
Arbeits- und Organisationspsychologie, 35, 2-14.
Zapf, D., Dormann, C., & Frese, M. (1996). Longitudinal studies in organizational stress research:
A review of the literature with reference to methodological issues. Journal of Occupational Health
Psychology, 1, 145-169.
Zung, W. W. K. (1965). A self-rating depression scale. Archives of General Psychiatry, 12, 63-70.
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Chapter 5
Optimism and Subjective Well-being in a Radical Change Situation in
East Germany
Does being an optimist help to deal with a prolonged stressful period and can these
beneficial effects of optimism be explained by the effective coping strategies used by optimists?
Researchers have pleaded for more longitudinal designs in order to gain insight into the causal
ordering of optimism, coping, and subjective well-being (Carver et al., 1993; Diener et al., 1999, p.
277; Lazarus, 1992, p. 245). Our study investigates the relation of optimism/pessimism and
subjective well-being and the mediating role of coping styles in a five year, five wave longitudinal
sample of East German inhabitants after the unification of East and West Germany. This study adds
to our knowledge in the following ways: First, it is one of the few longitudinal studies and the only
study with more than two or three measurement waves testing the effects of optimism and
pessimism on subjective well-being and the mediating effects of coping. Second, it has been argued
that subjective well-being has trait- and state like properties (Diener, Suh, Lucas & Smith, 1999, p.
280). However, the implications of this have not been spelled out theoretically and empirically. By
using growth curve methodology, we can systematically differentiate fast and slow moving changes
in optimism and subjective well-being.
Conceptualization of change
Most psychological constructs can be differentiated into three components, a completely
stable part, a slowly changing trend-like part, and a fast changing state-like component. Even
dispositions may show changes over time (Kenny & Campbell, 1989, Mischel & Shoda, 1998; in
the domain of coping: Lazarus, 1993). With the completely stable part, we mean a genetic or early
childhood predisposition which only changes because of biological parameters (e.g., dementia). The
slow moving trend may imply a developmental change. For example, in East Germany, people may
slowly discover the implications of having freedom, for example, in choosing a job or becoming an
entrepreneur. This is not an idea that changes quickly (within the framework of a few months) but
may take years to develop. Finally, fast moving changes are not day-by-day transient changes but
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are state-components which can change from week to week or month to month. For example,
having just found a new job increases one’s optimism and subjective well-being for several months
(e.g., honeymoon effect). Dispositional optimism, by definition regarded as a personality trait, but
also subjective well-being can have these three components (Diener et al, 1999, p.281). The high
stability of subjective well-being is well documented (Headey & Wearing, 1989, Ormel &
Schaufeli, 1991). Our theoretical model is inspired by the interpretation of change by Nesselroade
(1991). Nesselroade (1991, p. 96) distinguished three kinds of variability: (1) intra-individual
variability (relatively rapid, more or less reversible changes like states), (2) intra-individual change
(relatively slow changes reflecting processes such as development, labeled as ‘trait change’) and (3)
inter-individual changes (highly stable, denoted as ‘traits’).
Many studies on the effects of optimism used either cross-sectional designs or longitudinal
designs with only two wave studies and these designs are not able to differentiate between these
three change components. Even though the interest in the trait-state distinction is high (Mischel &
Shoda, 1998, Kenny & Campbell, 1989) there are no studies demonstrating differential effects of
the completely stable, slowly changing and rapidly changing components of optimism on subjective
well-being. The availability of longitudinal data including more than two waves is a prerequisite to
separate these components.
Differentiation between optimism and pessimism
In this study we concentrate on optimism, defined as the tendency to have positive general
outcome expectancies (Scheier & Carver, 1985) and the effects of optimism on subjective well-
being.
In recent years the construct validity of optimism has been debated. Many studies used the
Life Orientation Test (LOT, Scheier & Carver, 1985) for measuring optimism and it was
consistently found that a two-factor model fitted the data better than a one-factor model (Cheng &
Hamid, 1997; Marshall, Wortman, Kusulas, Hervig & Vickers, 1992; Mook, Kleijn , Van der Ploeg,
1992; Mroczek, Spiro, Aldwin, Ozer & Bossé, 1993; Räikkönen, Mattthews, Flory, Owens &
Gump, 1999; Robinson-Whelen, Kim, MacCallum, Kieholt-Glaser, 1997; Scheier, Carver &
Bridges, 1994; Schwarzer, 1994, p. 170). In these two-factor solutions all positively formulated
items loaded on one factor (optimism) and all negatively formulated items loaded on the other
factor (pessimism). Carver and Scheier (1985) argued that response tendencies could be blamed for
the emergence of two factors and that for most purposes the LOT could be considered as measuring
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optimism as a one-dimensional construct. From this perspective optimism and pessimism are
opposites of one underlying continuum. However, there are findings that optimism and pessimism
have different relationships with other variables and have different predictive values. For example,
Schwarzer (1994), Marshall et al. (1992) claimed that pessimism is associated with neuroticism and
negative affect, whereas optimism is linked to extraversion and positive affect. Although the debate
on whether the LOT is bi-dimensional is not completely settled (Spector, Van Katwijk, Brannick &
Chen, 1997), we decided to treat optimism and pessimism as separate constructs in order to explore
their potential differential effects on coping styles and subjective well-being.
Effects of optimism/pessimism on subjective well-being
Optimism/pessimism has been discussed within the frameworks of stress research and
subjective well-being. Optimism is related to symptoms of physiological and psychological health
in many stress studies (for excellent reviews of the literature see Scheier & Carver, 1992 and Taylor
& Aspinwall, 1996). In the stress literature optimism is interpreted as a resistance factor and
pessimism is treated as a vulnerability factor (Kessler, Price & Wortman, 1985, p. 541; Taylor &
Aspinwall, 1996). The reasons for these consistent relationships are thought to lie in differential
primary and secondary appraisal (Chang, 1998; Khoo & Bishop, 1996), in better social networks for
optimists (Geers, Reilly & Dember, 1998), or in psychoneuroimmunological factors (Abraham,
1994, p. 184). The most frequent mentioned mediator is coping which will be discussed below.
However the role of optimism as a major predictor of subjective well-being is not without
debate. Diener et al (1999, p. 281) argued that it is difficult to disentangle whether the cognitive
processes of optimism are the cause or the result of higher well-being. DeNeve and Cooper (1998)
discarded optimism in their meta-analysis by arguing (on footnote p. 199) that there is a conceptual
overlap between optimism and subjective well-being which makes showing relationships between
these variables trivial. A similar argument has been made for pessimism to be part of negative
affectivity (e.g., neuroticism: Smith, Pope, Rhodewalt & Poulton, 1989; and self-mastery: Marshall
& Lang, 1990). Evidence against this argument has been provided by several researchers (Chang,
1998; Räikkönen, Mattthews, Flory, Owens & Gump 1999; Scheier, Carver & Bridges, 1994;
Williams, 1992), showing the unique contribution of optimism in predicting outcome variables over
and beyond neuroticism.
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This debate can only be resolved by using longitudinal studies that show two things. First,
that optimism/pessimism is indeed related to subjective well-being, and second that it remains
significant after controlling for initial level of subjective well-being. Once, these two questions are
answered within a longitudinal study, the issue of mediation will be addressed.
This study is both unique in its design as well in its sample size. To our knowledge such a
large scale longitudinal study has not been published yet.
The mediating role of coping
The most dominant theory argues for indirect effects mediated by coping strategies:
Optimists make more use of efficient coping strategies like problem-oriented coping, whereas
pessimists use less effective strategies like emotional-focused strategies (Carver, Scheier &
Weintraub, 1989). Carver and Scheier (1992) used self-regulation theory to explain why optimists
are using more effective coping strategies. Self-regulation theory states that people persist in
achieving their goals as long as they believe that the outcomes would be positive. Because optimists
believe that they can expect more positive outcomes than pessimists, they are more strongly
motivated to retain their level of efforts. However, there is far more evidence that optimists use
different types of coping strategies, than that coping mediates the relation between optimism and
well-being (Carver et al, 1993). Moreover most of the available studies established only concurrent
relations and did not use a longitudinal design to predict future well-being (partialling out initial
well-being). Up to this point the prospective mediation hypothesis has not been adequately tested
(Carver et al, 1993).
The hypothesis that coping mediates the effects of optimism introduces theoretical
complexities from a transactional stress theory point of view. On the micro level stress and coping
are dynamic in time so that both appraisals (primary and secondary) and coping reactions can
rapidly change across the stages of a stressful transaction (Lazarus & Folkman, 1984). Therefore,
problem and emotion-focused coping can be used in rapid interchange during several stages of the
coping process and also can occur simultaneously to enhance their effectiveness (Scheier & Carver,
1994). Lazarus, in his transactional stress approach, contends that coping is a dynamic process and
that ways of coping can rapidly change in accordance with the demands of the appraisal of the
stressors at the time. No coping strategy is always effective and no coping strategy is always
ineffective. On the other hand, to make coping at all researchable within our context, it is necessary
to collapse concrete coping strategies across time (Lazarus, 1993). As Lazarus (1992, p. 243) says:
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“To study coping over time and across diverse sources of stress in the same persons in sufficient
number to address both its process and trait aspects, and to do this with an appreciation of the whole
person, calls for complex, long-term research designs.” In the coping literature a distinction
between coping strategies and coping styles is often made. For some research purposes the concept
of a coping style (or sometimes called dispositional or trait coping) may be useful to characterizes
the typical way a person acts in many stressful situations across many times (Ben-Zur, 1998;
Bijttebier & Vertommen, 1997, p. 848; Carver & Scheier, 1994, p.185; Schwarz, Neale, Marco,
Shiffman, & Stone, 1999; Taylor & Aspinwall, 1996; Terry, 1994). Recently, Schwarz et al (1999)
used a sophisticated longitudinal design (ecological momentary assessment) and found that
individual differences in coping styles exist, accounting for 15-40% of the variance in momentary
coping. In this paper we concentrate on the stable parts of coping and will investigate the mediating
role of coping styles in the relationship between optimism and subjective well-being.
The situation in East Germany
The setting of this study is particularly interesting, because drastic changes have taken place
during the time of the study. Immediately after the fall of the Berlin wall the atmosphere was
euphoric, but after a year East Germany slid into an economic recession and unemployment rates
rose dramatically. It slowly became apparent that the promised land of wealth and prosperity was
still a long way to go. This setting, characterized by strong political, economic, and social turmoil is
a good place to study the effects of optimism. The situation in East Germany after the unification in
1990 created both new challenges as well as threats, which were never experienced before. Chances
to become entrepreneurs increased side by side with unknown problems like long-term
unemployment. Bureaucratic procedures changed, stressors, for example, time pressure at work
increased, new supervisory principles appeared, and the old social structures vanished (Fay & Frese;
in press). All of this happened in a relatively short time. There were winners and losers in this
transition from socialism to market capitalism. If there is any situation that should produce drastic
changes in optimism/pessimism and subjective well-being, this should be one. The events of East
Germany during the 5 years after unification – the period or our study – are presented in Table 20.
As the short description in Table 20 shows, the economic situation in East Germany changed most
radically in the years late 1990 to 1991. Democracy and capitalism came mid 1990. The work
places were not transformed immediately, this happened at the end of 1990 and in 1991.
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Table 20 Historical context in East Germany
Time Historical Events Study Waves
October, November 1989 Mass demonstrations in Leipzig, Dresden and Berlin November 1989 The Berlin wall opened March 1990 First free election in East Germany July 1990 Economic unification, the DM (the West German
currency) is introduced in East Germany; the first changes appear at the work places, East German companies are started to be sold off, mainly to West German firms work places are still very much like they were under socialism
T0
October 1990 Political unification November 1990 work places started to be changed T1 December 1990 First general election in all of Germany Year of 1991 Serious economic crisis in East Germany, many work
related education programs started by government
August, September 1991 dramatic changes in work places, many people had to change jobs
T2
Years of 1992 and 1993 The economic crisis in East Germany deepened; wages increased to ca. 70 - 80% of Western level; many government programs to stimulate growth; more and more resentment towards West German managers among East Germans
August, September 1992 T3 August, September 1993 T4 Years of 1994 and 1995 The economic situation in East Germany stabilizes on
a low level; unemployment is high, in some towns it approaches 50%; there are pockets of very high productivity in the East, however, average productivity of East German workers is about 70% of those in the West; most industrial jobs have been lost; West Germany also slides into an economic recession with high unemployment
August, September 1995 T5
Theoretical Predictions
We will describe both a direct and a mediating model. These models are shown in Figure 25
and it is described to which “change” component the hypothesis is referring.
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__________________________________________________________________________________________________________________ O
ptimism
/pessimism
Subjective W
ell-being __________________________________________________________________________________________________________________
H
ypothesis: Stable components of
optimism
/pessimism
are related to stable com
ponents of subjective well-being
Hypothesis: T
rends in optimism
/pessimism
are related to trends in subjective w
ell-being which
can be explained by effectiveness of coping styles H
ypothesis: Fast changes in optimism
/pessimism
and fast changes in subjective w
ell-being are related
Figure 25. Theoretical hypothesis and the relation w
ith several parts of optimism
/pessimism
and subjective well-being
time
subject 1
subject 2
subject 3
subject 4
mean
com
pletely stab
le parts
time
subject 1
subject 3
subject 2
subject 4
mean
slow system
atic changes
time
subject 5
trend
line
ge
fast an
ch
s
time
subject 5
trend
line
ge
fast
an
ch
s
time
subject 1
subject 2
subject 3
subject 4
mean
complete
ly stable
parts
time
subject 1
subject 3
subject 2
subject 4
mean
slow system
atic changes
slow
changes in subjective w
ell-being
Hypothesis: Initial
optimism
/pessimism
is related to
coping styles as m
edia-tors
170
Relationships of the Stable Components of Optimism/Pessimism and Subjective Well-
Being. Our hypothesis that there is a relationship of the stable components of optimism/pessimism
and subjective well-being is based on the idea that all three variables have a strong genetic
component. This has been shown to be true for subjective well-being particularly (Diener et al,
1999, p. 279).
Relationships of Initial Optimism/Pessimism to Changes in Well-Being. This hypothesis
tests if being optimistic (pessimistic) at the start of the period of this study will lead to long term
positive (negative) changes in well-being. This follows from self-regulation theory (Scheier &
Carver, 1985). People who see positive outcomes in the future will continue to strive to achieve
them. Although occasionally disengagement from one’s goal may have adaptive value, particularly
in situations where continued effort is futile (Carver, Scheier & Pozo, 1992), we think that showing
persistence and remaining committed to one goals is the better strategy than disengagement.
Ultimately, not giving up may lead to success and it may provide mastery experiences and create
new opportunities. This process may feed upon itself and thus explains a benign cycle for optimists
and a vicious cycle for pessimists. The time order of this model satisfies one of the prerequisites for
a causal interpretation: the initial status of optimism precedes later changes in well-being. The time
lag is necessary because it takes time to deal with the new challenges and stressors of the post-
communist situation and it needs time to gradually translate these into changes in well-being.
Relationships of Trends in Optimism/Pessimism and Well-Being. This hypothesis refers to
the slowly changing components of both optimism/pessimism and subjective well-being and it
hypothesizes that these changes are related. Explanation of this relationship may be that an effective
coping style leads to both psychological as well as environmental changes. For example, continuing
one’s efforts in looking for a job under mass unemployment or studying hard for a new education
may be successful in the end. Both can be considered as mastery of stressors and both changes
one’s relationship to the environment (e.g., labor market). Conversely, an ineffective coping style
like wishful thinking combined with premature giving up one’s attempts to find a job may lead to
long-term unemployment which decreases one’s well-being and increases one’s pessimism in the
long run. In summary, changes in optimism/pessimism and changes in subjective well-being can
both be considered as outcome variables which are related because they are generated by the same
causes (e.g., effective coping style).
Relationships between Fast Changes of Optimism/Pessimism and Fast Changes of Well-
Being. A sort of honeymoon effect occurs when a positive event (for example, getting some good
news) produces positive effects on optimism and well-being. This is a short-lived effect. However,
171
it is not an uninteresting effect because cross-sectional studies may actually capitalize on this effect
to get a high correlation between optimism/pessimism and well-being.
Mediation. This model implies that optimism/pessimism – subjective well-being
relationships are mediated by coping. Such a mediation process is not relevant for the completely
stable parts of optimism/pessimism and subjective well-being, because it does not assume a causal
relationship between them (genetic predisposition and previous life experiences are third variables
producing a spurious correlation between optimism/pessimism and subjective well-being). We did
not test the mediation hypothesis for the fast changes because we do not have adequate process data
for such a procedure.
Therefore, the mediation hypothesis is only relevant for one hypothesized relationship: The
relationship of the stable components of optimism/pessimism and changes in subjective well-being.
Optimism at the start of an episode will be related differentially to coping styles. Coping styles, in
turn, are differentially related to subjective well-being. There are several coping styles and therefore
a simple mediation model is inappropriate. As Figure 26 shows there can be several mediational
paths and we hypothesize that all effects of optimism on subjective well-being via coping styles
should be positive: Optimists have more effective coping styles, which in turn have a positive
influence on their well-being14. In contrast pessimists can be characterized by having an ineffective
coping style, which will negatively affect their well-being. In particular, we expect that there are
positive relations between optimism and problem-focused coping, which includes trying to get help
from social networks and planning to deal with one’s problems. Pessimists have an emotionally
focused coping style and will use more wishful thinking and self-criticism.
Coping may not only be determined by optimism/pessimism, it may also affect future
changes in optimism/pessimism. Thus, coping may have a reciprocal relationship with
optimism/pessimism. In a way, problem-focused coping is likely to lead to more mastery
experiences and, therefore, will lead to a higher degree of optimism. If effective coping styles
would result in both positive changes in optimism/pessimism as well as in subjective well-being,
14 In the general case, complex mediational models can have paths with opposite effects and theoretically the total effect
can be zero. Thus, compensational mechanisms can produce suppressor effects (Gully, Frone, Edwards, 1998). Thus, if
direct effects in a model without mediators are absent, this does not necessarily imply that mediational effects are
absent. As Bollen stated (1989):”The old saying that correlation does not prove causation should be complemented by
the saying that a lack of correlation does not disprove causation (p.52).
172
the coping style variables act as a set of third variables (partly) explaining the relationship between
changes in optimism/pessimism and changes in subjective well-being.
Figure 26. Simple and complex mediation.
Independent variable
mediator Dependent variable
+ +
Initial optimism Changes in subjective well-being
+ +
- -
Effective coping style
Simple full mediation model
Complex full mediational model
173
Method
The data in this study were gathered in the AHUS project. AHUS is a German acronym for
“active actions in a radical change situation”. The goal of the project was to study the effects of
drastic changes that took place after the unification of East and West Germany and one of the
research questions was which people could cope better with the many stressors they encountered.
This study used only the last five waves over a five year time period (the data of the first wave were
not used; more on this later). Other publications of this study concentrated on personal initiative
(Frese, Kring, Soose, & Zempel, 1996; Frese, Fay, Hilburger, Leng, & Tag, 1997; Frese, Garst, &
Fay, 1998; Speier & Frese, 199) and stressors and strains (Dormann, Zapf & Speier, in press; Garst,
Frese & Molenaar, in press). The issue of optimism/pessimism has not been dealt with in any other
publication.
Sample
A representative sample was drawn in Dresden, a large city in the south of East Germany; it
is the capital of Saxonia, houses a large Technical University and is relatively well-off (for
example, compared with cities in the north of East Germany). The sampling was done by randomly
selecting streets, selecting every third house and in each house, every fourth apartment (in smaller
houses every third one). People between the ages of 18 and 65 with full-time employment at the
start of the study participated (thus, we sometimes had more than one person per family). The
refusal rate of 33% was quite low for a study of this kind. Confidentiality was assured; if subjects
preferred anonymity, this was done with the help of a personal code word.
In wave 1, (July 1990), 463 people participated in Dresden (the first wave, T0, was not
included in this study, more on this will be discussed later). At T1 (November, December, 1990)
202 additional people were asked to participate15. At T2 (September 1991), the N was 543, at T3
(September 1992) the N was 506, at T4 (September 1993), N = 478, at T5 (September 1995), N =
489. Experimental mortality did not prove to change the make-up of the sample. The sample is
representative of the Dresden population on the relevant parameters (for example, for age, social
class, male/female percentage at work). Fifty-three percent of the sample was male and 47% female.
At T2 age ranged from 17 to 65 years (M = 39, SD = 11.4). Most subjects worked in the service
15 Additional people were added to ascertain whether repeated participation had an influence on the variables of the
questionnaire. This was not the case.
174
industry (35,9%) and as employees in trade or manufacturing enterprises (30.9%). Overall, there
were 18.9% office workers on jobs that required little qualification, 27.4% worked as managers or
professionals with high qualification requirements, 12.5% were higher level public servants mostly
employed in schools and universities (e.g., university professors are public servants in Germany),
and 16.5% worked in skilled respectively 14.9% unskilled blue collar positions. At the start of the
study there were no unemployed in our sample, but later unemployment rose leading to the
following unemployment figures for the subsequent waves: n = 42 (7%) at T1, n = 59 (11%) at T2,
n = 38 (7.8%) at T3, n = 35 (7.5%) at T4 and n = 37 (8.1%) at T5. At later waves some subjects also
did not have a job for reasons other than unemployment (e.g., retirement, schooling, parental leave).
Measures
All optimism and subjective well-being measures were ascertained with a questionnaire. The
coping style variables were also measured by a questionnaire but were prepared within an interview
setting. Planning was measured in the interview.
Optimism and Pessimism. The Life Orientation Test (LOT) of Carver & Scheier (1985) was
used. The LOT was fully administered in five waves. Unfortunately due to a clerical error in the
first wave one of the items of the LOT was not included in the questionnaire. Therefore, the first
wave was not included in the study. As the LOT scale was part of an extended questionnaire we did
not include the filler items. Optimism included all the positive items, pessimism all the negative
ones.
Subjective Well-Being Variables. Diener, Suh, Lucas & Smith (1999) argue that subjective
well-being should not be treated as a monolithic entity, but as consisting of separate components
that exhibit unique relations with other variables of its nomological network. Hence, in this article
we used depression, irritation, worrying and psychosomatic complaints as separate constructs.
Diener et al (1999, p. 278) argue that subjective well-being depends on reactions in multiple
physiological and psychological systems, and psychosomatic complaints refer more to physiology,
whereas worrying is rooted in the cognitive system. The measures, depression, psychosomatic
complaints, irritation and worrying, were adaptations of Mohr’s (1986) scales – a group of
frequently used scales in Germany, because they are well validated. Garst, Frese & Molenaar (in
press) demonstrated that these scales possessed measurement invariance for a period of at least five
years.
Depression (4 items) was originally adapted from Zung (1965) and all of those items that
referred to physical problems (e.g., not being able to sleep) were excluded to reduce the overlap
175
with psychosomatic complaints. Items were “A good deal seems senseless to me” and “I have sad
moods”. This depression scale attempts to measure mild forms of depression and probably even
persons with high scores would not be diagnosed as suffering from depression in a clinical sense
(Coyne & Downey, 1991, p. 405-406). A seven point Likert scale was used and the extreme
response categories were described as “almost always” to “never”. The internal consistencies for the
five waves were .72, .81, .80, .79 and .82.
Psychosomatic complaints (8 items) was originally adapted from Fahrenberg (1975) and
related to aches and other negative bodily sensations. The respondents can easily detect the
symptoms and no medical assistance is needed for its diagnosis. The contents of some items were:
“Do you feel pain in your shoulders?” and “Do you have feelings of dizziness?”. A five point
Likert scale was used with response categories, which ranged from ‘almost daily’ to ‘never’. The
alphas ranged from .83 to .85. To reduce the size of the measurement models we constructed 3
item-parcels out of the 8 items. An item-parcel is a combination of the scores of several items so
that a much smaller number of measured variables have to be included into the model (Marsh, Hau,
Balla & Grayson, 1998). The allocation of the items to the parcels was based on the results of an
exploratory factor analysis.
Irritation (5 items) and worrying (3 items) were both derivatives of the scale irritation
developed by Mohr (1986) because preliminary analysis indicated that two (moderately correlated)
factors could be distinguished. The internal consistencies for the irritation scales ranged from .84 to
.85.
Worrying referred to the preoccupation of work-related problems in one’s spare time (“Even
during holidays I think a lot about problems at my work”). The scope of the original irritation scale
was narrowed down to feelings of irritation and nervousness (I’m easily agitated”). A seven point
Likert scale was used. Alphas ranged from .83 to .87.
Coping styles consisted of a German translation of the Ways of Coping Checklist (Folkman,
Lazarus, Dunkel-Schetter, DeLongis, & Gruen, 1986) and the following scales were administered:
Problem-focused coping, wishful thinking, emotional focused coping, seeking social support and
self-criticism. Our procedure was a combination of state and style approaches. At each wave, the
interviewer asked the respondent to name a specific stressor at work that had happened within a 7-
day period. This stressor was then used as stimulus material for the Ways of Coping Checklist. All
items were summed for waves T1 to T5 to estimate the coping style. The coefficient alpha values
for these scales were .87 for problem-focused coping, .86 for wishful thinking, .86 for emotional-
focused coping, .83 for seeking social support, and .71 for self-criticism. Our approach is in line
176
with the suggestion by Lazarus (1992) and is an attempt to measure the typical preference to
approach problems in particular ways (Kessler, Price & Wortman, 1985, p.551).
Planning was ascertained by an interviewer rating after the interview. The score was based
on the sum of three items with regard to level of concreteness and detail of plans and their long-
term orientation. The rating was done after an extensive interview, which included questions on
personal initiative, professional career, and future plans. Planning should be seen as one specific
instance of problem focused coping. The scale planning was measured with a different procedure
and, therefore, does not carry the risk of common variance with optimism/pessimism, well-being,
and the other coping factors. Coefficient alpha for the scale, aggregated over five waves, was .86.
To evaluate all the models covariance matrices and means were estimated with the computer
program NORMS (Schafer, 1997) and these matrices and mean vectors were used as input for
LISREL (Version 8.30, Jöreskog & Sörbom, 1993). The NORMS program is specifically designed
for handling missing data problems. We used the EM Algorithm of NORMS. The EM algorithm
(Dempster, Laird & Rubin, 1977) is a general technique for finding maximum-likelihood estimates
for models with partial missingness. It is based upon the assumption that data are "missing at
random" (MAR), which is a much milder assumption than the assumption that "missingness occurs
completely at random" (MCAR). MAR only requires that the missing values behave like a random
sample of all values within subclasses defined by observed data” (Schafer, 1997, p. 11). The sample
size used for a particular LISREL analyze was calculated by the mean of the different sample sizes
of the input matrix (N = 423 for depression; N = 420 for psychosomatic complaints; N = 421 for
irritation; N = 416 for worrying).
To evaluate the overall fit of the models, we report the chi-square statistic, the Akaike index
(AIC; Akaike, 1987) Root Mean Square Error of Approximation (RMSEA; Browne & Cudeck,
1993) and the comparative fit index (CFI; Bentler, 1990). One disadvantage of using the chi-square
statistic in comparative model fitting is that it decreases when parameters are added to the model.
Therefore we also report the AIC index, because it takes parsimony (in the sense of as few
parameters as possible) as well as fit into account (Jöreskog & Sörbom, 1993). However, if two
models are nested, we report the difference chi-square test (Bollen, 1989). Browne & Cudeck
(1993) suggested using Steiger's Root Mean Square Error of Approximation (RMSEA) as a
measure of discrepancy per degree of freedom with a value of 0.05 indicating a close fit and values
up to 0.08 representing reasonable errors of approximation in the population. The CFI is based upon
a comparison of the fit of the hypothesized model to the fit of the null baseline model and most
177
researchers consider values greater than .90 as an indication for a good fit, although recent research
suggests a cutoff value close to .95 (Hu & Bentler, 1999).
In order to evaluate effect sizes we will report the parameters of interest, the standard errors
and the z values. Since we have directional hypotheses we used one-sided tests of significance: If
the ratio of a parameter estimate and its standard error exceeds the value of 1.65 the parameter will
be called significant. However, many researchers using structural equation modeling call a
parameter significant if the ratio exceeds the value of 1.96, so we will also report if this is the case.
Modeling Strategy
Our modeling strategy consisted of three parts. In the first part we tested the measurement
models. In the second part we investigated the stability of the means and individual differences. The
third part dealt with testing the structural models. For all three parts the latent means were required,
hence all estimated models simultaneously analyzed the covariance matrix and the mean vector.
Measurement Models
A description of the measurement models for the subjective well-being variables can be
found in Garst, Frese & Molenaar (in press), so here we only describe the measurement models for
optimism and pessimism. The strategy of the measurement modeling involved three basic steps. In
the first step (Model 1) a longitudinal measurement model with a banded error16 structure was
tested. Models with optimism as one single construct can be compared with a two-factor model
with the optimism and pessimism items loading on two correlated constructs. The one and two-
factor solutions are nested and the difference chi-square test (Bollen, 1989) could therefore be used
for selecting the best model.
16 In the measurement model a common latent factor, an item-specific factor and a random error term can predict an
item response. In cross-sectional models it is not possible to separate the specific item variance and the random error
variance. Both are summed into the unique variance of the item (Raffalovich & Bohrnstedt, 1987). But in longitudinal
studies the specific item factor can be specified as the correlation between the residuals of identical items measured at
different occasions. Identical and repeatedly administered items invoke specific responses for a person and the unique
components are therefore allowed to correlate over time. Vonesh and Chinchilli (1997) and Steyer, Ferring, and Schmitt
(1992) describe several error structures; in this study the time between adjacent measurements varied and, therefore, we
preferred the unrestricted banded error variant. In a banded error structure there are covariances specified between the
unique factors of identical items (measured at different occasions).
178
The next two steps tested measurement invariance (Little 1997; Meredith, 1993). For growth
models the assumption that across all time points the same construct has been measured is crucial
(Plewis 1996; Kenny & Campbell 1989). Thus, the second step (Model 2) tested for equality of
factor loadings over time. Factor loadings are regression coefficients where the observed variable is
regressed upon an unobserved latent factor. A change in relationships of the latent construct and the
items over time is an indication of a Gamma change (Golembiewski, Billingsley & Yeager, 1976)
which implies a change in the respondent’s interpretation of the item content (Chan, 1998; Oort,
1996). If there is a sizeable gamma change, comparisons of the relevant constructs over time are
impossible. In a third step (Model 3) the equivalence of item intercepts over time were tested. If all
factor loadings of identical items are equal over time a change in the item intercepts indicates a
general change in the level of the item response. This implies that the item is more or less attractive
and this shift cannot be explained by a change in the latent trait. This phenomenon is called beta
change (also called a response shift) and occurs if a respondent changes his or her meaning of the
item response scale’s value (Oort, 1996). Testing the equivalence of item intercepts requires that
both the covariance matrix and the vector of means should be analyzed. Some authors (Byrne,
Shavelson & Muthén, 1989; Pentz & Chou, 1994, Muthén, 1998) argue that it is sufficient to have
indicators for each construct with invariant measurement parameters. These items function as the
anchor items and keep the latent scale at a comparable level (cf. vertical equating in Item Response
Theory). So, a few violations can be tolerated and partial measurement invariance is a more realistic
goal.
Stability of the means and individual differences. Before testing longitudinal models it is
useful to inspect the pattern of the latent means and the stability of the individual differences. If the
goodness of fit is acceptable we can extract this information from the measurement models.
Comparing the mean trajectories of several latent constructs informs about the parallelism of the
development in these constructs. Stability coefficients inform about the degree to which there are
changes in the latent constructs over time. If there is a fair amount of change this justifies the fitting
of structural models in the next section in order to explain those changes.
Structural models
Appendix E provides a short description of the latent growth curve models used. Briefly,
growth curve models focus on intra-individual changes and interindividual differences in change
patterns. An obvious example is that some school children may start at a lower level of reading but
have steeper learning curves than other children. Thus, both the starting positions and the learning
curves may be different for different pupils. Figure 27 describes slopes and intercepts.
179
Figure 27. Growth Curve Model with correlations between growth curve factors. Note: I = intercept factor; S= slope factor; not shown autocorrelations between unique factors of items; a: Correlation between slope factors tested in hypothesis: relationships of trends in pessimism and worrying. The slope factor S is a latent construct that represents the slope coefficient for each individual (as
deviation from the mean slope). A high factor score for S means that the slope for that individual
I S
T1 T2 T3 T4 T5
11
1 11Pessimism
I
1111
1S
T1 T2 T3 T4 T5Worrying
a
180
deviates strongly from the mean slope. If the mean slope is zero (no mean changes over time) a high
positive factor score implies a strong positive change for that person and a low positive value means
that there is little positive change. Thus, S tells us something about the interindividual differences in
change processes (more on this in the Appendix). Therefore, changes in optimism/pessimism and
changes in subjective well-being can be represented by the slope factors. However, in a linear
growth curve model the slope factor only captures the linear change over time for each person.
The intercept factor signifies the starting point of the growth trajectories for each person
(one statistical prerequisite is to fix the time scaling to the value of 0 for the first measurement wave
– more on this in the Appendix). The initial status for optimism/pessimism and subjective well-
being can be represented by the intercept factors. However, the intercept factor is not equal to the
latent construct itself at the first measurement wave, because the last is also determined by state
influences (note the time-specific disturbance term in Figure 27).
Because the sample size in this study is too small to specify models including all our
variables we will report models which consist of subsets of variables. Therefore, for each of the
four well-being variables we had two separate models for optimism and pessimism. In this way
differential effects of optimism and pessimism on well-being can be studied. For
optimism/pessimism as well as for the well-being variables the measurement models were included,
so that we deal with latent variables; therefore, the growth curves are not confounded by
measurement error.
The first step was to model a maximum model. The maximum model does not impose
restrictions on the structural relations and thus maximally accounts for the covariation between
latent constructs. Its goodness of fit refers only to the appropriateness of the measurement models
included. This model will be used as a baseline for comparing the fit of more restricted models.
In a second modeling step, linear growth curve models with latent variables were estimated
for each combination of optimism/ pessimism and one of the well-being variables. Three growth
models will be estimated: An unspecified model which allows the growth factors to freely covary
(see Figure 27), a direct model, which specifies paths between both intercept and the slope factors
(see Figure 28), and a mediator models whereby the coping style variables mediate the relation-
ships between the intercept and the slope factors (see Figure 29). Each of the Figures 27 to 29
displays the model for pessimism and one well-being variable – worrying (the other models are
equivalent).
181
Figure 28. Direct effects model for growth curve factors of pessimism and worrying. Note: I = intercept; S= slope; not shown autocorrelations between unique factors of items; only two coping styles variables displayed. a: Correlation between intercept factors tested in hypothesis tested in hypothesis: relationship between stable components of pessimism and worrying. b: Coefficient from path intercept factor pessimism to slope factor worrying tested in hypothesis: relationship of initial pessimism and changes in worrying. c: Partial correlation between slope factors tested in hypothesis: relationships of trends in pessimism and worrying.
I S
T1 T2 T3 T4 T5
11
1 11Pessimism
I
1111
1S
T1 T2 T3 T4 T5Worrying
ca
b
182
S
T1
T2
T3
T4
T5
1
1
1
1
1
Pessimism
Worrying
I
1
1
1
1
1
S
T1
T2
T3
T4
T5
I
C1
C2
C3
C4
C5
C6
Figure 29. Mediation model with coping styles variables as mediators (C1: planning; C2: self-criticism; C3: emotional-focused coping; C4: seeking social support: C4: problem-focused coping; C5: wishful thinking). The measurement model is not shown.
183
It is important to note that all these three models will yield the same goodness of fit
measures. This follows from the specification of the direct and mediator models: All covariances
are accounted for and no additional restrictions will be imposed, so the fit will be the same as the
unspecified model.
A third modeling step estimated linear growth curve models with an additional set of
correlated residuals (see Figure 30). These models are the same as the previous models except that
they allow the residuals of the latent constructs of optimism/pessimism and subjective well-being to
be correlated. The small arrows at T1, T2, etc. of these latent constructs (also called disturbances)
signify the deviations for each person from their individual growth curve for a particular time-point.
The correlations of the residuals of pessimism and the residuals of worrying at T1, T2 etc. test
whether there is a relationship of the fast moving changes in optimism/pessimism and the fast
changes in the subjective well-being variables at each particular wave. Thus, we test if there is a
tendency that a deviation from the individual growth curve of optimism/pessimism will be
accompanied by a deviation in the same direction from the individual growth curve of subjective
well-being. The significance of the correlations among the residuals refers to the relations between
the non-stable non-trend-like changes in optimism/pessimism and well-being.
The growth curves models are based on linear curves. If the fit of linear curves is not
satisfactory, quadratic or even higher order polynomials models can be fitted, although the
interpretation of these models is more difficult (Muthén and Muthén, 1998). It is important to note
that all models can only be conceived as approximations to reality (Browne & Cudeck, 1993;
Cudeck, 1991) and a linear growth model is parsimonious and still capturing important aspects of
the change over time even if in reality there are some deviations from linearity (Rogosa, Brandt &
Zimowski, 1982, p. 728; Willet, 1989).
In growth curve models there are other indicators of the usefulness of the models next to the
goodness of fit particularly the amount of explained variance of the growth curves and the
significance of the growth curve parameters. If only a small portion of the variance can be explained
by the linear growth curve, the major part would consist of residual variance referring to deviations
around the individual growth curves. This indicates that state variance would prevail over the
systematic changes. Also, the significance of the growth parameters needs to be inspected. If one of
the growth parameters does not reach the level of significance, this implies that a simpler model
would suffice. For instance, if both the estimates of the mean and the variance of the slope
184
Figure 30. Model with correlated disturbance terms (Model 3 in Table 31).
I S
T1 T2 T3 T4 T5
11
1 11
Pessimism
I
1111
1S
T1 T2 T3 T4 T5
Worrying
correlationsbetweendisturbanceterms
185
factor are not significant, a more parsimonious random intercept model would be more appropriate.
This last model does not contain a slope factor, but only has an intercept factor, representing
constant baselines for each individual. This highly restricted model argues that no systematic
changes over time occur, but for each subject there are only state fluctuations around the subject’s
constant baseline.
In summary, after reporting the goodness of fit measures, we will present both the amount of
explained variance of the growth curves and the significance of the growth curve parameters.
There are four relationships on which we have hypotheses: The relationship between the
intercepts, the relationship between the intercepts and the slopes and the relationships between the
slopes and finally the relationships between the time-specific residuals. The first three hypotheses
will be tested by parameters estimated in the linear growth curve model and the last hypothesis will
be tested by comparing the fit of the linear growth curve model with the fit of a model which adds
covariances between the disturbances (this last model will be described later).
Thus, the following parameters will be tested in the first linear growth model: First, the
relationships between the stable components will be tested by the correlation between the intercept
factors of optimism/pessimism and subjective well-being in the unspecified model (see Figure 27).
In the model including pessimism and worrying the correlation between both intercept factors
means that the starting points of both trajectories are correlated. Thus, if a person is above the mean
in pessimism, the person tends to be above the mean in worrying.
Second, the relationship between initial optimism/pessimism and slow changes in subjective
well-being (see Direct Model in Figure 28) will be tested by the regression coefficient of the path
from the intercept factor of optimism (pessimism) to the slope factor of subjective well-being. This
means that in the model including pessimism and worrying the starting point of pessimism predicts
the rate of change for worrying. In other words a high level of pessimism leads to a higher than
average increase in worrying. In the Direct Model there are also paths from the intercept factors of
pessimism and worrying to their respective slope factors, which implies that pre-existing
differences are partialled out.
Third, the relationship of two trends – the trend for optimism/pessimism and the trend for
subjective well-being – can be tested by the correlation of both slope factors (see Figure 27).
However, it is better to control for pre-existing differences and to adjust for potential bottom- and
ceiling effects and to test the partial correlation (correlation between the residuals in Figure 28). In
the pessimism-worrying model the partial correlation between both slope factors tells us something
about how individual differences in the pessimism trajectories are related to individual differences
186
in worrying trajectories (after controlling for the starting points of the pessimism and worrying
trajectories). An example may be that some people are steadily increasing in both in their pessimism
and in their worrying, while other people may change in the opposite direction for both variables.
The final model includes the coping style variables as mediators between the intercept
factors and slope factors (see Figure 29). In addition to mediational effects this model also contain
direct effects; therefore these indirect models are in fact partial mediation models. The disturbances
among the mediators are allowed to freely covary, because there is no theoretical justification that
the independent variables (both intercept factors) should fully explain the covariances between the
coping style variables. As a consequence of these specifications no additional restrictions will be
imposed and the fit of the model will be the same as the model without the mediators.
The mediation hypothesis can be tested in two ways: The first way is to look at the
significance of the separate paths from the intercept factor of optimism/pessimism to coping and
from coping to the slope factor of subjective well-being. The second test is a global test and looks at
the significance of the indirect effects of the intercept factor of optimism/pessimism on the slope
factor of subjective well-being. This is equivalent to testing the significance of the reduction of the
size of the direct effect after including the mediators into the model (Kenny, Kashy & Bolger,
1998). In the latter case, we do not know the specific workings of the relationships.
Results
Descriptive Data
In Table 21 to 25 the means, standard deviations and the cross-sectional intercorrelations of
the summated scores of all the scales are presented for each measurement occasion separately. In
Table 26 the zero order correlations between optimism/pessimism and subjective well-being scale
scores for all time periods are shown. These correlations show the familiar pattern of negative
correlations between optimism and pessimism; the negative correlations of optimism with the
subjective well-being variables (which are of course; ill-health variables) and positive correlations
of pessimism with the subjective well-being variables. All hypotheses will be tested by looking at
the analyses of the latent constructs and the variables constructed with the help of growth curve
modeling.
187
Table 21
Means, Standard D
eviations, and Intercorrelations at T1
Subscale M
SD
1
2 3
4 5
6 7
Optim
ism/Pessim
ism
1. O
ptimism
(subscale) 5.34
1.09
2. Pessim
ism (subscale)
3.74 1.06
-.23**
3. Optim
ism (com
plete scale; pessim
ism item
s recoded) 4.80
.84 .79**
-.78**
Subjective Well-being
4. D
epression 2.74
.92 -.26**
.35** -.39**
5. Psychosom
atic complaints
2.13 .80
-.04 .19**
-.15** .46**
6. Irritation 3.21
1.17 -.14**
.27** -.26**
.48** .49**
7. W
orrying 3.63
1.54 -.13**
.16** -.18**
.22** .27**
.39**
N
ote. N =
592 (listwise deletion); * p <
.05. ** p < .01.
Table 22
Means, Standard D
eviations, and Intercorrelations at T2
Subscale M
SD
1
2 3
4 5
6 7
Optim
ism/Pessim
ism
1. O
ptimism
(subscale) 5.13
1.04
2. Pessim
ism (subscale)
3.63 1.04
-.31**
3. Optim
ism (com
plete scale; pessim
ism item
s recoded) 4.75
.84 .81**
-.81**
Subjective Well-being
4. D
epression 2.71
.97 -.22**
.39** -.37**
5. Psychosom
atic complaints
2.18 .80
-.02 .20**
-.13** .48**
6. Irritation 3.28
1.10 -.10*
.30** -.25**
.46** .49**
7. W
orrying 3.80
1.41 -.08
.17** -.15**
.23** .28**
.43**
N
ote. N =
537 (listwise deletion); * p <
.05. ** p < .01.
188
Table 23
Means, Standard D
eviations, and Intercorrelations at T3
Subscale M
SD
1
2 3
4 5
6 7
Optim
ism/Pessim
ism
1. O
ptimism
(subscale) 5.12
1.08
2. Pessim
ism (subscale)
3.65 1.04
-.29**
3. Optim
ism (com
plete scale; pessim
ism item
s recoded) 4.73
.85 .81**
-.79**
Subjective Well-being
4. D
epression 2.70
.98 -.38**
.39** -.48**
5. Psychosom
atic complaints
2.22 .81
-.05 .21**
-.16** .39**
6. Irritation 3.25
1.13 -.17**
.30** -.29**
.46** .47**
7. W
orrying 3.82
1.44 -.10*
.13** -.14**
.22** .31**
.45**
N
ote. N =
490 (listwise deletion); * p <
.05. ** p < .01.
Table 24
Means, Standard D
eviations, and Intercorrelations at T4
Subscale M
SD
1
2 3
4 5
6 7
Optim
ism/Pessim
ism
1. O
ptimism
(subscale) 5.06
1.05
2. Pessim
ism (subscale)
3.54 1.03
-.27**
3. Optim
ism (com
plete scale; pessim
ism item
s recoded) 4.76
.83 .80**
-.79**
Subjective Well-being
4. D
epression 2.66
.94 -.29**
.48** -.48**
5. Psychosom
atic complaints
2.22 .79
-.09* .28**
-.23** .43**
6. Irritation 3.16
1.09 -.22**
.35** -.36**
.49** .49**
7. W
orrying 3.81
1.45 -.15**
.09 -.15**
.20** .31**
.42**
N
ote. N =
467 (listwise deletion); * p <
.05. ** p < .01.
189
Table 25
Means, Standard D
eviations, and Intercorrelations at T5
Subscale M
SD
1
2 3
4 5
6 7
Optim
ism/Pessim
ism
1. O
ptimism
(subscale) 5.11
1.01
2. Pessim
ism (subscale)
3.49 1.05
-.29**
3. Optim
ism (com
plete scale; pessim
ism item
s recoded) 4.81
.83 .79**
-.81**
Subjective Well-being
4. D
epression 2.64
.98 -.32**
.44** -.47**
5. Psychosom
atic complaints
2.22 .79
-.07 .17**
-.15** .45**
6. Irritation 3.17
1.11 -.18**
.33** -.32**
.49** .43**
7. W
orrying 3.82
1.44 -.12*
.10* -.13**
.29** .28**
.47**
N
ote. N =
482 (listwise deletion); * p <
.05. ** p < .01.
Table 26
Correlation m
atrix of scale scores of optimism
and pessimism
with subjective w
ell-being variables
D
epression
Psychosomatic com
plaints
Irritation
Worrying
T
1 T
2 T
3 T
4 T
5
T1
T2
T3
T4
T5
T
1 T
2 T
3 T
4 T
5
T1
T2
T3
T4
T5
Optim
ism
T1
-.28* -.22* -.24* -.26* -.22* -.03
.01 .00
-.02 -.05
-.13* -.10* -.06 -.12* -.14*
-.12* -.10* -.10* -.14* -.10*
T2
-.25* -.23* -.28* -.24* -.23* -.06
-.04 -.05
-.06 -.06
-.09 -.08
-.10 -.16* -.10*
-.07 -.05
-.07 -.12* -.04
T
3 -.30* -.26* -.39* -.28* -.29*
-.07 .02
-.05 -.04
-.04 -.19* -.17* -.18* -.16* -.13*
-.11* -.11* -.09 -.13* -.09
T
4 -.28* -.26* -.33* -.30* -.28*
-.16* -.12* -.12* -.12* -.15* -.19* -.17* -.22* -.25* -.25*
-.12* -.10* -.10 -.15* -.14*
T
5 -.28* -.22* -.26* -.26* -.32*
-.08 -.07
-.07 -.06
-.08 -.12* -.14* -.12* -.18* -.19*
-.10* -.12* -.08 -.15* -.12*
Pessimism
T
1 .36* .34* .36* .36* .34*
.17* .15* .15* .17* .17* .22* .21* .24* .22* .23*
.10* .15* .14* .13* .09
T2
.32* .39* .36* .35* .34* .22* .22* .22* .21* .19*
.24* .28* .28* .25* .23* .07
.14* .12* .10 .08
T
3 .31* .33* .38* .39* .40*
.14* .14* .18* .26* .23* .20* .25* .31* .28* .26*
.07 .11* .11* .15* .11*
T
4 .24* .28* .36* .47* .41*
.20* .22* .19* .29* .26* .16* .25* .27* .31* .34*
.05 .09
.06 .07
.08
T5
.28* .28* .39* .41* .47* .19* .15* .16* .18* .21*
.21* .27* .30* .30* .36* .02
.09 .10* .09
.12* N
ote. N =
423 for depression; N =
420 for psychosomatic com
plaints; N =
421 for irritation; N =
416 for worrying
190
Measurement models for optimism/pessimism
For a description of the well-being measurement models we refer the reader to Garst, Frese
& Molenaar (in press). In Table 28 the goodness-of-fit measures of the optimism/pessimism
measurement models are shown. A five-wave longitudinal factor model combining optimism and
pessimism into one latent construct (Model 1 in Table 28) did not fit very well. A longitudinal
model with separate constructs for the optimism and the pessimism (Model 2 in Table 28) was
superior in its fit indexes (∆χ2 = 563.23, ∆df = 35, p < 0.00; RMSEA = 0.032; CFI =0.960).
Imposing equality constraints on the factor loadings (Model 3) did not lead to a significant worse
chi-square (∆χ2 = 27.33, ∆df = 24, p < 0.289). However, further restrictions by constraining the
item intercepts to be equal over time (Model 4) produced a significant worse chi-square (∆χ2 =
65.14, ∆df = 24, p < 0.00). The freeing of only two item intercepts in T4 and T5 was sufficient to
obtain a model (Model 4a) which did not differ significantly from the model with completely equal
factor loadings (Model 3). In summary, full measurement invariance was not reached, but only
minor violations were noticed and partial measurement is a sufficient condition to make the
optimism/pessimism constructs comparable over time.
Table 28
Goodness-of-Fit Measures for Measurement Models Optimism/pessimism
Model χ2 p df RMSEA AIC CFI
1 One factor model 1601.93 0.000 650 0.062 2021.93 0.882
2 Two factor model 851.45 0.000 615 0.032 1341.45 0.960
Difference of 2 and 1 750.48* 0.000 35
3 Equal factor loadings 884.19 0.000 639 0.032 1326.19 0.960
Difference of 3 and 2 32.74 0.110 24
4 Equal loadings and intercepts 949.37 0.000 663 0.034 1343.37 0.953
Difference of 4 and 3 65.18* 0.000 24
4a Equal loadings and intercepts 921.06 0.000 661 0.032 1319.06 0.957
Difference of 4a and 3 36.87 0.024 22
5 Equal latent means 972.59 0.000 669 0.035 1354.59 0.952
Difference of 5 and 4a 51.53* 0.000 8
Note: * Chi square difference test is significant (α = 0.01)
191
Stability of the latent means and individual differences
A model (Model 5 in Table 28) restricting the latent means of optimism and pessimism to be
equal over time could be rejected (∆χ2 = 51.53, ∆df = 8, p < 0.00). In Table 29 the means and
standard deviations of the latent constructs optimism and pessimism are shown.
Table 29
Means and Standard Deviations of Latent Constructs Optimism and Pessimism
Optimism Pessimism
Mean SD Mean SD
T1 5.18
(.31)
1.01 2.32
(.23)
.59
T2 4.98
(.30)
.94 2.26
(.22)
.58
T3 4.95
(.30)
.97 2.29
(.23)
.58
T4 4.93
(.30)
.91 2.23
(.22)
.56
T5 5.02
(.30)
.88 2.18
(.22)
.58
Note: Standard errors between parentheses.
The means of optimism consecutively decreased over time; only in T5 there was a small increase.
However, the changes in means seem small in relation to the standard deviations of latent optimism.
Remarkably, the latent means of pessimism also decreased over time (except in T2), but again the
effect sizes were rather modest in comparison with the variances of latent pessimism. The latent
means of the subjective well-being variables were almost stable (reported in Garst et al, in press).
In Table 30 the correlations between the latent constructs optimism and pessimism are given
for all measurement occasions. The synchronous correlations between optimism and pessimism fall
within the range -.32 and -.47. Not only can optimism and pessimism be regarded as independent
constructs, the correlations were also moderate and do not warrant a treatment as a single construct.
Table 30 also presents the stability coefficients of optimism and pessimism. The latent correlation
between T1 and T5 is .62 for optimism and .53 for pessimism. The stability coefficients for the
same time-interval for the subjective well-being variables were .57 for depression, .76 for
192
psychosomatic complaints, .62 for irritation and .48 for worrying. It seems that the construct
psychosomatic complaints was more stable than either optimism or pessimism, whereas worrying
seems less stable. Overall, there was little stability in individual differences across a long time
frame. This information is important because growth curve models require changes in the relative
positions of subjects over time and it is quite clear from Table 30 that over the T1 – T5 (four years
plus nine months) period many changes have taken place.
Table 30
Correlations between Latent Optimism and Pessimism Constructs
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
(1) T1 optimism 1.00
(2) T1 pessimism -0.32 1.00
(3) T2 optimism 0.72 -0.36 1.00
(4) T2 pessimism -0.28 0.64 -0.46 1.00
(5) T3 optimism 0.74 -0.36 0.77 -0.37 1.00
(6) T3 pessimism -0.24 0.63 -0.35 0.79 -0.41 1.00
(7) T4 optimism 0.62 -0.39 0.71 -0.45 0.77 -0.48 1.00
(8) T4 pessimism -0.20 0.48 -0.28 0.63 -0.33 0.77 -0.40 1.00
(9) T5 optimism 0.62 -0.33 0.72 -0.39 0.73 -0.37 0.77 -0.32 1.00
(10) T5 pessimism -0.19 0.53 -0.21 0.59 -0.32 0.66 -0.40 0.70 -0.47 1.00
Goodness of fit of growth curve models
In Table 31 the goodness-of-fit measures of the growth curve models are shown. Each
model includes either optimism or pessimism and one of the well-being constructs. The first model
in each case is the maximum model and functions as a baseline model, because all the latent
constructs are allowed to covary freely and the only restrictions arise from the specifications of the
measurement model. All maximum models fit very well: all CFI values are at least .95 (Hu &
Bentler, 1999) and all values of the RMSEA are below .035.
193
Table 31
Goodness-of-fit Measures for Structural Models.
Optimism Pessimism
χ2 df RMSEA AIC CFI χ2 df RMSEA AIC CFI
Depression 1 Maximum 1287.74 842 .033 1857.74 .959 1266.33 842 .032 1836.33 .958 2 Linear LGC 1450.66 919 .034 1866.66 .951 1398.33 919 .033 1814.33 .953 Difference 2 and 1 162.92* 77 132.00* 77 3 Correlated resid. 1421.95 914 .034 1847.95 .953 1351.43 914 .031 1777.43 .956 Difference 3 and 2 28.71* 5 46.90* 5 Difference 3 and 1 134.21* 72 85.10 72 Psychosomatic C. 1 Maximum 927.70 635 .031 1461.70 .966 866.10 635 .027 1400.10 .969 2 Linear LGC 1061.32 712 .032 1441.32 .961 987.68 712 .028 1367.68 .964 Difference 2 and 1 133.62* 77 121.58* 77 3 Correlated resid. 1052.85 707 .032 1442.85 .961 977.58 707 .028 1367.58 .964 Difference 3 and 2 8.47 5 10.10 5 Difference 3 and 1 125.15* 72 111.48* 72 Irritation 1 Maximum 1728.86 1076 .035 2330.86 .949 1598.87 1076 .031 2200.87 .956 2 Linear LGC 1883.70 1153 .036 2331.70 .944 1697.11 1153 .031 2145.11 .954 Difference 2 and 1 154.84* 77 98.24 77 3 Correlated resid. 1874.91 1148 .036 2332.91 .945 1684.61 1148 .031 2142.61 .955 Difference 3 and 2 8.79 5 12.50 5 Difference 3 and 1 146.05* 72 85.74 72 Worrying 1 Maximum 987.43 635 .034 1521.43 .963 942.37 635 .031 1476.37 .965 2 Linear LGC 1120.49 712 .034 1500.49 .958 1042.93 712 .031 1422.93 .962 Difference 2 and 1 133.06* 77 100.56 77 3 Correlated resid. 1116.95 707 .034 1506.95 .958 1039.18 707 .031 1429.18 .962 Difference 3 and 2 3.54 5 3.75 5 Difference 3 and 1 129.52* 72 96.81 72 NOTE: Linear LGC: linear latent growth curve model refers to unspecified model (Figure 27), direct model (Figure 28), and mediational model (Figure 29). Correlated resid.: model with time-specific correlations between residuals of optimism/pessimism and subjective well-being variables (see Figure 30). * Chi-square Difference test is significant (alpha = 0.01). N = 423 for models including depression; N = 420 for psychosomatic complaints; N = 421 for irritation; N = 416 for worrying.
The second model displayed in Table 31 is a linear growth model. As noted before the unspecified,
direct and mediational models (see again Figure 27, 28, and 29) yielded the same fit measures, so
the fit measures of the second model in Table 31 refers to all three models. The chi-square
difference tests are all significant, which indicate that they are worse than the maximum model.
This is not surprising given the fact that the maximum model imposes no restrictions on the
194
structural relationships. However, the hypotheses based models are more parsimonious. This has
positive effects on the AIC and so many of these hypotheses based models show lower values of the
AIC. The other fit indices, for example the RMSEA and the CFI make it possible to conclude that a
linear growth model can be considered a reasonable solution. Furthermore, we note that the linear
growth curves can explain a large amount of the total variance in the latent constructs. The lowest
amount of explained variance was .72 for worrying and pessimism and the highest one was .84 for
psychosomatic complaints
The third model displayed in Table 31 is equivalent to the second model except that it
allows the disturbances for each measurement occasion to covary (compare Figure 30). The chi-
square difference tests indicate that the disturbances are necessary only for the models that include
depression. We come back to this point, when we discuss the hypotheses.
In summary, growth curve models yielded acceptable goodness of fit measures and
specifying additional covariances for the disturbances was only necessary for models including
depression.
Prerequisites For Testing the Hypothesis
In addition to yield acceptable goodness of fit measures, the models should be parsimonious
and not contain too many parameters. Most important is that the variances of the slope factors are
significant, because this implies that there are differences between people in the rate they change. In
Table 32 the estimates of the variances and the mean of the slope factors are shown. All variances
are significant. However, two estimates of the mean of the slope factors were not significant (for
psychosomatic complaints and worrying), indicating that the population growth curve for these
variables could be flat (population slope is zero) and no mean changes could be detected. The mean
slopes of both optimism and pessimism were negative, indicating that the means decreased, a
pattern that is consistent with the results found in the measurement models.
195
Table 32
Variance and Mean estimates of slope factors.
Variance Mean
Optimism 0.68** -0.23**
Pessimism 0.36** -0.24**
Depression 1.14** -0.21**
Psychosomatic complaints 0.30** 0.07
Irritation 0.70** -0.15**
Worrying 3.14** 0.12
** z value > 1.96 (z value: ratio between parameter estimate
and its standard error)
* 1.96 < z value > 1.65
Because the relationships between optimism/pessimism and the subjective well-being
variables are central in this paper it is useful to take a look at the zero order correlations before
discussing the specific hypothesis. The correlations of the latent variables for all time periods of our
study are shown in Table 33. Remarkable are the high synchronous correlations between pessimism
and depression, psychosomatic complaints, and irritation. High are also the negative synchronous
correlations between optimism and depression.
Hypotheses Tested With Direct Models
Relationships of the Stable Components of Optimism/Pessimism and Subjective Well-Being. It is
hypothesized that the stable components of optimism/pessimism and subjective well-being are
related. The stable components are represented by the intercept factors, which represent the starting
values of the linear growth curves at the first measurement wave and Table 34 shows that the
intercepts of optimism and pessimism were significantly correlated with the well-being factors
(with the exception of one). The correlations in Table 34 were higher than the synchronous
196
Table 33
Correlation M
atrix of Latent C
onstructs Optim
ism and Pessim
ism w
ith Subjective Well-being V
ariables
Depression
Psychosom
atic
complaints
Irritation
W
orrying
T1 T
2 T3 T
4 T5
T
1 T2 T
3 T4 T
5
T1 T
2 T3 T
4 T5
T
1 T2 T
3 T4 T
5
Optim
ism
T1
-.35 -.23 -.29 -.31 -.29 -.06 .01 -.04 -.03 -.11
-.16 -.14 -.09 -.15 -.19 -.14 -.15 -.12 -.16 -.12
T
2 -.27 -.26 -.32 -.27 -.27
-.07 -.04 -.10 -.07 -.09 -.08 -.12 -.14 -.19 -.16
-.07 -.09 -.10 -.15 -.07
T
3 -.33 -.29 -.46 -.33 -.38
-.12 -.03 -.15 -.08 -.13 -.16 -.18 -.20 -.17 -.17
-.11 -.13 -.09 -.12 -.09
T
4 -.31 -.30 -.38 -.37 -.36
-.19 -.13 -.18 -.17 -.23 -.18 -.20 -.23 -.28 -.32
-.13 -.12 -.11 -.15 -.16
T
5 -.32 -.24 -.32 -.32 -.43
-.10 -.10 -.10 -.08 -.15 -.10 -.15 -.13 -.19 -.24
-.10 -.14 -.10 -.15 -.15
Pessimism
T
1 .43 .41 .41 .44 .39
.25 .23 .23 .23 .23 .33 .27 .31 .29 .30
.14 .21 .19 .15 .10
T
2 .40 .47 .47 .47 .42
.29 .27 .26 .21 .19 .31 .34 .33 .29 .27
.11 .21 .16 .13 .09
T
3 .36 .38 .47 .49 .48
.23 .23 .30 .37 .32 .25 .27 .33 .31 .29
.08 .14 .13 .16 .09
T
4 .29 .34 .44 .63 .49
.25 .27 .24 .35 .31 .24 .30 .28 .39 .40
.06 .10 .05 .06 .04
T
5 .33 .30 .46 .52 .56
.29 .24 .24 .26 .28 .21 .26 .28 .32 .38
-.02 .05 .06 .05 .06
Note. N
= 423 for depression; N
= 420 for psychosom
atic complaints; N
= 421 for irritation; N
= 416 for w
orrying.
197
correlations in T1 in Table 33. This can be explained by the decomposition in systematic and state
variance, which had a similar effect as the well-known attenuation due to uncorrelated measurement
error. The highest correlations in Table 34 involved pessimism and particularly the correlations
between the intercepts of pessimism and depression (r = .54) and irritation (r = .44) were high.
Thus, there is some support for our first hypothesis that there is a correlation between the highly
stable components of optimism/pessimism and well-being. This speaks for genetic or early
childhood components that are not changed much in later life.
Table 34
Correlations between intercept factors of optimism/pessimism and
intercept factors of subjective well-being variables.
Optimism Pessimism
Depression -.36** .54**
Psychosomatic complaints -.06 .33**
Irritation -.19** .44**
Worrying -.15** .26**
** z value > 1.96 (z value: ratio between parameter estimate and
its standard error).
Relationships of Initial Optimism/Pessimism to Changes in Subjective Well-Being. Were initial
levels of optimism and pessimism predictive for changes in subjective well-being? The results are
shown in Table 35 (first column, “total effects”).
There were significant effects of initial optimism (as represented by the intercept factor) on
the slope factors of depression (-.19) and psychosomatic complaints (-.20). Both effects were
negative, which means that people with higher starting points of their trajectories of optimism
tended to have smaller (than the average) slopes for depression and psychosomatic complaints.
Furthermore, there was a significant negative effect (-.21) of initial pessimism on the slope factor of
worrying. The direction of this effect was not anticipated: it means that pessimists at T1 tended to
have a decrease in worrying (compared to the average). At first sight this suggests that worrying
helped in some way to deal with pessimism (we return to this later). The other paths were not
significant.
198
It is important to note that these are partial regression coefficients, because there is also a
path from the intercept factor of the specific well-being variable to the well-being slope. This means
that pre-existing differences in well-being are controlled for.
The paths from the intercept factor of well-being to the slope factor of well-being were
negative (just one is not significant) which means that people with a low degree of well-being
increased their well-being (compared to the average person). This may be a result of a floor and
ceiling effect or the result of some kind of adaptation process which for example also underlies
cyclical mood swings (Solomon & Corbit, 1974).
Relationships of Trends in Optimism and Subjective Well-Being. Were systematic changes in
optimism and pessimism related to systematic changes in well-being? The systematic changes are
represented in a linear growth curve model by the slope factor. Table 36 shows the correlations
between the slope factors of optimism/pessimism and well-being (first and fourth column, headed
“Unspecified Model”).
Table 36
(Partial) correlations between slope factors of optimism/pessimism and
slope factors of subjective well-being
Optimism Pessimism
Unspecified
Model
Direct
Model
Mediation
Model
Unspecified
Model
Direct
Model
Mediation
Model
Depression -.15 -.23 -.20 .83** .91** .93**
Psychosomatic
complaints
.21 .00 .07 .36* .31* .29
Irritation -.19 -.34** -.33** .71** .73** .78**
Worrying -.08 -.15 -.17 .28* .26* .29**
** z value > 1.96 (z value: ratio between parameter estimate and its standard error).
The correlations were estimated in the unspecified models (see again Figure 27). None of the
correlations between the slope factors of optimism and the slope factors of the well-being variables
were significant. This is different for correlations between changes in pessimism and changes in
well-being. All of the correlations were significant and positive. In the direct model (see Figure 28)
pre-existing differences in optimism/pessimism and well-being are controlled for and the partial
199
correlations between the slope factors were tested (second and fifth column, headed “Direct
Model”). There was only one significant partial correlation between the slopes factor of optimism
and the slope factors of the well-being variables (for irritation: -.34). All partial correlations
between the slope factors of pessimism and well-being were positive and significant. There were
very strong significant partial correlations between slope factor of pessimism and the slope factors
of depression (.91), and irritation (.73). This speaks for a relationship between the changeable parts:
The trajectories of pessimism seem very parallel with the trajectories of both depression and
irritation. The third and the sixth column of Table 36 will be discussed later when the results of the
spurious model will be reported.
Relationships between Fast Changes of Optimism/Pessimism and Fast Changes of Well-Being.
Were short-term changes in optimism/pessimism related to short term changes in well-being? As
mentioned before, there is evidence in Table 31 only for models including depression. However, in
these models the pattern of correlations did not show a high consistency and for some measurement
occasions the correlations were not significant. For the other well-being variables there was no
significant improvement of fit when these short-term changes correlations were added into the
models. Overall there seems not much support for the hypothesis that fast changes of
optimism/pessimism and well-being were related.
Mediational Model.
The mediational model (see again Figure 29) includes all paths from the intercept factors
(the independent variables in the mediating model) to the coping style variables (mediators) and all
paths from the mediators to the two slope factors (the outcome variables). The covariance between
the disturbance terms of the slope factor was estimated. All covariances between the disturbances of
the coping style variables were also estimated. Additionally, the direct effect of the intercept factor
on the slope factor was estimated, so in fact the model only specifies a partial mediational model.
This model is not imposing further restrictions compared with the direct linear growth curve model.
Therefore, the fit is exactly the same as the direct growth curve model (see Model 2 in Table 31).
The results of the mediational model consist of two parts: first the indirect effects will be
described, and next the direct effects will be discussed.
200
Indirect effects. We will first describe the separate paths and then we will present the results
of the global test of the indirect effects. In Tables 37 to 40 the regression coefficients are shown for
the mediator models. The first entry of Table 37 implies that the path from the intercept factor of
optimism to planning is -.04 within the model that includes depression (note that there are different
paths depending upon which well-being variable is included in the model). All our models
controlled for pre-existing subjective well-being.
The results show that optimism had significant paths on emotional-focused coping and on
problem-focused coping (regardless of which well-being variable is included in the model). Thus
controlling for initial well-being produced a significant effect of optimism on emotional focused
coping. It is remarkable that both forms of coping that are usually conceptualized to work
differentially were positively affected by optimism.
Pessimism had a negative path on planning and positive paths on emotional coping and
wishful thinking (again regardless of which well-being variable was included in the model). These
are all passive forms of coping: little planning, emotional focused and wishful thinking. This was
expected from coping theory and literature.
In Table 38 the standardized regression coefficients are shown for the paths from the
intercept factor of subjective well-being to the coping style variables. Initial well-being was a strong
predictor of self-criticism, emotional-focused coping, seeking social support, and wishful thinking
over and beyond the effects of initial optimism/pessimism. These effects were higher for depression
and irritation and lower for psychosomatic complaints and worrying.
Worrying showed a different pattern, however, that may be very important. Worrying
showed a positive effect on planning and on problem-focused coping. Worrying can be interpreted
to be an activating emotion and therefore worrying affects that people become more active in their
coping styles (again, controlling for initial pessimism/optimism effects).
Initial depression, psychosomatic complaints and irritation had strong effects on wishful
thinking and to a lesser extent on emotional-focused coping. The standardized effects for initial
depression on wishful thinking were .49 and .35 in the optimism and pessimism model respectively.
The smaller effect in the pessimism model can be explained by the inclusion of the pessimism
intercept factor, which presumably had shared predictive power. The effects seemed smaller in the
pessimism models, probably because pessimism had a stronger affective component and partialling
out the effects of initial pessimism remove some of the impact of initial well-being. However, these
effects of initial well-being on coping style did not occur in the worrying model.
201
Table 37
Standardized Regressioncoefficients of Paths from
Intercept Factors Optim
ism/Pessim
ism to C
oping Style Variables.
Coping Style V
ariables O
ptimism
Pessim
ism
M
odel
Depression
Model
Psychosom
Model
Irritation
Model
Worrying
Model
Depression
Model
Psychosom
Model
Irritation
Model
Worrying
Planning -0.04
-0.02 -0.01
0.03 -0.20**
-0.18** -0.23**
-0.27**
Self-criticism
-0.04 -0.08
-0.06 -0.08
-0.03 0.03
-0.02 0.04
Em
otional-focused coping 0.27**
0.17** 0.22**
0.16** 0.17**
0.17** 0.18**
0.27**
Seeking social support 0.10*
0.06 0.08
0.08 -0.06
-0.03 -0.04
-0.03
Problem-focused coping
0.16** 0.16**
0.17** 0.20**
-0.03 -0.08
-0.08 -0.11*
Wishful thinking
0.20** 0.05
0.11** 0.05
0.13* 0.22**
0.21** 0.32**
Note: Psychosom
: psychosomatic com
plaints; the effects of intercept factors optimism
/pessimism
on coping style variables were estim
ated in
separate models each containing either optim
ism or pessim
ism variables
** z value > 1.96 (z value: ratio betw
een parameter estim
ate and its standard error).
202
Table 38
Standardized Regressioncoefficients of Paths from
Intercept Factors Subjective Well-being to C
oping Style Variables.
Coping Style V
ariables D
epression Psychosom
Irritation
Worrying
M
odel
Optim
ism
Model
Pessimism
Model
Optim
ism
Model
Pessimism
Model
Optim
ism
Model
Pessimism
Model
Optim
ism
Model
Pessimism
Planning -0.06
0.06 -0.03
0.03 0.02
0.12** 0.30**
0.37**
Self-criticism
0.14** 0.18**
0.08 0.07
0.16** 0.17**
0.07 0.08
Em
otional-focused coping 0.31**
0.13* 0.28**
0.21** 0.29**
0.16** -0.03
-0.12**
Seeking social support 0.16**
0.16** 0.16**
0.17** 0.14**
0.14** 0.19**
0.19**
Problem-focused coping
-0.01 -0.05
0.07 0.09
0.07 0.07
0.22** 0.22**
Wishful thinking
0.49** 0.35**
0.41** 0.33**
0.40** 0.29**
0.14** 0.06
Note: Psychosom
: psychosomatic com
plaints; the effects of the intercepts factor on coping style variables were estim
ated both in models
containing either optimism
or pessimism
.
* 1.96 < z value >
1.65 (z value: ratio between param
eter estimate and its standard error)
** z value > 1.96
203
Table 39
Standardized Regressioncoefficients of Paths from
Coping Style V
ariables to Slope Factors of Subjective Well-being.
Planning
Self-criticism
Em
otion-focused Social support
Problem-focused
Wishful thinking
M
odel
Optim
Model
Pessim
Model
Optim
Model
Pessim
Model
Optim
Model
Pessim
Model
Optim
Model
Pessim
Model
Optim
Model
Pessim
Model
Optim
Model
Pessim
Depression
-0.13* -0.15**
0.00 0.01
0.19** 0.15*
0.09 0.09
-0.13* -0.15*
0.11 0.07
Psychosom
-0.14 -0.15
0.04 0.09
0.07 0.01
0.10 0.11
-0.10 -0.15
-0.12 -0.13
Irritation -0.04
-0.06 0.05
0.05 0.02
0.01 -0.06
-0.06 -0.11
-0.12 -0.02
0.01
Worrying
0.08 0.05
0.06 0.08
0.14* 0.16**
0.03 -0.01
-0.01 -0.03
-0.07 -0.02
Note: O
ptim: optim
ism; pessim
: pessimism
; psychosom: psychosom
atic complaints; the effects of coping style variables on slope factors of
subjective well-being w
ere estimated in m
odels containing either optimism
or pessimism
.
* 1.96 < z value >
1.65 (z value: ratio between param
eter estimate and its standard error)
** z value > 1.96
204
Table 40
Standardized Regressioncoefficients of Paths from Coping Style Variables
to Slope Factors Optimism/pessimism.
Coping style variables
Model
Depression
Model
Psychosom
Model
Irritation
Model
Worrying
Planning
Optimism 0.20** 0.22** 0.20** 0.24**
Pessimism -0.37** -0.35** -0.37** -0.35**
Self-criticism
Optimism 0.05 0.02 0.04 0.03
Pessimism -0.05 -0.03 -0.02 -0.02
Emotional-focused coping
Optimism -0.15 -0.13 -0.09 -0.14
Pessimism 0.06 0.03 -0.01 0.03
Seeking social support
Optimism -0.11 -0.11 -0.10 -0.10
Pessimism 0.11 0.12 0.12 0.12
Problem-focused coping
Optimism 0.10 0.12 0.12 0.12
Pessimism -0.02 -0.07 -0.07 -0.06
Wishful thinking
Optimism 0.23* 0.23** 0.18* 0.16
Pessimism 0.03 0.11 0.12 0.08
Note: Psychosom: psychosomatic complaints; the effects of coping style
variables on slope factors of optimism/pessimism subjective well-being
were estimated in separate models each containing one of the subjective
well-being variables.
* 1.96 < z value > 1.65 (z value: ratio between parameter estimate and
its standard error)
** z value > 1.96
205
Initial depression and irritation had significant positive effects on self-criticism. Initial well-being is
also a significant predictor for seeking social support (for all well-being variables).
Table 39 shows the paths from coping to the well-being slope factors – the second part of
the mediator analysis. The first entry in this table -.13 means that planning led to a reduction in the
change of depression over time (compared with the average person). In general, planning affected
depression negatively, emotional focused coping affected it positively and problem-focused coping
negatively. In other words, more active forms of coping – such as planning and problem-focused
coping – reduced depression, while an attempt to cope with emotions increased depression.
Psychosomatic complaints and irritation were not significantly affected by coping styles. Worrying
was affected by emotional-focused coping. Apparently, people are not really dealing with their
emotions with this coping style but tend increasingly to think and worry about the stressors
involved. Thus, there were mediator effects for the three coping styles: Planning, emotion-focused,
and problem-focused coping. All three were affected by optimism and pessimism and affected in
turn the development of depression and worrying. An interesting result was that both optimism and
pessimism affected emotional-focused coping positively.
Next we will describe the global tests of the significance of the indirect effects. The results
are shown in the third column of Table 35. There were two significant results: Both initial optimism
and initial pessimism had positive effects on the slope factor of depression (.07 and .06,
respectively). The positive indirect effect of optimism on depression was not anticipated. As
presented above, optimists had a preference for problem-focused coping (-.16) and this lead to a
reduction in depression (-.13). However, this anticipated effect was outweighed by the fact that
optimists also used more emotional-focused coping which increased depression (.27 × .19 = .051).
Furthermore, optimists used also more wishful thinking and although not significant this increased
depression (.20 × .11 = .022). All effects combined were significantly positive. However, the direct
effect of initial optimism on depression was much stronger (-.26) as can be seen in the second
column of Table 35. The direct effects will be discussed later. The second significant indirect effect
was initial pessimism had a significant positive effect on depression (.06). Pessimist planned less
and planning reduced depression (-.20 × -.15 = .03). Furthermore, pessimists had a small preference
for emotional-focused coping and this increased depression (.17 × .15 = .0255). Overall, there was
some evidence that initial optimism/pessimism had indirect effects via coping styles on subjective
well-being.
Direct effects. The mediation models were specified as partial mediation models by also
allowing direct paths from the intercept factors to the slope factors. In the second column of Table
206
35 the direct effects of the intercept factors optimism/pessimism on the slope factors are displayed.
There were three significant direct effects: initial optimism had negative effects on the slope factors
of depression (-.26) and psychosomatic complaints (-.19). Initial pessimism resulted in an decrease
of worrying (-.24). All three direct effect reported previously in the discussion of the direct models
appeared to also as direct effects in the mediational models.
Summarizing the effects of the mediational models it is clear that the direct effects were
stronger than the indirect effects. A remarkable finding is that initial optimism had both significant
negative direct and significant positive effects indirect effects, resulting in a net effect which was
significantly negative (-.19) in first column of Table 35.
Spurious model
Coping style variables can act as a third variable in explaining the correlation between
changes in optimism/pessimism and changes in subjective well-being. The correlated trend-trend
hypothesis was confirmed for pessimism and all the well-being variables and for the trend in
optimism and irritation. In Table 36 in the third and sixth column the partial correlations between
both slope factors are shown. There was no evidence for a reduction of the size of the partial
correlation in the indirect models in comparison to partial correlation in the direct models (see
second and fifth column). Standard structural equation software does not allow testing for the
significance of the difference between two free parameters (the zero and partial correlations), but in
our case testing was not necessary: Four partial correlations were even higher than the zero order
correlations. Thus, introducing the coping style variables into the models did not reduce the size of
the correlation. This means that a spurious correlation model does not apply to the data. The failure
of the spurious model can be explained by the lack of significant paths from the coping style
variables to both slope factors. It was already shown that most effects of the coping style variables
on the slope factors of well-being were small and nonsignificant, similar results could be noticed
(see Table 40) for the effects of the coping style variables on the slope factors of
optimism/pessimism. There were, however, three exceptions. Planning had a strong negative effect
on the slope factor of pessimism (.36 on average for the four models) and a moderately strong
positive effect on the slope factor of optimism (.22 on average). The third exception was the
positive effects of wishful thinking on the slope factor of optimism (not in model containing
worrying).
207
Discussion
Consistent with previous research, it was found that a two-factor model for the LOT scales
fitted the data much better than a one-factor model. In addition, different relations with well-being
variables were found: pessimism correlated stronger with depression and irritation than optimism.
Further evidence against a one-dimensional interpretation consisted of the declining trends of the
latent means of both optimism and pessimism. The downward trend of pessimism was not
anticipated, because East Germans were described by newspapers to be initially euphoric and in
spite of the many worries that beset them a strong positive outlook for the future dominated
(Kunhke, 1991). After political unification, disillusionment in eastern Germany rose sharply
(Britannica, 1999). The anticipated rapid economic recovery seemed to be an illusion and
expectations for the future were getting more realistic. This picture is not supported by the trends in
optimism and pessimism. Apparently, optimism and pessimism cannot be conceived as barometers
for the historical climate, but instead measure only personal tendencies that are changed by very
personal situations rather than by the global climate within a country.
Our use of growth curve models allowed us to decompose psychological constructs into
several components, differing in stability. Optimism showed both a large portion of systematic
developmental changes as well as time-specific fluctuations. That there is room for time specific
fluctuations is shown by the relatively low stabilities: The stabilities for the latent constructs
optimism and pessimism were over a period of five years, .62 and .53. Comparable stabilities were
found for the subjective well-being variables, which are not intended to measure traits. Two sources
of evidence could be found that both systematic as well as time-specific changes influenced the
stabilities of optimism and pessimism. First, the pattern of correlations demonstrated that scores
more distant in time correlated lower than observation more proximal in time. This indicated the
presence of systematic changes. Second, growth curve models fitted the data well. We found both
interindividual differences in growth trajectories as well as sizeable state variances for each time
period. The lower than expected stabilities for optimism and pessimism reconciles the trait
interpretation of Carver and Scheier with the ‘outcome’ interpretation of DeNeve.
Optimism/pessimism could both be treated as important predictors for subjective well-being as well
as the changes in optimism/pessimism could be treated as partly predictable outcomes variables.
Systematic slow changes in especially pessimism developed parallel with changes in depression.
Both aspects of optimism and pessimism are supported by the data and growth curve models are
well suited to treat these aspects in an adequate manner.
208
In our growth curve models we studied the stable aspects, the slowly changing and the fast
changing components of optimism/pessimism. By concentrating on the systematic changes (slope
factor), optimism/pessimism is treated as a potential outcome variable, in the same way as the well-
being variables. In terms of our hypotheses we found the following results.
The stable components of pessimism and all subjective well-being variables, as indicated by
their intercept factors, were significantly positively correlated. Much weaker negative correlations
were found for the stable component of optimism and its correlation with psychosomatic complaints
was almost zero and nonsignificant. This supports the idea that negative affectivity and neuroticism
is related to pessimism (Burke, Brief & George, 1993). Although we do not claim that our measures
of subjective well-being are completely valid measures of either negative affectivity or neuroticism,
we think especially depression and irritation can be considered as reasonable proxies for those
constructs (Burke et al, 1993). The relation between pessimism and negative feelings may be
explained by the theory of Gray (1991, 1994), who argues that there are two different physiological
nervous systems. The first one is the Behavior Approach System and is affected by rewards. The
second system, the Behavior Inhibition System, is stimulated by innate fear stimuli and signals of
punishments. Gray claims that much of the individual differences in personality can be explained by
differences in these two underlying brain system. Pessimism and negative feelings may be related
because both are produced by the part of the nervous system that deals with avoiding negative
stimuli. It is important to note that our finding of the relationship between pessimism and
depression was based on well fitting measurement models which treated pessimism and depression
as independent constructs. So pessimism is not just a manifestation of depression.
Was initial optimism/pessimism predictive for changes in well-being? Initial optimism
predicted both declining tendencies in growth curves for depression and psychosomatic complaints.
Remarkably, although optimism was initially less correlated with both depression and
psychosomatic complaints than pessimism, it was a better predictor for changes in these well-being
variables. This suggests that other mechanisms than the emotional system are involved as causal
agents. This may be related to the fact that optimists tend to be more open to new experiences or
new stimulation (Marshall, Wortman, Kusulas, Hervig, & Vickers, 1992), which suggest that they
deal more actively with stressors. Initial pessimism predicted declining trajectories in worrying, a
result which was not expected.
The hypothesis that the trends in pessimism and well-being were related were supported as
indicated by the very high correlations between the slope factors for pessimism and depression and
irritation. This was not the case for worrying and psychosomatic complaints. Changes in optimism
were not parallel with changes in well-being, only the slope factors of optimism and irritation were
209
significantly negative correlated. Again the stronger link between negative feelings and pessimism
was supported. However in this case we are not dealing with either genetic or early childhood
causes of the relationship but with current trends that co-occur. Most probably they feed upon each
other in a sort of feedback cycle: The more one is pessimistic; the more one gets depressed and
irritated; the more one gets irritated and depressed; the more one becomes pessimistic (cf: Beck’s
cognitive triad; Beck, 1976).
There was little support for the hypothesis that the fast changes of optimism/pessimism and
fast changes of well-being were related. The models that allowed correlations between disturbances
did not improve the goodness of fit of the models (the only exception was depression).
The dominant explanation for the link between optimism and subjective well-being is that
differences in coping mediates the relationships between optimism/pessimism and well-being. We
tested this with two strategies: First by testing the fit of a mediational model (this is a “global test”)
and by inspecting the significance of the individual paths. The global test revealed two significant
indirect effects: Both initial optimism and initial pessimism had positive significant indirect effects
on changes in depression. Both indirect effects were either canceled out or outweighed by opposite
direct effects. Inspecting the indirect paths taught us that optimists used both more emotional-
focused and problem-focused coping which had contradictory effects on changes in depression.
However, the positive effects of emotional-focused coping on depression outweighed the negative
effects of problem-focused coping, resulting in a positive indirect effect. Pessimists used also more
emotional-focused coping and used less planning. Both resulted in positive changes in depression.
In general the mediating role of coping styles was not as strongly supported as expected. The effects
of coping styles variables on the slope factors of well-being were very small and most coefficients
were not significant. Since in general coping styles neither predicted the slope factors of
optimism/pessimism, coping styles could not be considered as the common cause for explaining the
relations between changes in optimism/pessimism and changes in well-being. However, we found
some evidence for a third variable explanation for planning. This coping style promoted optimism
and decreased pessimism and also reduced depression. The effectiveness of planning is consistent
with the importance of pro-active coping as described by Aspinwall & Taylor (1997). Important
aspects of proactive coping model are the temporal sequencing of coping efforts and the use of
feedback. Planning and proactive coping may be more effective because it facilitates the elicitation
of feedback. Information of what coping attempts were successful and what strategies did not work
can be used for adapting coping strategies. This may result in more positive control expectations,
which may be generalized to a more optimistic outlook for the future.
210
An alternative explanation for the role of pessimism could be that its predictive power
consisted of shard variance with constructs like neuroticism and negative affectivity. However; this
interpretation is unlikely as all models controlled for pre-existing levels of subjective well-being.
In our studies we also found a clear effect of well-being on coping. Initial subjective well-
being was a good predictor for coping styles: In general feeling bad predicted a strong preference
for wishful thinking and to a lesser extent for emotional-focused coping and seeking social support.
This was not the case for initial worrying that predicted a preference for planning and problem-
focused coping and seeking social support. Apparently, worrying does not just have a negative
effect. One side may be destructive which may be similar to rumination, a concept introduced by
Nolen-Hoeksema (1994). She defined rumination as the preoccupation with one’s depressive
symptoms. Another side of worrying may be more constructive and may be important in the first
stages of proactive coping: recognition of potential stressors and initial appraisal (“Should I be
worried about this?”)(Aspinwall & Taylor, 1997, p.419).
Notwithstanding some significant effects of coping styles on changes in subjective well-
being, the crucial question remains why the effects of coping were rather disappointing. The use of
coping styles instead of coping strategies should make it easier to find strong relations between
optimism/pessimism and well-being. Begley (1998, p. 313) states that “dispositions are not
predictive of single actions, but only of action tendencies”. Optimism, conceived as a disposition,
should be more highly correlated with coping styles (dispositional coping) than with coping
strategies. Fishbein & Ajzen (1975) argued similarly that predictors and criterion should be
measured on the same level of generality.
There are a few notable limitations to this study. First, we did not control for differences in
type and severance/importance of the stressful events respondents selected for providing their
coping responses. There are pros and cons of our approach to measuring coping. As presented
before, we used work stressors that the participants remembered from last week. If the person did
not remember one, we suggested areas which are typically stressful and asked if there were any in
these areas. We had them describe the situation briefly but we did not an analysis of these
descriptions. Our approach of looking at coping styles led us to collapse all the different coping
questionnaires across time into one score. Our measurement models show this to be useful.
However, this approach does not allow to study the details of the coping interaction (Lazarus &
Folkman, 1984), particularly not at the particulars of the stressors and the coping resources
available. Therefore, we cannot exclude the possibility that the coping responses were determined
by differences in the stressors reported by the subjects. However, because we aggregated the
measures of coping across five occasions we assumed that the stressors are at least representative
211
for the individual reporting them and, that we, therefore, also measured the typical coping response
of the participants.
The second limitation of this study is that we could not include all variables into one
comprehensive model because this would have exceeded the capacity of the software and would
have produced an unfavorable ratio of sample size to number of free parameters Bentler (1989, p.
6). Also, we could not investigate the additional predictive power of initial optimism over initial
pessimism. On the other hand, we think that even with these limitations, we have been able to
extract interesting findings from these data.
Thirdly, one of the typical problems that beset stress and well-being research is the fact that
most of this research relies on questionnaires and is, therefore, prone to be biased by common
variance (Begley, 1998; Zapf, Dormann & Frese, 1997). However, our growth curve models
reduced this problem in two ways: First, the completely stable part of common method variance
was reduced by partialing out pre-existing values (Dormann, 1999) and second, the time-specific
(unstable) part was modeled by allowing covariances between the disturbance terms (which were
only necessary in models including depression). Theoretically the correlation between linear trends
could be confounded by a linear change in common methods factors. However, this seems very
unlikely.
Finally, a limitation that holds for all passive longitudinal designs is worth mentioning, that
is, that causal inferences cannot be made. Structural Equation Modeling can determine whether a
model is consistent with the data, but there may be other equivalent models that fit the data equally
well. Alternative explanations cannot be ruled out.
Notwithstanding these limitations, this study is unique both in its longitudinal design and
impressive sample: To the best of our knowledge the effects of optimism/pessimism on subjective
well-being have never before been studied over a period stretching five years and including five
measurement waves using a medium sized sample. The longitudinal design allowed us to
decompose changes into several parts, using a sophisticated statistical approach and to formulate
and to test several hypotheses for each change component.
212
References
Abraham, C.S. (1994). From predictor variables to cognition models in health psychology: A
commentary on Schwarzer's theoretical analysis. Psychology and Health, 9, 181-185.
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
Anderson, J.C., & Gerbing, D.W. (1988). Structural equation modeling in practice: A review and
recommended two step approach. Psychological Bulletin, 103, 411-423.
Aspinwall, L.G., & Taylor, S.E., (1997). A Stitch in Time: Self-Regulation and Proactive Coping.
Psychological Bulletin, 121, 417-435
Beck, A.T. (1976). Cognitive therapy and the emotional disorders. New York: International
Universities Press.
Begley, T.M. (1998). Coping strategies as predictors of employee distress and turnover after an
organizational consolidation: A longitudinal analysis. Journal of Occupational and Organizational
Psychology, 71, 305-329.
Bentler, P. M. (1989). EQS: Structural equations program manual. Los Angeles: BMDP Statistical
Software.
Bentler, P.M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107,
238-246.
Ben-Zur, H. (1999). The effectiveness of coping meta-strategies: Perceived efficiency, emotional
correlates and cognitive performance. Personality and Individual Differences, 26, 923-940.
Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.
Encyclopdia Britannica (1999). Problems of economic unification. [CD-ROM].
Browne, M.W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K.A. Bollen &
J.S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
Bijttebier, P., & Vertommen, H. (1999). Coping strategies in relation to personality disorders.
Personality and Individual Differences, 26, 847-856.
Burke, M.J., Brief, A.P., & George, J.M. (1993). The role of negative affectivity in understanding
relations between self-reports of stressors and strains: A comment on the applied psychology
literature. Journal of Applied Psychology, 78, 402-412.
Byrne, B.M., Shavelson, R.J., & Muthén, B. (1989). Testing for the equivalence of factor
covariance and mean structures: The issue of partial measurement invariance. Psychological
Bulletin, 105, 456-466.
Carver, C.S., Pozo, C., Harris, S.D., Noriega, V., Scheier, M.F., Robinson, D.S., Ketcham, A.S.,
Moffat, F.L., & Clarck, K.C. (1993). How coping mediates the effect of optimism on distress: A
213
study of women with early stage breast cancer. Journal of Personality and Social Psychology, 65,
375-390.
Carver, C.S., & Scheier, M.F. (1992). Effects of optimism on psychological and physical well-
being: Theoretical overview and empirical update. Cognitive Therapy and Research, 16, 201-228.
Carver, C.S., & Scheier, M.F. (1994). Situational coping and coping dispositions in a stressful
transaction. Journal of Personality and Social Psychology, 66, 184-195.
Carver, C.S., Scheier, M.F., Pozo, C. (1992). Conceptualizing the process of coping with health
problems. In H.S. Friedman (Ed.). Hostility, coping and health. (pp. 167-187). Washington, D.C.:
A.P.A.
Carver, C.S., Scheier, M.F., & Weintraub, J.K. (1989). Assessing coping strategies: A theoretically
based approach. Journal of Personality and Social Psychology, 56, 267-283.
Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach
incorporating Longitudinal Mean and Covariance Structures analysis (LMACS) and Multiple
Indicator Growth Modeling (MLGM). Organizational research Methods, 1, 421-483.
Chang, E.C. (1998). Dispositional optimism and primary and secondary appraisal of a stressor:
Controlling for confounding influences and relations to coping and psychological and physical
adjustment. Journal of Personality and Social Psychology, 74, 1109-1120.
Cheng, S.T., & Hamid, P.N. (1997). Dispositional optimism in Chinese people: What does the Life
Orientation Test measure? International Journal of Psychology, 32, 15-22.
Coyne, J.C., & Downey, G. (1991). Social factors and psychopathology: Stress, social support, and
coping processes. Annual Review of Psychology, 42, 401-425.
Cudeck, R. (1991). Comments on Chapter 15. “Interpreting and estimating indirect effects assuming
time lags really matter.” (Harry F. Gollob and Charles S. Reichardt). In L. M. Collins & J.L. Horn
(Eds.), Best methods for the analysis of change: recent advances, unanswered questions, future
directions (pp. 126 -136). Washington, D.C.: A.P.A.
Curran, P.J. (in press). A latent curve framework for the study of developmental trajectories in
adolescent substance use. In J. Rose, L. Chassin, C. Presson, & J. Sherman (Eds.), Multivariate
Applications in Substance Use Research. Hillsdale NJ: Erlbaum.
Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood estimation from
incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
DeNeve K.M., & Cooper, H. (1998). The Happy Personality: A Meta-Analysis of 137 Personality
Traits and Subjective Well-Being. Psychological Bulletin, 124. 197-228.
Diener, E., Suh, E.M., Lucas, R.E., & Smith, H.L. (1999). Subjective well-being: Three decades of
progress. Psychological Bulletin, 125, 276-302.
214
Dormann C. (1999). Modeling unmeasured third variables in longitudinal studies on organizational
stress. The case of social stressors at work, irritation, and depression. Doctoral Dissertation.
Johann Wolfgang Goethe Universität Frankfurt am Main.
Dormann, C., & Zapf, D. (1999). Social support, social stressors at work and depressive symptoms:
Testing for moderator effects with structural equations in a 3-wave longitudinal study. Journal of
Applied Psychology, 84, 874–884.
Fahrenberg, J. (1975). Die Freiburger Beschwerdeliste (FBL) (The Freiburger Beschwerderdeliste
(FBL)). Zeitschrift für Klinische Psychologie, 4, 79-100.
Fay, D., & Frese, M. (in press). Self-starting behavior at work: Towards a theory of personal
Initiative. In J.Heckhausen (Ed.) Motivational psychology of human development: Developing
motivation and motivating development.
Fishbein, M. & Ajzen, I. (1974). Attitudes towards objects as predictors of single and multiple
behavioral criteria. Psychological Review 81, 59-74.
Folkman, S., Lazarus, R. S., Dunkel- Schetter, C., DeLongis, A., & Gruen, R. J. (1986). Dynamics
of a Stressfull Encounter: Cognitive Appraisal, Coping and Encounter Outcomes. Journal of
Personality and Social Psychology, 50, 992-1003.
Frese, M., Fay, D., Hilburger, T., Leng, K., & Tag, A. (1997). The concept of personal initiative:
Operationalization, reliability and validity in two German samples. Journal of Occupational and
Organizational Psychology, 70, 139-161.
Frese, M., Garst, H., Fay, D. (1998). Control and complexity in work and the development of
personal initiative (PI): A 5-wave longitudinal structural equation model of occupational
socialization. Manuscript submitted for publication.
Frese, M., Kring, W., Soose, A., & Zempel, J. (1996). Personal Initiative at work: Differences
between East and West Germany. Academy of Management Journal, 39(1), 37-63.
Garst, H., Frese, M. & Molenaar P.C.M. (in press). The Temporal Factor of Change in Stressor-
Strain Relationships: A Growth Curve Model on a Longitudinal Study in East Germany. Journal of
Applied Psychology.
Geers, A.L., Reilley, S.P., & Dember, W.N. (1998). Optimism, pessimism, and friendship. Current
Psychology, 17, 3-19.
Golembiewski, R.T., Billingsley, K., & Yeager, S. (1976). Measuring change and persistence in
human affairs: types of change generated by OD designs. Journal of Applied Behavioral Science,
12, 133-157.
Gray, J.A. (1991). Neural systems, emotions, and personality. In J. Madden IV (Ed.), Neurobiology
of learning, emotion, and affect (pp. 273-306). New York: Raven Press.
215
Gray, J.A. (1994). Framework for a taxonomy of psychiatric disorders. In S.H.M. van Goozen, N.E.
van de Poll & J.Sergeant (Eds.). Emotions: Essays on emotion theory (pp. 29-59). Hilldale NJ:
Erlbaum.
Gully, S.M., Frone, M.R., & Edwards, J.R. (1998). Problems and pitfalls in mediational tests. Paper
presented at the Annual Meeting of the Society of Industrial and Organizational Psychology, Texas.
Headey, B. & Wearing, A. (1989). Personality, life events, and subjective well-being: towards a
dynamic equilibrium model. Journal of Personality and Social Psychology., 57, 731-739.
Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit indexes in covariance structure analysis:
Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
Jöreskog, K.G., & Sörbom, D. (1993). LISREL8 user’s reference guide. Chicago: Scientific
Software International, Inc.
Kenny, D.A., & Campbell, D.T. (1989). On the measurement of stability in over-time data. Journal
of Personality, 57, 445-481.
Kenny, D.A., Kashy, D.A., & Bolger, N. (1998). Data analysis in social psychology. In D.Gilbert,
S. Fiske, & G. Lindzey (Eds.). Handbook of social psychology (4th ed., Vol 1, pp. 233-265).
Boston, MA: McGraw-Hill.
Kessler, R.C., Price, R.H., & Wortman, C.B. (1985). Social factors in psychopathology: Stress,
social support, and coping processes. Annual Review of Psychology, 36, 531-572.
Khoo, S., & Bishop, G.D. (1996). Stress and optimism: Relationships to coping and well-being.
Psychologia, 39, 29-40.
Kuhnke, R. (1991). Optimisten mit viele Sorgen (Optimists with many worries). Spiegel Spezial.
Lazarus, R.S., & Folkman, S. (1984). Stress, appraisal, and coping, New York: Springer.
Lazarus, R.S. (1992). Coping theory and research: Past, present, and future. Psychosomatic
Medicine, 55, 234-247.
Lazarus, R.S. (1993). From psychological stress to the emotions: A history of changing outlooks.
Annual Review of Psychology, 44, 1-21.
Little, T.D. (1997). Mean and covariance structures (MACS) analysis of cross-cultural data:
Practical and theoretical issues. Multivariate Behavior Research, 32, 53-76.
MacCallum, R.C., Kim, C., Malarkey, W.B., & Kiecolt-Glaser, J.K. (1997). Studying multivariate
change using multilevel models and latent curve models. Multivariate Behavioral Research, 32,
215-253.
Mandys, F., Dolan, C.V., & Molenaar, P.C.M. (1994). Two aspects of the simplex model:
Goodness of fit to linear growth curve structures and the analysis of mean trends. Journal of
Educational and Behavioral Statistics, 19, 201-215.
216
Marsh, H. W., Hau, K-T., Balla, J. R., & Grayson, D. (1998) Is more ever too much? The number of
indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33, 181-
220.
Marshall, G.N., & Lang, E.L. (1990). Optimism, self-mastery, and symptoms of depression in
women professionals. Journal of Personality and Social Psychology, 59, 132-139.
Marshall, G.N., Wortman, C.B., Kusulas, J.W., Hervig, L.K., & Vickers Jr., R.R. (1992).
Distinguishing optimism from pessimism: Relations to fundamental dimensions of mood and
personality. Journal of Personality and Social Psychology, 62, 1067-1074.
Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance.
Psychometrika, 58, 525-543.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
McArdle, J.J., & Woodcock, R.W. (1997). Expanding test-retest designs to include developmental
time-lag components. Psychological Methods, 2, 403-435.
Mischel, W., & Shoda, Y. (1998). Reconciling processing dynamics and personality dispositions.
Annual review of Psychology, 49, 229-258.
Mook, J., Kleijn, W.C., & van der Ploeg, H.M. (1992). Positively and negatively worded items in a
self report measure of dispositional optimism. Psychological Reports, 71, 275-278.
Mohr, G. (1986). Die Erfassung psychischer Befindensbeeinträchtigungen bei Industriearbeitern
(Measuring disturbances of psychological well-being in industrial blue collar workers). Frankfurt:
Peter Lang.
Mroczek, D.K., Spiro III, A., Aldwin, C.M., Ozer, D.J., & Bossé, R. (1993). Construct validation of
optimism and pessimism in older men: Findings from the normative aging study. Health
Psychology, 12, 406-409.
Muthén, B. (1997). Latent variable modeling with longitudinal and multilevel data. In A. Raftery
(Ed.), Sociological Methodology (pp. 453-480). Boston: Blackwell Publishers.
Muthén, B.O., & Curran, P.J. (1997). General longitudinal modeling of individual differences in
experimental designs: A latent variable framework for analysis and power estimation.
Psychological Methods, 2, 371-402.
Muthén, B. & Muthén, L. (1998). Training session Stockholm August 1998 on: Analysis of
longitudinal data: Growth modeling using latent variables.
Nesselroade, J.R. (1991). Interindividual differences in intraindividual change. In L. M. Collins &
J.L. Horn (Eds.), Best methods for the analysis change: Recent advances, unanswered questions,
future directions (pp. 92-105). Washington, D.C.: A.P.A.
217
Nolen-Hoeksema, S., Parker, L.E., & Larson, J. (1994). Ruminative coping with depressed mood
following loss. Journal of Personality and Social Psychology, 67, 92-104.
Oort, F.J.O. (1996). Using restricted factor analysis in test construction. Dissertation University of
Amsterdam.
Ormel, J., & Schaufeli, W.B. (1991). Stability and change in psychological distress and their
relationship with self-esteem and locus of control: A dynamic equilibrium model. Journal of
Personality and Social Psychology, 60, 288-299.
Pentz, M.A., & Chou, C.P. (1994). Measurement invariance in longitudinal clinical research
assuming change from development and intervention. Journal of Consulting and Clinical
Psychology, 62, 450-462.
Plewis, I. (1996). Statistical methods for understanding cognitive growth: A review, a synthesis and
an application. British Journal of Mathematical and Statistical Psychology, 49, 25-42.
Plomin,R., Scheier, M.F., Bergeman, C.S., Pedersen, N.L., Nesselroade, J.R., & McClearn, G.E.
(1992). Personality and Individual Differences, 13, 921-930.
Raffalovich, L.E., & Bohrnstedt, G.W. (1987). Common, specific, and error variance components
of factor models. Sociological Methods & Research, 15, 385-405.
Räikkönen, K., Matthews, K.A., Flory, J.D., Owens, J.F., & Gump, B.B. (1999). Effects of
optimism, pessimism, and trait anxiety on ambulatory blood pressure and mood during everyday
life. Journal of Personality and Social Psychology, 76, 104-113.
Robinson-Whelen, S., Kim, C., MacCallum, R.C., & Kiecolt-Glaser, J.K. (1997). Distinguishing
optimism from pessimism in older adults: is it more important to be optimistic or not to be
pessimistic? Journal of Personality and Social Psychology, 73, 1345-1353.
Rogosa, D.R, Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurement of
change. Psychological Bulletin, 92, 726-748.
Schafer, J.L. (1997). Analysis of Incomplete Multivariate Data, London: Chapman & Hall.
Scheier, M.F., & Carver, C.S. (1985). Optimism, coping, and health: Assessment and implications
of generalized outcome expectancies. Health Psychology, 4, 219-247.
Scheier, M.F., Carver, C.S. (1992). Effects of optimism on psychological and physical well-being:
Overview and empirical update. Cognitive Therapy and Research, 16, 201-228.
Scheier, M.F., Carver, C.S., & Bridges, M.W. (1994). Distinguishing optimism from neuroticism
(and trait anxiety, self mastery, and self-esteem): A reevaluation of the Life Orientation Test.
Journal of Personality and Social Psychology, 67, 1063-1078.
218
Schwarz, J.E., Neale, J., Marco, C., Shiffman, S.S., & Stone, A.A. (1999). Does trait coping exist?
A momentary assessment approach to the evaluation of traits. Journal of Personality and Social
Psychology, 77, 360-369.
Schwarzer, R. (1994). Optimism, vulnerability, and self-beliefs as health-related cognitions: A
systematic overview. Psychology and Health, 9, 161-180.
Smith, T.W., Pope, M.K., Rhodewalt, F., & Poulton, J.L. (1989). Optimism, neurotism, coping, and
symptom reports: An alternative interpretation of the Life Orientation Test. Journal of Personality
and Social Psychology, 56, 640-648.
Speier, C. & Frese, M. (1997). Generalized self-efficacy as a mediator and moderator between
control and complexity at work and personal initiative: A longitudinal field study in East Germany.
Human Performance, 10, 171-192.
Steyer, R., Ferring, D., & Schmitt, M.J. (1992). States and traits in psychological assessment.
European Journal of Psychological Assessment, 8, 79-98.
Solomon, R.L., & Corbit, J.D. (1974). An opponent-process theory of motivation: I. Temporal
dynamics of affect. Psychological Review, 81, 119-143.
Spector, P.E., Van Katwyck, P.T., Brannick, M.T., & Chen, P.Y. (1997). When two factors don't
reflect two constructs: How item characteristics can produce artifactual factors. Journal of
Management, 23, 659-677.
Taylor, S.E., & Aspinwall, L.G. (1996). Mediating and moderating processes in psychosocial stress.
In H.B. Kaplan (Ed.), Psychological stress: Perspectives on structure, theory, life-courses, and
methods. (pp. 71-110) Academic Press, San Diego.
Terry, D.J. (1994). Determinants of Coping: The role of stable and situational factors. Journal of
Personality and Social Psychology, 66, 895-910.
Vickers, K.S., & Vogeltanz, N.D. (2000). Dispositional optimism as a predictor of depressive
symptoms over time. Personality and Individual Differences, 28, 259-272.
Willett, J.B. (1989). Some results on reliability for the longitudinal measurement of change:
Implications for the design of studies of individual growth. Education and Psychological
Measurement, 49, 587-602.
Willett, J.B., & Sayer, A.G. (1994). Using covariance structure analysis to detect correlates and
predictors of individual change over time. Psychological Bulletin, 116, 363-381.
Willett, J.B., & Sayer, A.G. (1995). Cross-domain analysis of change over time: Combining growth
curve modeling and covariance structure analysis. In G.A. Marcoulides & R.E. Schumacker (Eds.).
Advanced structural equation modeling: Issues and techniques (pp. 125-157). Mahwah, NJ:
Erlbaum.
219
Williams, D.G. (1992). Dispositional optimism, neuroticism, and extraversion. Personality and
Individual Differences, 13, 475-477.
Vonesh, E.F., & Chinchilli, V.M. (1997). Linear and nonlinear models for the analysis of repeated
measurements. New York: Marcel Dekker.
Zapf, D., Dormann, C., & Frese, M. (1996). Longitudinal studies in organizational stress research:
A review of the literature with reference to methodological issues. Journal of Occupational Health
Psychology, 2, 145-169.
Zung, W. W. K. (1965). A self-rating depression scale. Archives of General Psychiatry, 12, 63-70.
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Chapter 6
Summary and Conclusion
This dissertation addressed the question of how former East Germans coped with the many
changes in the revolutionary times after the unification and which people profited most?
Specifically the following questions were addressed:
1) Were there occupational socialization effects of working characteristics (job control and job
complexity) on personal initiative and was there evidence that these effects were mediated by
control cognitions? Did people who showed more personal initiative eventually receive the
better jobs? (Chapter 1).
2) Did the transition to a free-market affect the level of work stressors and what effect had these
changes on strains? How could the relation between stressors and strains best be modeled
(Chapter 2).
3) Did being an optimist help one to cope with the many adaptations people had to make and, more
specifically, did it affect subjective well-being? Was there evidence that these effects of
optimism/pessimism on subjective well-being were mediated by coping styles? (Chapter 3).
These research questions should be seen in light of the specific historical context: the turbulent
period after the unification. Planned economy, which its centralized economic control, was rapidly
replaced by a free-market economy (Britannica, 1999). As a consequence many companies were
closed or taken over by Western companies. The restructuring of the economy was accompanied by
an enormous increase in unemployment. For those who were lucky enough to keep their job many
adaptations were required. A core element of the old socialistic system was the expected obedience
of community members to the sanctions of their superiors. This strongly contrasts with modern
Western working values where employees have to be much more actively involved in pursuing the
goals of the company. After abandoning planned economy with its decision making and power
highly concentrated on the top, people had to adapt to the different power structure of modern
organizations in which decision making is spread more evenly to all levels of the hierarchy. High
competition ruled out the immobility characteristic of mass organizations and collectives and
pushes companies to high performance with increasingly emphasis on virtues like constant
innovation, providing better customer service, and consistently monitoring changes in consumer
preferences. This had a profound effect on what was expected of employees. No longer was it
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sufficient to comply with strictly formalized task requirements. Since it is impossible for
organizations, operating in dynamic environments, to constantly redesign jobs, the gap between
optimal job behavior and formalized job rules must be filled by a new set of task prescriptions and
job attitudes of the employees. These new, more global, task prescriptions should include a more
active orientation and be more guided by the higher than the lower level goals of the organization.
As an example, if an employee working in a distribution center lets him or herself guide by the goal
of keeping customers satisfied, than delivering orders beyond working time or occasionally giving
extra service is in line with customer policies, although formally it may not be part of his or her job
or may even contradict some lower level procedures.
This new interpretation of what is expected of workers in modern dynamic organizations is
nicely captured by the construct of personal initiative. Personal initiative can be defined as a
sequence of actions that are instigated by self-assigned behavioral goals, which go beyond the more
narrowly defined core job requirements and this self-starting behavior is followed by a high degree
of persistence to overcome obstacles that threaten to thwart the accomplishment of these goals.
These behavioral goals have a long-term perspective, are pro-company oriented, and more inspired
by higher than lower level organizational goals.
In Chapter 1 it was hypothesized that by increasing job control and by adding more
complexities to the job, more optimal conditions were created to further stimulate personal
initiative. Thus by including more control and complexity the step towards more autonomous
behavior (like personal initiative) would be smaller. The effects of job characteristics on the
psychological functioning of the person were called occupational socialization. The most important
job characteristics in this socialization process were control at work and the complexity of the job.
Control at work was defined as the amount of influence a person can exercise over his or her actions
and over job conditions in order to fulfill the goals of the job. Complexity at work is related to the
number of elements a person has to take into account in making appropriate work decisions. It was
hypothesized that if a person had more influence over a greater number of elements in order to
accomplish his or her task this would lead to enduring changes within the person. These changes
captured many aspects of a person and thus were defined on an abstract level. This higher-level
construct was called control cognitions. Control cognitions is related to the self-concept of mastery
orientation and affects control aspirations, control expectations and self-efficacy. Control cognitions
were expected to regulate also actions which would fall beyond the core tasks of the person and to
enhance personal initiative. Since successful initiative should expand the domain over which one
can exert control and extending these boundaries should be reflected in higher control cognitions
reciprocal effects between personal initiative and control cognitions should be expected. Finally, it
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was hypothesized that personal initiative affected job characteristics because persons high on
initiative would find better jobs or jobs with more enriched tasks. Thus, working characteristics
should affect control cognitions which in turn would have an impact on personal initiative. And to
complete the circle, personal initiative would lead to changes in working characteristics. In Chapter
1 we tested this model against several alternative models and the goodness of fit favored the
proposed model. The length of the period needed for personal initiative to exert its influence on
working characteristics was approximately one year (except the last lag which was two years). All
paths coefficients were in the expected direction and most of them were significant. In Chapter 1 it
was concluded that this model supported the theory in many respects. Although the model is called
an occupational socialization model, it argues for a bi-directional influence: Not only the job shapes
the person, the person can change the job as well by showing personal initiative, resulting in either
finding a new, more autonomous job or by changing the content of the old job.
Although the effects of working characteristics on personal initiative (mediated by control
cognitions) were synchronous the effects should not be interpreted as instantaneous effects. A more
plausible interpretation of synchronous effects is that the effects occurred within the period between
two measurement occasions. Since measurements were discrete these effects could only be
observed in the next wave. How on a micro-level these processes unfolded in time could only have
been studied if process data would have been available. All we can conclude is that within a
relatively short period occupational socialization effects could be established. The time needed for
the effects of personal initiative on working characteristics were longer. Persons who showed more
personal initiative improved working conditions, indicating that they got the better jobs. There were
reciprocal effects: jobs which allowed more control for the worker made people more active and
more in control of their environments: They were becoming more the active agents instead of being
passively reacting to their environments.
The fact that working conditions changed radically in East Germany was confirmed in Chapter
1 by the low stabilities for the work characteristics variables (control and complexity combined). It
was expected that Western production standards soon would pervade the workplace. What effects
could this have for stressors at work and its effects on strains? This was the topic of Chapter 2.
First, we investigated whether the trends in the means of the stressors reflected the general view that
many changes had occurred in the organizations and on the workplace. The following stressors
were included in Chapter 2: Job insecurity, working under time pressure, organizational problems,
social stressors and uncertainty.
It was commonly known that the technological backwardness and low productivity of East
German companies in 1990 would make it impossible to compete on an unrestricted market and this
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would inevitably lead to unemployment. However, the dramatic rise of the unemployment figures
was a shock for almost everyone (Britannica, 1999). Especially in the north of East Germany
unemployment rates rose to staggering heights, although in Dresden, the city where the sample was
drawn, unemployment figures were lower. The means of the stressor fear of becoming unemployed
showed an increase after the first measurement occasion, but showed a decrease again already after
the second measurement wave. This drop was earlier than expected and selection effects may have
been responsible for this decrease: People with high fears of becoming unemployed lost indeed their
jobs the next period and produced missing values for the next wave.
Increased efficiency demands invaded the organizational culture and this was reflected by the
upward trend of the means of the stressor time pressure. Adopting Western standards had benefits
for stressors as well: The means of the stressor organizational problems decreased during this five-
year period.
It was expected that competition on the work floor should make the social climate less friendly,
but the means of social stressors were completely stable. Perhaps, these stressors did not function as
a barometer measuring the comradeship, cohesion and the friendliness, which characterized the
social climate in the former East Germany.
It was known that in the former Eastern bloc work requirements were not clearly prescribed
(Pearce, Branyicki & Bukacsi, 1994) and that modern management tools provided less ambiguous
job descriptions. However, the stressor uncertainty showed only a small decrease after the first
wave to remain stable for the rest of the period. Perhaps opposing forces may explain the stability of
the means of the stressor uncertainty: A more active approach was now demanded from East
German workers and this may have created role ambiguity for those who were socialized to strict
obedience. Simply doing what they were told was no longer sufficient for workers. The paradox of
sometimes having to act autonomously implied that they had to trust their own judgment when and
how to act and this may be confusing for many workers.
In summary, some stressors showed an upward trend in the mean levels (time pressure), some
stressors means declined (organizational problems) while the means of social stressors remained
completely stable. What implications did this have for the trends in the means of strains? Some
studies reported strain levels that remained surprisingly stable (Ormel & Schaufeli, 1991; Headey &
Wearing, 1989). The mean levels of depression, psychosomatic complaints, irritation and worrying
were indeed almost stable. Apparently, the opposing trends in specific stressors may have led to
compensatory effects.
Changes in the means reflect trends representative for the population as a whole. On an
individual level considerable variation can occur. The stabilities of both stressors and strains
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showed that the relative positions of people changed considerably over a five-year period.
Apparently people changed into different directions: Some improved relatively while others
position worsened.
Since the relative position of stressor and strain scores of people changed, it made sense to test
several models which could explain these changes. First, an interindividual difference model was
tested. This model argues that relationships between self-reports of stressors and strains could be
explained by one common factor (which may be related to negative affectivity). This model could
clearly be rejected. It was noticed, however, that although this model did not fit the data, it did not
exclude the possibility that one common factor (e.g., negative affectivity) partly had influenced both
stressors and strains reports. Since it was very unlikely that it was the sole factor explaining stressor
- strain relationships more substantial models were tested.
Before testing other stressor – strain models the question of how to model change itself, had to
be addressed. Was change best depicted as an explicit function of time in which the direction of
change was constant for the complete period for each individual? Or should the underlying change
process best be modeled as predictable changes combined with time-specific stochastic influences
that were independent among the different measurement occasions? These models are called latent
growth curve models and autoregressive models, respectively. It was found that for the strain
models the fit indices of the growth curve models were slightly better and the stressor models were
best fit with autoregressive models. A hybrid model was introduced combining the best model for
stressors (AR) with the preferred model for strains (growth curves) with the addition of
synchronous paths from stressors to strains.
The relationships between the systematic slowly moving parts of both stressors and strains
could be represented by the correlation between the slope factors of stressors and strains in cross-
domain growth curve models (Willett & Sayer, 1995). This stressor-strain trend model was tested
for each combination of a stressor and a strain and it was found that several sizeable correlations
could be established. Thus, changes in the domain of stressors tended to covary with a parallel
change in the domain of strains for these combinations. Growth trajectories of time pressure and
uncertainty tended to go parallel with the curves of worrying and social stressors with
psychosomatic complaints.
In the stress literature the most prominent models assume a causal relation from stressors to
strains. However, since the stress - strain process can best be modeled as an ongoing process
(Edwards, 1998) also models that assume reverse causation deserve attention. Two alternative
models were proposed: The Drift model assumes that persons initially suffering from high strains
will not be able to cope and gradually fall back to even worse conditions. The Refuge model
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predicts an opposite process: People with initial high strain levels will succeed in finding less
demanding jobs. In cross-domain growth curve models reverse causation hypothesis could be tested
by the correlation between the intercept factor of strain variables and the slope factor of stressor
variables. The results supported the Refuge models, but the effects were small and it was concluded
that in the population opposing Reverse Causation mechanisms could co-occur and partly had
cancelled each other out. Using recent developed software (Muthén, 1999) these effects could be
isolated if information about latent classes was available.
A Sleeper Effect Model tested if initial levels of stressors had effect on later changes in strains.
This was tested in the cross-domain growth curve models by the correlation between the intercept
factor of a stressor variable and the slope variable of a strain variable. There was no support the
Sleeper Effect Model.
The last tested model specified short - term effects for stressors on strains. The Short - Term
Reaction Model was tested by the hybrid model. Many significant stressors – strains relationships
were found, and especially for the effects of the stressor time pressure on worrying. These stressor
effects could be interpreted as affecting the state component of strains, because the individual
trendlines were partialled out. Equivalently, this model can be interpreted as specifying trendlines
after controlling for the synchronous effects of the stressors. Thus, a model without time-varying
covariates (synchronous stressor effects) would have confounded the systematic regular trend of
each individual with time-specific stressor effects.
In summary, the result of Chapter 2 showed that work stressors both affected the slowly
changing components (see Stressor-Strain Trend Model) as well as the state component of strains
(see Short-Term Reaction Model).
In Chapter 1 and 2 work conditions (job characteristics, like job control and job complexity,
and work stressors) were included to explain psychological processes. In Chapter 3 the focus was
on factors within the person. The research question addressed in Chapter 3 was how optimism was
related to subjective well-being. The personality trait optimism is described in the literature as a
protective factor (sometimes called a resource or resilience factor) in processes where people have
to cope with severe stressors. In similar vein, pessimism is regarded as a vulnerability factor. A
confusing result, obtained by testing several measurement models, was that the scale intended to
measure optimism, the Life Orientation Test (LOT) as a uni-dimensional construct, fell apart in two
only moderately correlated factors, optimism and pessimism. This result is consistent with the
reports of many other researchers who used the LOT scale. Moreover, the pattern of relations with
other variables was also very different for optimism and pessimism. The latter was strongly related
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to depression and somewhat less to irritation. These results favored the treatment of optimism and
pessimism as separate constructs.
Both the means of optimism and pessimism showed a decreasing trend, which can be
considered as further evidence against the treatment of optimism and pessimism as opposite poles
of one underlying continuum. The decline of the means of pessimism was unexpected. Immediately
after the unification many eastern Germans felt euphoric, hoping for freedom, social justice, and a
high standard of living. After political unification, disillusionment in eastern Germany rose sharply.
The massiveness of unemployment came as a shock and as early as the spring of 1991 there were
mass demonstrations against unemployment in the streets of Leipzig. The rebuilding of the Easter
economic stagnated and some spoke of an economic desert. Apparently, the instrument for
measuring pessimism could not be considered as a political or economical barometer, but instead
measured more enduring personal tendencies.
The stabilities for optimism and pessimism were comparable with those of the subjective
well-being variables (called strain variables in Chapter 2). Although the measurement instrument
intended to measure a personality trait, many changes in the relative positions of the scores of
persons could be observed. To explain these changes latent growth curve models were tested and
these models yielded acceptable goodness of fit measures. Both direct and indirect models were
specified. The last models included coping style variables (aggregated over five waves) as
mediators. The stable components of optimism/pessimism and subjective well-being correlated
significantly, which may be explained by genetic and early childhood factors. Initial optimism
(exemplified by the intercept factor) had a significant effect on the slope factor for depression and
psychosomatic complaints. This was most of all due to direct effects. Coping styles played a much
more modest role than we expected. Although some effects were significant, the effect sizes were
very modest. Coping styles could be predicted by pessimism (pessimists planned less, and used
more emotional-focused coping and wishful thinking). Optimists used more problem-focused
coping and surprisingly also more emotional-focused coping.
Much stronger were the effects of initial subjective well-being (represented by the intercept
factors) on coping styles. How people felt at the start of study (immediately after the unification)
could predict moderately well how they would cope during the subsequent period. People who felt
bad (high on depression, psychosomatic complaints and irritation) attempted to alleviate the
negative emotions by wishful thinking, emotional-focused coping and seeking social support. No
relations were found with planning and problem-focused coping. In contrast people who worried
more at the start of the period had a coping style that could be characterized by planning and
problem-focused coping. The constructive element of worrying was not anticipated. The modest
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role coping styles played as mediators could to a great extent be explained by the small effects of
coping styles on changes (slope factors) in the subjective well-being variables. Only a few
significant results could be noticed: planning and problem-focused coping led to less than average
slopes in depression, whereas emotion-focused coping increased depression and worrying.
Not only were pessimism and depression correlated from the start (both intercept factors
were correlated), also their growth curves were (r = .91). To a lesser extent the same picture could
be observed for pessimism and irritation. We can conclude that pessimism is strongly related to
negative emotions.
The overall conclusion of this dissertation is a plea for reciprocal determinism (Bandura,
1997). Both environmental characteristics (work characteristics and stressors at work) and personal
characteristics (personal initiative, control cognitions, optimism, and coping styles) determined
outcomes (strain or synonymously subjective well-being) reciprocally. Those who were in
unfavorable conditions (less control and higher stress levels) suffered more than those who could
act more autonomously and were not exposed to severe stressors. While this may be true: People
were able to change their conditions by showing initiative and adequate coping styles (planning and
problem-focused coping). Being optimistic was an advantage.
Methodological concerns
As all studies some shortcomings have to be noticed. Most of the methodological concerns
have been addressed in the respective chapters. However, some issues need to be elaborated.
Nested relationships
For people without a job the work-related variables are not missing (implying that the values
are potentially observable), but not defined. Treating these data as missing would imply that a
counterfactual assumption had to be made: What are the most plausible values for that person if we
assume that the person would have had a job (which we know is not the case). We would have
preferred to include in our models both the employment status and the work-related variables and
its relations with other psychological variables.
A multi-group solution was unfortunately not an option. Since we had longitudinal model
including 5 or 6 waves, there were many small subgroups with identical observed data patterns and
the n of many subgroups was smaller than the number of variables (leading to singular covariance
matrices for these subgroups).
In the econometric literature the problem of semi-continuous distributions or nested relations
is also known and they recommend a two-step regression model with a binary variable
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(employment status in our case) and a continuous variable for the variable of interest.
Unfortunately, the possibility to analyze nested relations is not implemented in LISREL. In the near
future suitable software will be available (Muthén, 1999; Neale, 1999). The models described in
Chapter 1 and 2 will then be reanalyzed.
Omitted variable bias
One of the most important threats to the validity of regression models is the occurrence of
‘omitted variable bias’ (Dormann, 1999). Omitted variable bias occurs if some variables are left out
of the model or if important paths are lacking. Misspecification can lead to biased estimates.
Combining the theoretical insights from the first three chapters, one can see that some models are
partly misspecified. In Chapter 2 it was demonstrated that work stressors affected strains, but in
Chapter 3 no stressors were included. In similar vein, Chapter 2 did not include coping and resource
variables (e.g., optimism). In Chapter 2 and 3 it was described that the analyses had been broken
down using subsets of variables. Unfortunately, including all variables into a single model was not
possible. Both restrictions of the capacity of the software as statistical considerations made this both
impossible and unwise.
It is hard to find any disadvantage for longitudinal designs. However, estimating growth
curve models does not easily permit to split the models in small models using only a few
measurement occasions.
Missing values
Most longitudinal studies suffer from attrition. This is a threat for generalizing the results
obtained in the sample to the intended population. If the data are Missing at Random (MAR)(Little
& Rubin, 1987) the probability of response depends only on the observed data (Vonesh &
Chinchilli, p. 40). In case of MAR application of the EM algorithm for estimating the covariance
matrix and the vector of means is a reasonable approach (Graham, 1997). However, this is not the
optimal choice since overfitting occurs and variances are biased downwards. A more sophisticated
method is data augmentation (Schafer, 1997). The last method has not been used in the previous
chapters, because it was not yet fully tested in its implications. If the missing data are nonignorable
(the probability of response depends on the unobserved data (Vonesh & Chinchilli, p. 40), no
adequate missing data strategy is available. It is reasonable to assume that at least to some extent the
missing data are nonignorable, leading to some bias in the estimation of the model parameters. This
is an unresolved problem many studies suffer from and at this moment there seems no easy solution
to become available in the near future.
230
Advantages of longitudinal research for making causal statements
What are the advantages of longitudinal designs?
For interpreting a relation between a variable X and Y as causal Cook & Campbell (1979) mention
three requisites:
1) Covariation between X and Y
2) Time order: for interpreting X as the cause for Y, X has to precede Y in time.
3) Alternative explanations can be ruled out.
Ad 1) Although it is commonly thought as a necessary condition, covariation can be masked by
suppressor effects. Suppressor effects can be produced by compensational mechanisms (Gully,
Frone, Edwards, 1998). As Bollen stated (1989):”The old saying that correlation does not prove
causation should be complemented by the saying that a lack of correlation does not disprove
causation (p.52)”. However, if the model is correctly specified (e.g., no omitted variable bias), there
should be covariation. It is known from dynamic system theory (Molenaar, 1998) that many
relations are smaller than expected because compensatory mechanisms become effective if a
variable approaches boundary values.
Ad 2) The time order is more helpful if the phenomenon which is considered to be the cause is a
clearly defined event with a clear beginning and ending. Whether or not a person is exposed to the
stimulus or the extent of exposure can in principle be established in a well-defined manner.
However, the data studied in this dissertation are potentially constantly changing and so are the
potential effects. This complicates statements about causality. What precedes what and what is the
time lag between causes and effects? Knowledge of the time order is still helpful, but since the time
lag is not known, causal interpretations are much harder to make. If two variables are repeatedly
measured, the number of potential relationships, each satisfying the time order condition, is much
greater. There can be synchronous effects, reciprocal effects and lagged effects with different
lengths of the lags. The duration and intensity of effects can also greatly vary and to complicate
matters even further: interaction effects could be observed in the case of prolonged exposure to the
stimulus.
Ad 3) The most difficult task for the researcher claiming causality is that all other explanations for
the covariation can be convincingly rejected. The most severe threat for structural equation models
is omitted variable bias (Jöreskog, 1997) that applies whenever the true cause is left out of a model.
This threat of misspecification exists irrespective if the model is longitudinal or cross-sectional.
Here we quote Cudeck (1991, p. 261):”A “correctly specified model” is, always has been, and
always will be a fiction. A more realistic view of models is that they are simplifications of
231
extremely complicated behavior. It is a mistake to assume that any model actually represents the
underlying process absolutely correctly, even after certain obvious faults have been corrected. All
that can be hoped is that the model captures some reasonable approximation to the truth, serving
perhaps as a descriptive device or summarizing tool”.
Objective versus subjective measurements
In many theories in work and industrial psychology the focus is on aspects of the work
environment. These are considered as important determinants for both the behavior of the workers
as well as for many relevant behavioral outcomes (such as productivity, absenteeism, turn-over,
satisfaction). Some theories emphasize the objective features of the work environment, whereas
other theories ignore the objectivity of these aspects and primarily focus on how they are perceived.
In job redesign and in some stress prevention programs the objective aspects are of crucial interest.
If individual differences are the main concern of the researcher it is more important how these
aspects are perceived.
Because objective measurements are not always available in many studies, questionnaire
(subjective) data are often used as proxies for the objective characteristics. However, measurement
models, developed for measuring traits and abilities, may not always be adequate for testing these
perceptual data sets. In test theory, where the focus is on individual differences, it is required that
test conditions are highly standardized. As a consequence the covariation between the items can be
explained by common factors, since it is plausible that unique item factors are independent of each
other. The factor model is appropriate for measuring individual differences in job perceptions in
cases where all workers have the exactly the same job and work under highly standardized work
conditions. Covariation between items may be explained by individual differences in the tendency
to over- or underreport (c.f. negative affectivity, Burke et al, 1993).
In the previous case the common factor refers to differences between persons. It is also
possible that common factors reside in the external world. In studies of tasks characteristic many
jobs may be studied. Lets suppose that valid objective measurements of these task characteristics
are available. Now individual differences in perceptions are excluded since objective measurement
implies that all observers would come to the same observation. A set of common factors may
explain the covariation between the indicators, since in general jobs consist of a set of well-
coordinated tasks. Again the factor model does a decent job, since there is only one set of common
causes, now residing completely in the external world. However frequently a set of ‘objective’
indicators from a certain domain will not be systematically related and hence the assumptions for
fitting a factor model will be violated.
232
Next we discuss more complicated cases. What happens if we confound both sources of
variation? Suppose that in the first example job restructuring will be implemented in such a way
that complete standardization is abandoned. Now workers get in varying degrees more control over
both the methods they uses as well as the quality of what they produce. Since the job redesign is set
up in such a way that both control aspects covary, there are now two common sources which can
explain the correlation between both subjective indicators: A subjective factor (tendency for over-
or underreporting) and an objective factor (caused by job redesign) are completely confounded. In a
factor model both items violate the assumption of local independence: The common factor can only
partly explain the covariance between the items.
In the previous example both control aspects were deliberately matched by the management.
However, in empirical data sets the covariance matrix of objective characteristics can have any
form: From completely uncorrelated to strongly positively of negatively correlated. These
complications led us to conclusion that our measurement of work characteristics (Chapter 3) and
stressors at work (Chapter 4) were based upon simultaneously valid, but conflicting measurement
models: A factor model and a causal indicator model. In cases where objective measurements are
not available, it is hard to find a suitable measurement model for these hybrid models and equally
weighting the items seems an acceptable strategy.
Standard errors and goodness of fit measures
The structural equation modeling software that was used (LISREL) requires as input one
single number representing the sample size. Standard errors and almost all goodness of fit measures
are a direct function of the sample size. It is hard to provide the ‘correct’ sample size if the
covariance matrix and the vector of means are estimated with pairwise deletion or alternatively with
the use of the EM algorithm (Schafer, 1997). There is at present no statistical theory for estimating
the correct standard errors and goodness of fit measures if the covariance matrix and mean vector
are estimated either using pair-wise deletion or the EM algorithm. In practice researchers choose
between the following options: The minimum sample size, the mean and the maximum sample size
(Marsh, 1998). A combination may be used as well: provide both the results for the model estimated
with the minimum sample size and the maximum sample size (Molenaar, 1998).
A promising alternative for obtaining correct standard errors if the assumption of Missing at
Random (Little & Rubin, 1987) holds, is maximizing the case-wise likelihood of the observed data.
In contrast to the LISREL program alternative structural equation modeling software like AMOS
(Arbuckle, 1995) and MX (Neale, Boker, Xie & Maes, 1999), provides the possibility for Full
Information Maximum Likelihood based on the direct maximization of the likelihood of the
233
observed data (Arbuckle, 1996, Wothke, 1997; Wood, 1997, p. 373). In a simulation study using the
AMOS program Wothke (1997) reported that using FIML estimation the standard errors were only
slightly estimated when the fraction of missing data was moderate or high. MX offers the
opportunity to estimate likelihood-based confidence intervals, which may be preferable over
standard errors in many cases (Neale, Boker, Xie & Maes, 1999, p. 90).
Another alternative for estimating standard errors and goodness of fit measures is
bootstrapping. However, not in all situations the bootstrap procedure performed well (Yung &
Bentler, 1996, p. 223) and further research is needed to provide guidelines in which cases
bootstrapping is the optimal choice in structural equation modeling with missing data.
For practical purposes we choose to use the mean sample size. This is probably not the most
sophisticated method. As a consequence all standard errors and goodness of fit measures cannot be
considered as exact but hopefully as reasonable approximations. The results of a simulation study
by Marsh (1998) are not conclusive.
Validity of correctly specifying growth curves and interpretation of states
We modeled growth as an explicit function of time and we have to admit that the form of
this relationship with time is determined by the number of measurement occasions: a continuous
relation is estimated with discrete data. If we could provide over many more measurement points
changes could be monitored more precisely and more complex growth curves could be estimated.
We defined states as deviations from the individual trajectory. As a consequence our definition of
state fluctuation versus systematic developments would dramatically change. Thus, the definition of
states is dependent on the availability of the number of measurement points within the period of
study. Ideally one would study fluctuations of different time lengths. The shorter the time interval
between consecutive measurements and the longer the period of the study the more information
about the dynamics of the processes could be obtained. However, in psychological research testing
and practice effects would probably severely threaten the validity of interview and questionnaire
data. In this dissertation no time series data were available, but instead a panel study has been
performed. Therefore, the definition of state fluctuation should be seen in light of the long intervals
between measurement occasions (ranging from three months to two years).
Level of Generality
Research can be organized along its level of generality between people (see Revelle on
personality processes, 1995; p. 297). The level of generality ranges from generalizing to all people
234
to focusing on single individuals. In quantitative research the level of generality can be reduced by
including moderators or specifying different models for subgroups. Relationships are no longer
treated as invariant, but may vary for different groups.
Originally we intended to specify models which allowed the functional form of growth
curves to be different for subgroups. In these models the group membership was not known in
advance, but instead should be estimated from the data. At the start of the study this was not yet
possible using existing software. However, recent software developments allow for heterogeneity
with respect to the influence of antecedents, growths shapes, and outcomes. These General Growth
Mixture Models can now be estimated using the Mplus software (Muthén, in press; Muthén and
Muthén , 1999). In Chapter 4 we reported that the Sleeper Effect was not supported. But the
prevalence of Sleeper Effects may be relatively rare in the population and only occurring if several
causes combine. More advanced statistical tools will give the researcher a potential for specifying
more fine-tuned models in which relatively rare phenomena, not representative for the whole
population will have a higher probability of being detected. The future of Structural Equation
Modeling seems indeed very promising.
References
Arbuckle, J.L.(1996). Full information estimation in the presence of incomplete data. In G.A.
Marcoulides & R.E. Schumacker (Eds.). Advanced structural equation modeling: Issues and
techniques, (pp. 243-277). Mahwah, NJ: Erlbaum.
Cook, T.D. & Campbell, D.T. (1979). Quasi-experimentation. Design and analysis for field
settings. Boston: Houghton Mifflin.
Marsh, H.W. (1998). Pairwise deletion for missing data in structural equation models: Nonpositive
definite matrices, parameter estimates, goodness of fit, and adjusted sample sizes. Structural
Equation Modeling, 5, 22-36.
Molenaar, P.C.M. (1998). Personal communication.
Wood, P.K. (1997). How the state of the art can inform the art of the practice. Structural Equation
Modeling, 4, 370-387.
Wothke, W. (1997). Longitudinal modeling with missing data. Paper presented at the Berlin
Summer School Conference (BSSC 97), June 25-30.
Yung, Y.-F., & Bentler, P.M.(1996). Bootstrapping techniques in the analysis of mean and
covariance structures. In G.A. Marcoulides & R.E. Schumacker (Eds.). Advanced structural
equation modeling: Issues and techniques, (pp. 195-226). Mahwah, NJ: Erlbaum.
235
Appendix A
In this Appendix it will be shown that
111222222111 .... −−−−−− qqqqqq ΩΜΑΩΜΑΩΜΑΩΜΑ (A1)
can be written as
( ) 122112211221 .......... ΥΥΥΥΜΜΜΜΧΧΧΧ −−−−−− qqqqqq (A2)
In this Appendix positive definiteness is assumed in cases matrix inversion is necessary.
All Αt matrices, placed between the Μt matrices, have been replaced by premultiplying with a
suitable matrix Χt. The first matrix Α1 and the last Ωq-1 matrix are already on the right position, so
we can write Χ1 = Α1 and Υq-1 = Ωq-1. This results in:
111222222111 .... −−−−−− qqqqqq ΥΜΑΩΜΑΩΜΑΩΜΧ (A3)
The next step is to replace Α2 by an unknown matrix Χ2 so that:
11122111 ΩΜΧΧΑΩΜΧ = (A4)
The unknown matrix Χ2 can be found by postmultiplying both sides with: 11
11
11
−−− ΧΜΩ
11
11
111112
11
11
112111
−−−−−− = ΧΧΜΩΩΜΧΧΧΜΩΑΩΜΧ (A5)
21
11
11
12111 ΧΧΜΩΑΩΜΧ =−−− (A6)
111222221112 .... −−−−−− qqqqqq ΥΜΑΩΜΑΩΜΩΜΧΧ (A7)
In similar vein the remaining Α matrices can be replaced by premultiplying with a suitable matrix
Χ. This results in:
112222111221 ........ −−−−−− qqqqqq ΥΜΩΜΩΜΩΜΧΧΧΧ (A8)
Similarly, we want to replace 112 −−− qqq ΥΜΩ by
211 −−− qqq ΥΥΜ , where Υq-2 is an unknown
matrix. Premultiplying both sides of the identity
112211 −−−−−− = qqqqqq ΥΜΩΥΥΜ (A9)
with 11
11
−−
−− qq ΜΥ gives:
1121
111211
11
11 −−−
−−
−−−−−
−−
−− = qqqqqqqqqq ΥΜΩΜΥΥΥΜΜΥ (A10)
236
so that
1121
1112 −−−
−−
−−− = qqqqqq ΥΜΩΜΥΥ . (A11)
In the same fashion all diagonal matrices in the middle can be replaced by pre- or
postmultiplying with a suitable matrix. It is important to note that the order of the algebraic
operations will result in different results. For instance, we could have started replacing the Ω
matrices first. If we again define Χ1 = Α1 this results in
122111222211 ........ ΥΥΥΥΜΑΜΑΜΑΜΧ −−−−−− qqqqqq (A12)
The next step is now to replace Α2 by an unknown matrix *2Χ so that:
11*2211 ΜΧΧΑΜΧ = (A13)
The unknown matrices *2Χ can be found by postmultiplying both sides with: 1
11
1−− ΧΜ .
11
1111
*2
11
11211
−−−− = ΧΧΜΜΧΧΧΜΑΜΧ (A14)
and
11
11211
*2
−−= ΧΧΜΑΜΧΧ . (A15)
This is different from the previous solution in (A6):
11
11
1121112
−−−= ΧΧΜΩΑΩΜΧΧ (A6)
Alternatively, the order of the algebraic operations can use a two-stage process: first shifting
theA matrices to the left (but right to 1Μ ) and theΩ matrices to the right but left to1−qΜ ). If we
denote tΡ for the matrices that replace theA matrices and tΖ for the matrices that replaces theΩ
matrices, then the end result of the first stage is:
11232122123211 ............ −−−−−−− qqqqqqq ΩΜΖΖΖΖΜΜΡΡΡΡΜΑ (A16)
To simplify our notation we define 1232
* .... −−= qq ΡΡΡΡΡ and 2321
* .... −−= qq ΖΖΖΖΖ .
(A16) can be written as:
11
*22
*11 .... −−− qqq ΩΜΖΜΜΡΜΑ
In the second stage we want to replace *Ρ and *Ζ by pre- and postmultiplying with suitable
matrices.
1***
1 ΜΧΡΜ =
237
Appendix B
In this appendix we want to show the equivalence between the following four formulations
of the covariance structure for an AR(1) model:
1) conventional LISREL specification with:
( ) ( ) εΘΛΒΙΦΒΙΛΣ +
−−= −− ''11
(B1)
where in a five-wave model Β is specified as follows:
=
0000
0000
0000
0000
00000
54
43
32
21
β
β
β
β
Β (B2)
2) Factor model using model (12)
εΘΛΖΤΖΦΖΤΖΛΣ +
= −− ''''12
1 (B3)
3) Factor model using model (7)
εΘΛΨ∆Φ∆ΛΣ +
+
∏
∏=
−
=
−
=
''1
1
1
1
q
tt
q
tt 2 (B4)
4) Geometric series (McArdle & McDonald (1984)
εΘΛΒΦΒΛΣ +
∑∑=−
=
−
=
''q
j
jq
j
j1
0
1
0 (B5)
where Β is specified as in(B2).
238
(B1) and (B5) are well-known results. In this appendix it will first be demonstrated that
model (B3) is equivalent to model (B1). Second, it will be shown that model (B4) can be
reparametrized as model (B5). Finally the equivalence between model (B4) and model (B3) will be
demonstrated.
Equivalence between model (B3) and model (B1)
It is sufficient to show the equivalence between ΖΤΖ-1 and (Ι-Β)-1
.
ΖΤΖ-1 =
∏∏ −
=+
−
=+ 1
1,1
3221
21
1
1,1
3221
21
1...000
...............
0...1
00
0...01
0
0...001
1...111
...............
0...111
0...011
0...001
...000
...............
0...00
0...00
0...001
q
iii
q
iii
postmultiplying the first with the second matrix yields:
∏∏∏∏∏ −
=+
−
=+
−
=+
−
=+
−
=+ 1
1,1
3221
21
1
1,1
1
1,1
1
1,1
1
1,1
322132213221
2121
1...000
...............
0...1
00
0...01
0
0...001
...
...............
0...
0...0
0...001
q
iii
q
iii
q
iii
q
iii
q
iii
Multiplying gives the same matrix as ( ) 1−− ΒΒΙ
∏∏∏−
+−
+−
+ 1...
...............
0...1
0...01
0...001
3
,1
2
,1
1
,1
323221
21
q
ii
q
ii
q
ii
(B6)
239
Equivalence between model (B3) and model (B1)
The identity ( ) ∞∞
=
− ++++==− ∑ ΑΑΑΑΑΑΑΙ ...3210
0
r1
r
is a well known result
(McArdle & McDonald, 1984, p.235). The series ends when Αr ≠ 0 while Αr+1 = 0. We show
that for an AR(1) model the length of the geometric series is determined by the number of waves,
denoted as q. What follows are the matrices for a five-wave AR(1) model (q = 5).
=
10000
01000
00100
00010
00001
0Β
=
0000
0000
0000
0000
00000
54
43
32
21
1
β
β
β
β
Β
=
=
0000
0000
0000
00000
00000
0000
0000
0000
0000
00000
0000
0000
0000
0000
00000
5443
4332
3221
54
43
32
21
54
43
32
21
2
ββ
ββ
ββ
β
β
β
β
β
β
β
β
Β
=
=
0000
0000
00000
00000
00000
0000
0000
0000
0000
00000
0000
0000
0000
00000
00000
544332
433221
54
43
32
21
5443
4332
32213
βββ
βββ
β
β
β
β
ββ
ββ
ββΒ
=
=
0000
00000
00000
00000
00000
0000
0000
0000
0000
00000
0000
0000
00000
00000
00000
5443322154
43
32
21
544332
433221
4
βββββ
β
β
β
βββ
βββ
Β
B5 = 0 so the series has 5 terms (it starts from 0). It is easy to generalize these results to
AR(1) models of any number of measurement occasions. The mechanism can be explained by the
definition of matrix multiplication AB = C: each cij is determined by the sum of products from the
240
elements of the ith row of A and the jth column of B. As shown above all matrices have only
elements below the subdiagonal which implies that the matrix used for premultiplying can only
reach the elements which are placed on lower rows of the right matrix. The elements of the product
matrix are always one band further away from the main diagonal than the matrix used for
premultiplying. The series starts at the main diagonal (identity matrix) and ends at the band which is
farthest away from the main diagonal. So the number of rows (or colums) determines the length of
the series and this equals the number of waves of AR(1) model.
Next we focus on the specification of the ∆t matrices:
=∏−
=
1
1
q
t∆
10000
01000
00100
0001
00001
10000
01000
0010
00010
00001
10000
0100
00100
00010
00001
1000
01000
00100
00010
00001
21
32
43
54
ββ
ββ
If we define 0ij as an 0 matrix except for one single element ij which is nonzero, we can write:
( )( )( )( )21324354
1
10000 ++++=∏
−
=ΙΙΙΙ∆
q
t
=
( )( )( )213243545443 000000 +++++ ΙΙΙΙ =
( )( )21324354325432434354544332 0000000000000 ++++++++ ΙΙΙ
It follows from the definition of matrix multiplication that 0ij0kl = 0 if j ≠ k, so 325400 = 0 . We
can simplify:
( )( )2132435443543243544332
1
100000000000 +++++++=∏
−
=ΙΙ∆
q
t
further multiplications gives
++++++++++ 213243324321545421434321323221 000000000000000Ι213243543243542143544354 000000000000 +++
241
21432154 , 0000 and 214354 000 are all 0 matrices, so the result is:
=∏−
=Ι∆
1
1
q
t
++++++++ 43543243213254433221 0000000000Ι21324354324354213243 0000000000 ++
Finally we show the following identities:
ΙΒ =0
544332211
0000 +++=Β
4354324321322
000000 ++=Β
3243542132433
000000 +=Β
213243544
0000=Β
Equivalence between Model (B3) and Model (B5).
To demonstrate the equivalence between the AR(1) using submodel (12) and the general
model (7), it is necessary to show the following identity:
1−ΖΤΖ = ∏−
=
1
1
q
tt∆ (B7)
We start with the right hand side of (B7). First we will decompose the ∆t matrices into three
matrices. Second, we will rearrange the matrices by a series of algebraic manipulations. This will
result in a new structure of only three matrices. Still one operation is needed to obtain the
formulation on the left side of (B7)
One can decompose all ∆t matrices in three matrices. The matrix in the middle is a fixed
matrix, which has to be pre- and postmultiplied with a coefficient matrix. Here we show the
decomposition for a five-wave study:
242
∆5 Μ5 Ω5 Α5
=
545454
10000
01000
00100
00010
00001
11000
01000
00100
00010
00001
0000
01000
00100
00010
00001
1000
01000
00100
00010
00001
βββ
∆4 Μ4 Ω4 Α4
=
10000
01
000
00100
00010
00001
10000
01100
00100
00010
00001
10000
0000
00100
00010
00001
10000
0100
00100
00010
00001
434343 βββ
∆3 Μ3 Ω3 Α3
=
10000
01000
001
00
00010
00001
10000
01000
00110
00010
00001
10000
01000
0000
00010
00001
10000
01000
0010
00010
00001
323232 βββ
243
∆2 Μ2 Ω2 Α2
=
10000
01000
00100
0001
0
00001
10000
01000
00100
00011
00001
10000
01000
00100
0000
00001
10000
01000
00100
0001
00001
212121 βββ
Hence, we can write:
==∏−
=2345
25
0∆∆∆∆∆
tt 222333444555 ΩΜΑΩΜΑΩΜΑΩΜΑ
The Ωt and Αt matrices are diagonal matrices, so we can replace their order without any
consequence:
223234345455 ΩΜΩΑΜΩΑΜΩΑΜΑ (B8)
It is easily verified that ΤΜΜΜΜ =2345 , so our aim is to find a new formulations with
2345 ΜΜΜΜ in the middle and which is equivalent to (B8). To achieve this we have to find the
appropriate set of matrices for pre- and postmultiplying, so that all matrices Αt and Ωt that reside
in the middle of (B8) will vanish. To let Α4 disappear, we have to premultiply Μ5 with an
unknown matrix Χ.
1545455−=⇒= ΜΜΑΜΧΑΜΧΜ (B9)
Substitution in (B9) gives:
22323434555 ΩΜΩΑΜΩΑΜΩΧΜΑ
The same operation is needed for Α3 and Α2 and we will denote the new matrices for
premultiplication Υ and Ζ, respectively:
15
15
1434554553455
−−−=⇒= ΜΜΩΜΑΜΩΜΥΜΩΥΜΑΜΩΜ
15
15
14
14
13234455
34455234455
−−−−−=
⇒=
ΜΩΜΩΜΑΜΩΜΩΜΖ
ΜΩΜΩΖΜΑΜΩΜΩΜ
244
Substitution gives:
223344555 ΩΜΩΜΩΜΩΧΥΖΜΑ
The reverse procedure is needed for moving out the Ω matrices and the new matrices for
postmultiplication will be denoted as Ε, Ρ and Ν, respectively.
231
2223 ΜΩΜΕΕΜΜΩ −=⇒=
2341
31
223234 ΜΜΩΜΜΡΡΜΜΜΜΩ −−=⇒=
23451
41
31
22342345 ΜΜΜΩΜΜΜΝΝΜΜΜΜΜΜΩ −−−=⇒=
Substitution of these results gives:
223455 ΝΡΕΩΜΜΜΧΥΖΜΑ (B10)
If we define ΧΥΖΑ5=Q and 2ΝΡΕΩ=W and use the earlier stated identity
ΤΜΜΜΜ =2345 , we can write WQΤ as a shorthand for (B10). We now have to replace the
matrix Q with Ζ from (B10) by finding a matrix Π for postmultiplication:
WQWWWQ ΤΖΤΠΠ∆ΤΤ 111 −−−=⇒=
It can be verified that 1−= ΖΖΠW so that 1−= ΖΤΖΖΤΖΠΖΤW
References
McArdle, J.J., & McDonald, R.P. (1984). Some algebraic properties of the Reticular Action Model
for moment structures. British Journal of Mathematical and Statistical Psychology. 37, 234-251.
245
Appendix C
In this Appendix w
e show how
the covariance matrix for the B
ollen and Curran hybrid m
odel can be obtained.
We start w
ith the structural equation: (
)
+
=−
**
1ΤΖΤΖ
(94)
We define again the covariance m
atrix of the unique factors in the measurem
ent model as E
[ εε] =
Θε , further w
e define Φ4 as a 2 × 2
symm
etric covariance matrix of the grow
th curve factors as in (36), 11
214
2122
φφ
φφ
=
, where φ
11 denotes the variance of the intercept factor,
φ22 the variance of the slope factor and, φ
21 the covariance between the intercept and slope factor. Φ
2 is defined as a diagonal q × q matrix of
residual variances (see equation (57)). Also w
e define ΤΗΝ
as in (38) as T* =
− − −
1 13
12
1...
.. 1 10
1
tt
tt
ttq
.
The covariance m
atrix of the observed variables is:
(
)()
'
'C
ovC
ov
yy
++
==
ΛΛ
Σ
Substituting (94) gives: (
)(
)[
](
)(
)[
]
++
++
−−
'C
ov
*
*1
**
1Τ
ΖΤΖΛ
ΤΖΤΖ
Λ
(C
1)
Using (
) ''
'=
three times, w
e consecutively can write:
246
()
()
[]
()
()
++
++
−−
''
'C
ov
Λ
ΤΖΤΖ
ΤΖΤΖ
Λ*
*1
**
1,
(C2)
()
()
[]
+
+
++
−−
''
''
''
''
Cov
ΛΖ
ΤΖ
ΤΤ
ΖΤΖΛ
1*
**
*1
,
(C3)
()
()
[]
() '
''
''
''
'C
ovC
ov
+
+
+−
−Λ
ΖΤ
ΖΤ
ΤΖΤΖ
Λ1
**
**
1.
(C4)
Assum
ing that the unique terms in ε are independent of both ξ* and ξ
, and assuming that the grow
th curve factors in ξ* are independent of the
autoregressive factors in ξ, w
e can write:
()
() '
''
''
''
'C
ovC
ovC
ov
+
+
−−
ΛΖ
ΤΖ
ΤΤ
ΖΤΖΛ
1*
**
*1
(C5)
Using the definitions for Φ
2 , Φ4 , and Θ
ε w
e can write:
εΘ
ΛΖ
ΤΖ
ΦΤ
ΦΤ
ΖΤΖΛ
+
+
−−
''
''
'1
2*
4*
1
(C6)
247
Next w
e show the equivalence betw
een the covariance structure of (C6) and the covariance structure of the hybrid m
odel obtained from
the conventional specification.
1*1
1ζ
ξη
+=
()
21
2*2
*12
212
ζξ
ξη
βη
+−
++
=t
t
()
31
3*2
*13
323
ζξ
ξη
βη
+−
++
=t
t
(C
7)
…
…
…
…
….
….
()
tt
ζξ
ξη
βη
+−
++
=−
−1
*2*1
11
,
Lets define Β
again as in (55) and T*
as in (38):
=
−0
00
0
....
....
..
0..
00
0..
00
0..
00
0
1,
32
21
β
ββ
Β
(55)
− − −=
1 13
12
*
1...
... 1 10
1
tt
tt
ttq
Τ
(38)
In matrix form
ulation (C7) can be w
ritten as:
++
=*
*Τ
Β
(C
8)
Moving Β
η to the left side gives:
248
+=
−*
*Τ
Β
(C
9)
Multiplying out η
:
()
+
=−
**
ΤΒ
Ι
(C10)
Premultiplying both sides w
ith ()
1 −−
yields the reduced form:
() (
)
+
−=
−*
*1Τ
ΒΙ
(C
11)
The covariance m
atrix of η is: (
)(
)()
(
)()
+−
+−
=−
−'
'C
ovC
ov
**
1*
*1
ΤΒ
ΙΤ
ΒΙ
(C
12)
Using (
) ''
'=
:
() (
)
()(
)
−
++
−−
−'
'C
ov1
**
**
1Β
ΙΤ
ΤΒ
Ι
,
(C
13)
and again using () '
''
=
:
249
() (
)(
)
−
++
−−
−'
''
'C
ov1
**
**
1Β
ΙΤ
ΤΒ
Ι
,
(C
14)
which can be w
ritten as:
()
() (
)
−
+
−
−−
''
''
Cov
Cov
1*
**
*1
ΒΙ
ΤΤ
ΒΙ
,
(C
15)
and after proper substitutions:
()
()
−
+
−−
−'
'1
*4
*1
ΒΙ
ΨΤ
ΦΤ
ΒΙ
(C
16)
in the framew
ork of submodel (12) Ψ
is Φ2 :
+−
−'
''
'Ζ
ΤΖ
ΦΤ
ΦΤ
ΖΤΖ1
2*
4*
1
(C17)
Including the measurem
ent model gives (C
6) again gives:
εΘ
ΛΖ
ΤΖ
ΦΤ
ΦΤ
ΖΤΖΛ
+
+
−−
''
''
'1
2*
4*
1
(C6)
250
Appendix D
In this Appendix we will demonstrate the equivalence between two multivariate longitudinal
models:
εΘΛ∆∆
∆Φ
∆∆∆
ΛΣ +
∏
∏
=
−
=
−
=
''
q
j tt
tq
j tt
t 1
12
1
12221
11
2221
1100 (D1)
where t = q – j + 1, and
εΘΛΒΙΒ
ΒΙΦ
ΒΙΒΒΙ
ΛΣ +
−−−
−−−
=−−
''1
2221
112
1
2221
11 00 (D2)
where Β is specified as follows:
=
=
000000
000000
000000
00000000
0000000
0000000
0000000
00000000
8783
7672
6561
43
32
21
2221
11
ββββ
ββ
ββ
β
ΒΒΒ
Β0
(D3)
We will not provide a general proof, but only demonstrate the equivalence for a four-wave
AR(1) model with lagged effects.
If we denote the free parameters in ∆t in (D1) as the equivalent βs in (D3), the ∆t matrices
can be written as:
251
111111 234 ∆∆∆
1000
0100
001
0001
1000
010
0010
0001
100
0100
0010
0001
21
32
43
ββ
β
(D4)
222222 234 ∆∆∆
1000
0100
001
0001
1000
010
0010
0001
100
0100
0010
0001
65
76
87
ββ
β
(D5)
212121 234 ∆∆∆
0000
0000
000
0000
0000
000
0000
0000
000
0000
0000
0000
61
72
83
β
β
β
(D6)
Β21 from (D2) can be defined as ∑−
=
1
121
q
jt∆
The following identity has to established:
∏
−
=
1
1 2221
11q
j tt
t
∆∆∆ 0
=
1
2221
11−
−−
−
ΒΙΒ
ΒΙ 0 (D7)
252
We start with working out the left hand side of (D7):
=
2221
11
2221
11
2221
11
22
2
33
3
44
4
∆∆∆
∆∆∆
∆∆∆ 000
++
222222212222112122111121
111111
234234234234
234
∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆ 0
(D8)
At this point it is more convenient to adjust the notation: the lower indices reflect which element is
nonzero in the matrix. Let Ιij and 0ij be defined as identity and null matrices, respectively, except
for only one element ij which is a free parameter (i ≠ j). The specific β parameter that is set free is
denoted by a sub-subscript.
Top left quadrant:111111 234 ∆∆∆ =
213243213243 βββ
ΙΙΙ (D9)
Bottom right: 222222 234 ∆∆∆ =
657687213243 βββ
ΙΙΙ
Bottom left quadrant: 212222112122111121 234234234 ∆∆∆∆∆∆∆∆∆ ++ =
213283213243 βββ
ΙΙ0 +217287
213243 βββΙΙ 0 +
617687213243 βββ
0ΙΙ
253
Next we concentrate on model (D2). Using the formula for a partitioned inverse1
( )( ) ( )( ) ( )
−−−−−
−−−−
−
122
11121
122
111
ΒΙΒΙΒΒΙ
ΒΙ 0 (D10)
The top left quadrant can be written as:( ) =− −111ΒΙ
213243213243 βββ
ΙΙΙ ,
the bottom right quadrant as: ( ) =− −122ΒΙ
657687213243 βββ
ΙΙΙ ,
and the left bottom quadrant as: ( ) ( )( ) =−−−− −− 11121
122 ΒΙΒΒΙ
− (657687
213243 βββΙΙΙ )−(
162738213243 βββ
000 ++ )(213243
213243 βββΙΙΙ ).
Multiplying out the last result in the left bottom quadrant gives:
(657687
213243 βββΙΙΙ )(
3843β
0 )(213243
213243 βββΙΙΙ ) +
(657687
213243 βββΙΙΙ )(
2732β
0 )(213243
213243 βββΙΙΙ ) +
(657687
213243 βββΙΙΙ )(
1621β
0 )(213243
213243 βββΙΙΙ ) (D11)
It is easily derived from the rules of matrix multiplication2 and the definition of the Ιij and 0ij
matrices that each of the three terms of (D10) reduces to a product of matrices containing only
1 Graybill describes the inverse of partitioned matrix as follows.
Β ΒΒ Β
11 12
21 22
1
−
=Α ΑΑ Α
11 12
21 22
, where
( )Α Β Β Β Β11 11 12 221
21
1= − − −
( )Α Β Β Α Β Β Β Β Β12 111
12 22 111
12 22 111
12
1= − = − −− − − −
( )Α Β Β Β Β Β Β Β Α Β Β22 22 21 111
12
1
221
221
21 11 12 221= − = +− − − − −
( )Α Β Β Α Β Β Β Β Β Β21 221
21 11 221
21 11 12 221
21
1= − = − − =− − − −
254
matrices which column number equals the row number of the subsequent matrix (for null or identity
matrices except for one free extra parameter matrices Μ: Μj,j-1Μj-1,j-2, Μj-1,j-2….).
For instance, the last term of (D11) (657687
213243 βββΙΙΙ )(
1621β
0 )(213243
213243 βββΙΙΙ )
reduces to 7687
3243 ββΙΙ
3843β
0 . The product of the last three matrices, 213243
213243 βββΙΙΙ , is
a lower triangular matrix with 1’s on the diagonal. Postmultiplying the matrix in the middle (which
has one nonzero element on the second row and the first column) with this product, is the same as
postmultiplying with an identity matrix:
(16
21β0 )(
213243213243 βββ
ΙΙΙ )=16
21β0
and the first term reduces to:
(657687
213243 βββΙΙΙ )(
1621β
0 ).
Premultiplying the last “zero” matrix with the third matrix has the same effect as premultiplying
with and identity matrix:
(65
21βΙ )(
1621β
0 )=16
21β0
Now the third term reduces to:
76873243 ββ
ΙΙ16
21β0 .
Applying the same logic to the first and the second terms, (D10) can be simplified to:
3843β
02132
2132 ββΙΙ +
8743β
Ι27
32β0
2121β
Ι +7687
3243 ββΙΙ
1621β
0 , which is the same as the
structure in the bottom left quadrant of (D9). Hence it has been proved that the alternative
specification (D1) is equivalent to the conventional specification (D2).
2 If rnnmrm ××× = BAC then ∑==
n
kkjikij bac
1
255
Appendix E
In the last decade, important improvements have been made in the statistical modeling of
longitudinal data. One important class is the random coefficient model and the SEM variant which
is called the latent growth curve model.
Good introductions of latent growth curve models already exist (see Curran (in press),
MacCallum, Kim, Malarkey, Kieholt-Glaser (1997), Muthén (1997), Muthén and Curran (1997),
Willett and Sayer (1994, 1995). However, a short explanation will be given here.
The Latent Growth Curve Model distinguishes a within-person level (individual level or
Level 1) and a between-person level (group level or Level 2). It is easiest to explain the model by
introducing the individual level first. In Figure E1, some data points for an arbitrary participant are
plotted. On the x-axis the time dimension is displayed.
T1 T0 T2 T3 T4 T5
b0
Figure E1. Linear growth curve for a single participant.
If a straight line can reasonably approximate the data, we can specify a linear growth curve:
ηti = β0i + β1i t + εti (E1)
where ηti represents the true score at time t for person i, β0i is the person’s intercept and β1i is the
person’s slope, t is the time of assessment and εti the person’s residual at time t.
256
We now extend the model to include multiple participants. In Figure E2 (top panel), the
growth curves for four participants are depicted and the bold line represents the population growth
curve.
T1 T0 T2 T3 T4 T5
Participant 1
Participant 2
Participant 4
Participant 3
Y
T1 T0 T2 T3 T4 T5
Participant 1
Participant 2
Participant 4
Participant 3
X
Figure E2. Four individual linear growth curves and the population growth curve (bold) for variable y shown in top panel and for variable x displayed in the bottom panel.
257
The lines differ in their starting points as well in their slopes. The introduction of multiple
participants may create variation in both the individual intercepts and slopes. In the Structural
Equation Modeling framework the intercepts and slopes are treated as latent variables and hence in
a linear model the observed scores of each participant can be explained by an intercept factor score,
a slope factor score and a time-specific residual. Accordingly, we change our notation and replace
β0i with η0i and β1i with η1i to express that these are treated as latent factors (intercept and slope
factor). In a linear growth model the factor loadings are fixed constants and are proportional to the
elapsed time from the first measurement occasion. In a six-wave study with equispaced data, we
can fix the values of the factor loadings to 0, 1, 2, 3, 4 and 5. We can now formulate a between
model (Level 2) where the individual slopes and intercepts are expressed as deviations from the
population slope and intercept respectively.
ηti = µ0 + η0i + (µ1 + η1i )t + εti (E2)
or, equivalently,
ηti = µ0 + µ1t + (η0i + η1i t + εti ) (E3)
The last formulation shows that the model can be specified as two additive components: a fixed part
(parameters without subject indices) and a random part (subject indices added). If we take the
expectancies of Equation E3 we find that these can be expressed by the parameters of the fixed part
(the mean intercept and the mean slope). The variances and covariances of Equation E3 refer to the
random part and the parameters are the variance of the intercept factor, the variance of the slope
factor, the covariance between both factors, and the variances of the time specific residuals.
It is convenient to fix the factor loading for the first measurement occasion at the value of
zero. In this case the intercept represents the expected initial value for a particular participant. In the
linear model, the model is a factor model with fixed factor loadings (referring to the time elapsed
from the first measurement occasion). A graphical model is shown in Figure E3. Note also that to
estimate the parameters that belong to the fixed part of the model, the vector of observed means has
to be supplied along with as the covariance matrix.
From the perspective of an applied researcher, it is more interesting to go beyond the
description of individual change and include predictors for the differences in individual trajectories.
For instance, if two variables have been measured on several occasions, it might be interesting to
258
1
t5-t1
t4-t1
t3-t1
t2-t1
1 1 1 1
ηt=1 ηt=2 ηt=3 ηt=4 ηt=5
slope factor intercept factor
η0 η1
Figure E3. Latent Linear Growth Curve Model specified as a factor model with all factor loadings fixed (note that the first slope factor loading is fixed to the value of zero). relate both developments. In these multivariate or cross-domain growth curve models hypotheses
can be formulated in which characteristics of one growth curve may have predictive value for
characteristics for another growth curve. For instance, participants who have a steeper slope in
variable x may also tend to have higher slopes on variable y. In this case changes in both processes
are related. Alternatively, participants who tend to have higher initial values on variable x may have
on average higher slopes on variable y. This is displayed in Figure E2 (variable y is displayed in the
top panel and variable x is shown in the bottom panel). Also, constant background variables may be
used for explaining differences in growth.
If a linear function is not appropriate to describe the data, quadratic or even higher order
polynomials can be used instead. But Willett (1989, p. 590) remarked that in many instances a
linear function might be an acceptable approximation. There are several interpretations for the
existence of time-specific residuals. First, there may be measurement error, but in the case that a
measurement model is included, the growth curve refers to the true variates. A second interpretation
is that the presence of states is responsible for the more irregular short-termed changes. Kenny &
Campbell (1989) argued that many psychological constructs probably have both traitlike and
statelike aspects. The use of growth curves enables a decomposition of intraindividual ‘trait
changes’ (Nesselroade, 1991) and state changes (see also McArdle & Woodcock, 1997). A third
interpretation of the residual variance is related to approximation error: The model is somewhat
259
misspecified. This might be caused by variables that are omitted from the model. After the
introduction of time-varying covariates to the model, the chosen growth function may better
describe the underlying development over time (after controlling for other time-specific influences).
Therefore, there are many explanations of why the changes in many data sets seem somewhat
erratic, but it may very well be that the underlying developments over time are much smoother and
individual linear trend lines may give a useful approximation of the developmental process.
An alternative way to specify a nonlinear model is to estimate some of the factor loadings
(except those necessary for identification). Statistically, a linear model is still estimated, but the
nonlinear interpretation emerges by relating the estimated factor loadings to the real time frame.
This is displayed in Figure E4.
T1 T0 T2 T3 T4 T5 T2* T3* T4* T5* T1* T0*
Real Timeframe
Estimated Timeframe
Figure E4. Nonlinear growth curve with free estimated factor loadings for T2 to T5.
In this figure, the first factor loading is fixed at zero and the second loading is also fixed (e.g., at the
value of 1). Apparently, by stretching and shrinking the time axis one can simulate an acceleration
and deceleration of the time dimension, again assuming a constant rate of change. Therefore, a new
time frame is estimated and the transformation to the real time frame gives the nonlinear
260
interpretation. For instance, the estimate of T2 is larger than the real time elapsed, so apparently
more positive change has taken place than would be predicted linearly.
A complication may arise in models containing two or more growth curves. If these curves
are all specified as nonlinear by freeing some of the factor loadings, it is not possible to test the
significance of some growth curve parameters. This can be explained as follows: For each growth
curve at least two factor loadings have to be fixed for identification purposes. However, which
loadings one chooses and to which values the loadings are fixed, the z values of some of the growth
parameter estimates in these multivariate nonlinear latent growth curve models. Because the
fixation schemes of the factor loadings of the growth curve models are arbitrary to some extent, the
unstandardized estimates and the standard errors are arbitrary as well (and their ratio is not
constant). Fortunately, the correlations between the intercept and slope factors are not influenced by
fixation schemes with the same choice for the zero point of the time axis. However, a shift in the
time axis by choosing a different zero point leads to additional complications (Rovine & Molenaar,
1998).
References
Curran, P.J. (in press). A latent curve framework for the study of developmental trajectories in
adolescent substance use. In J. Rose, L. Chassin, C. Presson, & J. Sherman (Eds.), Multivariate
applications in substance use research. Hillsdale NJ: Erlbaum.
Kenny, D.A., & Campbell, D.T. (1989). On the measurement of stability in over-time data. Journal
of Personality, 57, 445-481.
MacCallum, R.C., Kim, C., Malarkey, W.B., & Kiecolt-Glaser, J.K. (1997). Studying multivariate
change using multilevel models and latent curve models. Multivariate Behavioral Research, 32,
215-253.
McArdle, J.J., & Woodcock, R.W. (1997). Expanding test-retest designs to include developmental
time-lag components. Psychological Methods, 2, 403-435.
Muthén, B. (1997). Latent variable modeling with longitudinal and multilevel data. In A. Raftery
(Ed.), Sociological Methodology (pp. 453-480). Boston: Blackwell Publishers.
Muthén, B.O., & Curran, P.J. (1997). General longitudinal modeling of individual differences in
experimental designs: A latent variable framework for analysis and power estimation.
Psychological Methods, 2, 371-402.
261
Nesselroade, J.R. (1991). Interindividual differences in intraindividual change. In L. M. Collins &
J.L. Horn, Best methods for the analysis change: Recent advances, unanswered questions, future
directions (pp. 92-105). Washington, DC.: American Psychological Association.
Rovine, M.J. & Molenaar, P.C.M. (1998). The covariance between level and shape in the latent
growth curve model with estimated basis vector coefficients. Methods of Psychological Research,
3, 95-107.
Willett, J.B. (1989). Some results on reliability for the longitudinal measurement of change:
Implications for the design of studies of individual growth. Education and Psychological
Measurement, 49, 587-602.
Willett, J.B., & Sayer, A.G. (1994). Using covariance structure analysis to detect correlates and
predictors of individual change over time. Psychological Bulletin, 116, 363-381.
Willett, J.B., & Sayer, A.G. (1995). Cross-domain analysis of change over time: Combining growth
curve modeling and covariance structure analysis. In G.A. Marcoulides & R.E. Schumacker (Eds.).
Advanced structural equation modeling: Issues and techniques, (pp. 125-157). Mahwah, NJ:
Erlbaum.
262
263
Samenvatting
Deze dissertatie bestaat uit twee gedeelten. Het eerste gedeelte is theoretisch en beschrijft een
algemeen longitudinaal model dat valt binnen de klasse van structurele vergelijkingsmodellen. Een
speciaal geval van dit algemene longitudinale model is al voldoende algemeen om enige uit de
literatuur bekende longitudinale modellen als bijzondere gevallen te beschouwen. Aan de orde
komen autoregressieve en latente groeimodellen. Echter, om een tweede orde autoregressief model
te beschrijven moet terug gegrepen worden op het meest algemene model. Er wordt beschreven
welke aannamen over hoe verandering tot stand komt ten grondslag liggen aan de verschillende
modellen. Veranderingen kunnen beschreven worden als expliciete functie van de tijd maar als ook
als een proces dat gedeeltelijk voorspelbaar is uit voorafgaande toestanden waaraan steeds
innovaties gebaseerd op toeval worden toegevoegd. Recentelijk werd een hybride model
geïntroduceerd door Bollen en Curran dat te beschouwen is als een samensmelting van een eerste
orde autoregressief model en een latente groeicurve. Een kleine aanpassing van het eerder
genoemde submodel bleek al voldoende te zijn om ook dit hybride model als een speciaal geval
hiervan te beschouwen. Ook bleek het eenvoudig te zijn om het algemene longitudinale model uit te
breiden tot multivariate modellen waarbij meerdere veranderingsprocessen tegelijkertijd beschreven
kunnen worden. Ten slotte werd ingegaan op de schaalinvariantie van latente groeimodellen.
Deel twee bestaat uit drie artikelen, waarbij longitudinale modellen toegepast worden in
vraagstukken uit de Arbeids- en Organisatiepsychologie. Deze hebben betrekking op data uit de
voormalige DDR. Dit onderzoeksproject is gestart onmiddellijk na de Duitse hereniging in 1990.
De centrale vraagstelling van dit project richt zich op het vaststellen van de determinanten van
psychisch welbevinden en het nemen van initiatief in een situatie die gekenmerkt wordt door vele
ingrijpende veranderingen.
Het eerste artikel behandelt een socialiserend-occupatie model waarbij de effecten van kenmerken
van werk werden onderzocht op de neiging van werknemers om initiatieven te ontplooien. Er werd
verondersteld dat de mate van regelmogelijkheden, waarover een werknemer beschikt om zijn/haar
taak uit te voeren en de complexiteit van het werk een socialiserende werking kan hebben. In het
bijzonder werd gesteld dat werk waarbij men weinig invloed kan uitoefenen op de arbeidstaken en
werk dat slechts uit eenvoudige handelingen bestaat, een slechte voedingsbodem vormt voor
opdoen van positieve leerervaringen. Daarentegen geeft werk met regelmogelijkheden en enige
complexiteit de gelegenheid om nieuwe vaardigheden aan te leren en daarbij grenzen te
overschrijden. Dit leidt tot een verandering in de oriëntatie van werknemers. Deze oriëntatie wordt
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gekenmerkt door het besef dat men beschikt over een gedragsrepertoire dat tot gewenste uitkomsten
kan leiden, door de overtuiging dat de omgeving beïnvloedbaar is, en door het streven zelf meer
invloed uit te oefenen ondanks de mogelijke nadelen die eraan verbonden zijn (meer
verantwoordelijkheid en kans op falen). Deze op de omgeving gerichte oriëntatie wordt geacht een
positief effect te sorteren op het ontplooien van initiatieven. Initiatief werd gedefinieerd als
autonoom pro-actief gedrag waarbij men zelf doelen stelt die verder gaan dan het eenvoudigweg
uitvoeren van de taak waarvoor men aangesteld is. Deze door de werknemer zelf gestelde doelen
vallen weliswaar binnen de door de organisatie nagestreefde doelstellingen, maar zijn niet
eenvoudigweg afleidbaar uit de direct opgedragen taak. Veelal hebben de zelf gestelde doelen
betrekking op de (middel)lange termijn. Verder werd initiatief zodanig gedefinieerd dat de
werknemer over een zeker doorzettingsvermogen moet tonen indien hindernissen de
verwezenlijking van deze doelen dreigen te belemmeren. Het resultaat van het ontplooien van
initiatieven werd over het algemeen geacht positief te zijn. Mogelijke gevolgen zijn dat werknemers
betere banen verkrijgen die meer invloed met zich mee brengen en een grotere complexiteit met
zich mee dragen. Ook kan het zijn dat initiatiefrijke werknemers een verbeterd takenpakket
toegewezen krijgen met meer regelmogelijkheden. Door initiatief te tonen kan de werknemer de
omgeving en zijn taak deels zelf bepalen. Aan de andere kant gaat het socialiserend occupatie
model ervan uit dat de werknemer ook enigszins gevormd door zijn/haar omgeving. Dit theoretisch
model werd getoetst met verschillende structurele vergelijkingsmodellen. De resultaten gaven aan
dat het best passende model een goede beschrijving gaf van de data. In belangrijke mate werd steun
gevonden voor de gevonden theorie. Helaas dienen deze resultaten als voorlopig te worden
bestempeld, omdat door beperking van de gebruikte software onvoldoende rekening kon worden
gehouden met complicaties die ontstonden doordat vele respondenten niet gedurende de volledige
onderzoeksperiode over werk beschikten. In de getoetste modellen werden de gegevens als
ontbrekend aangemerkt, waardoor impliciete assumpties gemaakt werden over de meest plausibele
populatiewaarden. Echter, aannamen over plausibele waarden in de populatie voor werkgerelateerde
variabelen voor mensen zonder werk zijn onbevredigend, omdat deze waarden ook in de populatie
behoren te ontbreken omdat zij simpelweg niet van toepassing zijn. Recente ontwikkelingen op het
gebied van statistische software waarbij latente klasse modellen en structurele
vergelijkingsmodellen worden geïntegreerd, maken het mogelijk om meer adequate modellen te
toetsen.
Het tweede artikel behandelt de relatie tussen stressoren op het werk en stressklachten. De
volgende stressoren werden gemeten: de onzekerheid over het behoud van werk, het werken onder
tijdsdruk, het omgaan met organisatorische problemen, sociale stressoren en onzekerheid als gevolg
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van rolambiguïteit en rolconflicten. De stressklachten omvatten depressieve klachten,
psychosomatisch klachten, gevoelens van irritatie en piekeren over het werk (buiten werkuren).
Verschillende modellen werden getoetst. In het eerste model werd één factor verantwoordelijk
gehouden voor het verklaren van zowel de stressoren als de stressklachten. In de literatuur wordt
negatieve affectiviteit genoemd die zowel de waarneming van stressoren als ook de stressklachten
kunnen verklaren. Er bleek geen empirische steun voor dit model te zijn.
De stressklachten konden goed benaderd worden door groeicurve modellen. In deze modellen wordt
voor iedere persoon een groeicurve opgesteld, die het verloop van de stressklachten als een continue
functie van de tijd weergeeft. Op elk meetmoment kunnen afwijkingen van deze curve optreden als
gevolg van tijdelijke schommelingen. Non-lineaire modellen werden gefit waarbij voor iedere
persoon de verandering in de tijd niet constant was, maar variatie vertoonde. Ook de stressoren
konden goed benaderd worden door groeicurven, hoewel hier de autoregressieve modellen een iets
betere fit te zien gaven. Het lag dan ook voor de hand een hybride model op te stellen waarbij de
stressklachten als groeicurven werden gemodelleerd en de stressoren een autoregressief beeld te
zien gaven. Tegelijkertijd werden er ook modellen gefit waarbij zowel de stressklachten als de
stressoren als groeicurven werden gemodelleerd. Het laatste model bood de mogelijkheid te
onderzoeken of de trends in de stressklachten correleerde met de trends in de stressoren.
Systematische veranderingen in piekeren over het werk bleek samen te gaan met trendmatige
veranderingen in het werken onder tijdsdruk en het ervaren van onzekerheid. De individuele trends
in sociale stressoren bleek in zekere mate parallel te zijn met de trends in psychosomatische
klachten.
In longitudinale modellen kan de tijdsvolgorde van gebeurtenissen gebruikt worden om
uitspraken te doen over oorzaak- gevolg relaties. In een van de opgestelde modellen werd gekeken
of personen met veel stressklachten aan het begin van de onderzoeksperiode een ander verloop van
hun stressoren lieten zien. Daarbij zijn twee theorieën ban belang. De ene theorie gaat ervan uit dat
mensen met veel stressklachten minder presteren en daardoor terugvallen tot steeds slechtere banen,
waardoor ze aan nog meer stressoren blootstaan. De anderen theorie voorspelt het
tegenovergestelde: mensen die veel stressklachten hebben, zullen alles in het werk stellen om zich
beter te voelen en dan ook minder belastend werk gaan zoeken. De laatste theorie werd meer
ondersteund, maar er werd geconcludeerd dat beide mechanismen een rol kunnen hebben gespeeld
voor verschillende subgroepen.
Een ander model dat gebruik maakt van de tijdsvolgorde is het incubatie model. Hier wordt
geponeerd dat het geruime tijd kan duren voordat de gevolgen van stressoren zich manifesteren in
stressklachten. Dit kan getoetst worden door de correlatie tussen het aanvangsniveau van stressoren
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en het verloop van de stressklachten. Voor dit model werd geen steun gevonden. Een probleem met
dit model is dat slechts het aanvangsniveau van stressoren bekeken werd, terwijl het verloop van de
stressoren zelf natuurlijk eveneens kortdurende effecten kan hebben op de stressklachten.
Kortdurende effecten konden worden getoetst met het hybride model, waarbij de
stressklachten als groeicurven werden gemodelleerd en de stressoren een autoregressief verloop
hadden. Hierdoor is het mogelijk de tijdspecifieke afwijkingen van de groeicurven te laten verklaren
door het momentane niveau van de stressoren. Dit model gaat ervan uit dat de stressklachten een
trendmatige verandering ondergaan, maar dat op elk moment afwijkingen kunnen ontstaan door een
meer of minder dan gemiddeld niveau van de stressoren. Het bleek dat synchrone effecten van
stressoren redelijk goed deze schommelingen in de stressklachten konden verklaren. Opvallend was
dat de synchrone effecten van het werken onder tijdsdruk sterke effecten hadden op de niet
trendmatige schommelingen in het piekeren over het werk (buiten werkuren). Er werd dan ook
geconcludeerd dat zowel korte termijn effecten als ook lange termijn effecten relaties optraden.
Het derde artikel onderzoekt de effecten van optimisme op het psychische welbevinden. In
de literatuur wordt veelvuldig gesproken over de positieve effecten van de
persoonlijkheidseigenschap optimisme. Optimisme wordt gedefinieerd als het hebben van positieve
toekomstverwachtingen in het algemeen. De gunstige invloed van optimisme zou verklaard kunnen
worden door een effectievere manier om met stress om te gaan. Optimisten zouden meer
probleemgericht omgaan met stress omdat ze in het algemeen verwachten dat dit positief zou
uitpakken. Daarentegen zouden pessimisten meer gericht zijn op het verminderen van de
stressklachten en zich minder bezig houden met het aanpakken van de problemen zelf. In het
algemeen wordt ervan uitgegaan dat een probleemgerichte aanpak effectiever is doordat stressoren
met wortel en al uitgeroeid worden.
In de literatuur wordt onderkend dat de schaal om optimisme te meten (Life Orientation
Test), bij factoranalyse een twee factor oplossing laat zien, waarbij de vier positief gestelde items
laden op de ene factor (optimisme) en de vier negatief geformuleerde items op de tweede factor
(pessimisme). Beide factoren bleken slechts een zwakke tot matige samenhang te vertonen. Verder
bleek dat beide factoren een verschillend patroon van samenhangen vertoonden met andere
constructen. Deze resultaten werden eveneens in deze studie teruggevonden. Sommige
onderzoekers menen dat methodologische artefacten verantwoordelijk zijn voor het uiteenvallen
van de optimisme schaal, maar overtuigende resultaten zijn vooralsnog niet gepubliceerd. Hierdoor
is het aan te bevelen om optimisme en pessimisme voorlopig als afzonderlijke constructen te
behandelen.
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Psychisch welbevinden werd gemeten met dezelfde schalen als de stressklachten uit
hoofdstuk 5, maar de term werd aangepast aan de vigerende terminologie uit de optimisme
literatuur.
In dit hoofdstuk werden eveneens groeicurven gemodelleerd en het bleek dat zowel de
veranderingen in optimisme als pessimisme goed te modelleren waren als lineaire groeicurven.
Eveneens werden er verschillen modellen onderzocht om de effecten van
optimisme/pessimisme op psychisch welbevinden te onderzoeken.
Zowel directe als indirecte modellen werden opgesteld. In de indirecte modellen werd de
voor de persoon kenmerkende stijl hoe men met stress omgaat (‘coping style’) als mediërende
variabelen gemodelleerd. De individuele stressaanpak werd gemeten door de afzonderlijke items
voor de gehele periode te sommeren. Door situatiespecifieke effecten uit te middelen werd getracht
de voor de persoon typische coping stijl te meten.
Slechts twee verschillende groeimodellen werden getoetst: een model zonder dat de
tijdsspecifieke residuen van de groeicurven van optimisme/pessimisme met elkaar correleerden en
een model waarbij deze wel correleerden. De betekenis van de correlaties tussen residuen is dat de
niet systematische schommelingen in optimisme (pessimisme) samenhangen met de korte termijn
fluctuaties in psychische welbevinden. Men kan door stemmingswisselingen geneigd zijn een wat
optimistische kijk te hebben en tevens het eigen welbevinden wat hoger in te schatten. Tevens
kunnen de systematische trends in optimisme en psychisch welbevinden parallel verlopen.
Modellen waarin depressie opgenomen was bleken beter te passen met gecorreleerde residuen,
terwijl de modellen met psychosomatische klachten, irritatie en piekeren over het werk beter pasten
zonder deze correlaties tussen de residuen. Echter, het patroon van de correlaties tussen de residuen
in de depressie modellen was zodanig inconsistent, dat een inhoudelijke interpretatie van deze
correlaties verworpen werd.
Verschillende hypothesen konden getoetst worden met behulp van de parameters van de
groeimodellen.
Het aanvangsniveau van vooral pessimisme en depressie en in mindere mate irritatie bleken
significant samen te hangen. Mogelijkerwijze kunnen erfelijke factoren of factoren uit de vroege
kindertijd deze samenhang verklaren.
De trends in pessimisme en de trends in depressie bleken zeer sterk samen te hangen. In wat
mindere mate gold dit voor de samenhang in de trends van pessimisme en irritatie. Trends in
optimisme en trends in psychisch welbevinden hingen nauwelijks samen.
Het aanvangsniveau van optimisme had een significant negatief effect op de verandering in
depressie en psychosomatische klachten. Indirecte effecten bleken hierbij geen rol te spelen. In het
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algemeen werden slechts weinig significante effecten van de coping stijl variabelen op
veranderingen in psychisch welbevinden gevonden. Uitzondering waren de negatieve effecten van
planning en probleemgerichte aanpak op individuele trends in depressie, terwijl een emotiegerichte
aanpak juist de depressie klachten bevorderderden.
Opmerkelijk was dat het omgaan met stress redelijk voorspelbaar was op grond van het
aanvangsniveau van psychisch welbevinden en de initiële status van optimisme en pessimisme.
Mensen die zich aan het begin van de onderzoeksperiode slecht voelden (depressief, veel
psychosomatische klachten, geïrriteerd), maakten meer gebruik van een stressaanpak gericht om de
symptomen te verzachten (emotiegerichte aanpak, dagdromen en wensdenken), terwijl mensen die
aan het begin van de periode veel piekerden over hun werk juist gekenmerkt werden door een
probleemgerichte aanpak (inclusief planning). Optimisten maakten zowel meer gebruik van een
probleem gerichte als ook een emotiegerichte aanpak. Het laatste was geheel onverwacht en niet
bekend uit de literatuur. Pessimisten maakten minder gebruik van planning, maar meer gebruik van
emotiegerichte aanpak en gaven zich over aan dagdromen en wensdenken.
Samenvattend kan geconcludeerd worden dat in deze dissertatie is aangetoond dat
groeicurve modellen voor de toegepaste onderzoeker een grote waarde hebben. Zeker met het
verschijnen van nieuwe software die het mogelijk maakt latente klasse modellen te integreren met
structurele vergelijkings modellen zijn vele nieuwe toepassingsmogelijkheden binnen het bereik van
de onderzoeker gekomen.