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A1
Structural equation modeling
Rex B Kline Concordia University
Montréal
ISTQL Set A Concepts, models, tools
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A2
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A3
Resources
o Kline, R, B. (2012). Assumptions of structural equation
modeling. In R. Hoyle (Ed.), Handbook of structural
equation modeling (pp. 111–125). New York: Guilford. o Kline, R. B. (2013). Exploratory and confirmatory factor
analysis. In Y. Petscher & C. Schatschneider (Eds.), Applied quantitative analysis in the social sciences (pp. 171–207). New York: Routledge.
o Kline, R. B. (2013). Reverse arrow dynamics: Feedback loops and formative measurement. In G. R. Hancock and R. O. Mueller, (Eds.), Structural equation
modeling: A second course (2nd ed.) (pp. 39–76). Greenwich, CT: IAP.
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A4
Topics
o Mon: Concepts, models, tools
o Tues: Data, path models
o Weds: Estimation
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A5
Topics
o Thurs: Model testing
o Fri: CFA models
o Sat: SR models
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A6
Practice
o Weds: LISREL SIMPLIS syntax
o Thurs: LISREL Path Diagram
o Fri: Ωnyx demo
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A7
four-variable example
observed variables
neg_str cur_prob prob_sol depress
covariance matrix
76.913
55.668 249.324
33.757 115.685 478.297
21.775 53.614 60.695 37.700
sample size is 205
relationships
cur_prob = neg_str
prob_sol = neg_str cur_prob
depress = neg_str cur_prob prob_sol
LISREL output: ND = 3 SC RS MI
path diagram
end of problem
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A8
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A9
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A10
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A11
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A12
exercise, hardy, fitness, stress, illness
4422.250
-75.810 1444.000
477.204 48.944 338.560
-111.388 -292.790 -80.132 1122.250
-332.394 -379.878 -333.393 711.647 3903.750
Exercise
Hardiness
Illness
DIl
1
Stress
1 DSt
Fitness
1 DFi
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A13
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A14
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A15
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A16
Worst practices
o MacCallum, R. C., & Austin, J. T. (2000).
Applications of structural equation modeling in psychological research. Annual Review of
Psychology, 51, 201–226.
o Shah, R., & Goldstein, S. M. (2006). Use of structural equation modeling in operations management research: Looking back and forward. Journal of Operations Management, 24, 148–169.
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A17
Best practices
1. Justify specifications
2. Report psychometrics
3. Verify assumptions
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A18
Best practices
4. Report summary statistics
5. Describe method
6. Model-table-text agree?
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A19
Best practices
7. Report unstandardized
8. Describe residuals
9. Equivalent models
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A20
Best practices
10. Rethink :
Limited role
Not a criterion
Path to folly
*
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A21
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A22
Keep your eyes on the prize
1
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A23
Any monkey can find a
model that fits the data
2
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A24
Closer to fit is not closer to
truth
3
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A25
Directionality is assumed, not
tested
4
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A26
Never forget equivalent
models
5
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A27
Smart modeling
o Know your area
o Simple is good
o Build, not trim
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A28
Smart modeling
o Advantages of building:
1. Avoid identification issues
2. Prioritize hypotheses
3. Back-up list
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A29
Smart modeling
o Add from list
o Done:
1. List exhausted
2. No citations for rest
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A30
2. Identification
3. Data collection
4. Analysis
5. Respecification
6. Reporting
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A31
no
yes
4a. Model fit adequate?
6. Report results
4c. Consider equivalent or near-equivalent models
4b. Interpret estimates
yes
Justifiable respecification?
no
5. Respecify model
no yes 2. Model identified?
3. Select measures, collect data
1. Specify model
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A32
Smart modeling
o Goals:
Parsimony
Respect theory
Avoid HARKing
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A33
Hello, SEM
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A34
SEM
o Family
o Integration of MR, FA
o Flexible, extensible
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A35
SEM o Inherits from MR ( ):
Multiple predictors
B, R2 effect sizes
Means, too
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A36
SEM
o Inherits from FA ( ):
Observed vs. latent
Latents as predictors
Measurement error
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A37
SEM
o Inherits from both ( ):
Capitalizes on chance
Specification error
Misuse through
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A38
SEM
o Synergistic ( ):
Latents as outcomes
Means of latents
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A39
SEM
o Synergistic ( ):
Indirect effects (mediation)
Error covariance structure
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A40
Models
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A41
Core models
o PA
o CFA
o SR
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A42
Path models
o Structural model
o Observed variables only
o Single indicators only
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A43
Path models
o Structural model:
Causal effects
Noncausal associations
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A44
Path models
o Causal effects:
Direct
Indirect
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A45
Path models
o Indirect effects:
Part of mediation
Indirect ⇒/ mediation
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A46
Path models
o Noncausal effects:
Common cause (spurious)
Correlated with cause
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A47
CFA models
o Multiple indicators only
o L → M only
o Factors covary only
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A48
CFA models
o Classical measurement theory
o Convergent validity
o Discriminant validity
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A49
SR models o Single, multiple indicators
o L → M or M → L
o L as predictors, outcomes
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A50
SR models o Highest level model
o Advanced = SR variation
o Know and love
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A51
Examples
o Roth, D. L., Wiebe, D. J., Fillingim, R. B., & Shay, K. A. (1989).
Life events, fitness, hardiness, and health: A simultaneous analysis of proposed stress-resistance effects. Journal of Personality and Social Psychology,
57, 136–142. o Kaufman, A. S., & Kaufman, N. L. (1983). K-ABC
administration and scoring manual. Circle Pines, MN: American Guidance Service.
o Shen, B.-J., & Takeuchi, D. T. (2001). A structural model of acculturation and mental health status among Chinese Americans. American Journal of Community
Psychology, 29, 387–418.
CFA
SR
PA
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A52
Exercise
Hardiness
Fitness
1
DFi
Illness
1
DIl
Stress
1 DSt
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A53
1
1 1 1 1 1 1 1 1
1
Sequential
EHM
Hand Movements
Number Recall
ENR
Word Order
EWO
Simultaneous
ETr
Triangles Spatial
Memory
ESM
Matrix Analogies
EMA
Gestalt Closure
EGC
Photo Series
EPS
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A54
Acculturation
EGS
1
General Status
1
Acculturation
Scale
EAS
1
Percent Life U.S.
EPL
1
1
Job
EJo
1
Interpersonal
EInt
1
Stress
DSt
1
Depression Scale
DDS
1
SES
1
Education
EEd
1
Income
EInc
1
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A55
Tools
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A56
Tools
o Commercial vs. free
o Stand-alone vs. environment
o User interface
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A57
Interaction modes
Computer tool Free Environment
needed Batch
(syntax) Wizard
(template) Drawing
editor
Stand-alone programs
Amos
EQS
LISREL
Mplus
Ωnyx
Packages, procedures, or commands in larger environments
sem, lavaan, lava,
systemfit R
OpenMx R
CALIS SAS/STAT
Builder, sem, gsem Stata
SEPATH STATISTICA
RAMONA SYSTAT
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A58
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A59
QQQ
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A60
GUI liabilities
o Complex models
o Multiple-samples analysis
o Multi-level analyses
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A61
GUI liabilities
o Syntax may be easier, faster
o Diagram as archive
o Publication quality graphic
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A62
LISREL
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A63
Amos
CurrentProblems
NegativeLife Stress
ProblemSolving
Depression
D_PSD_De
1
1
D_CP
1
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A64
EQS
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A65
Mplus
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A66
Stata
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A67
Exercise
Hardiness
Illness
DIl
1
Stress
1 DSt
Fitness
1 DFi
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A68
Tool support
o Amos:
Blunch, N. (2013). Introduction to structural equation
modeling using IBM SPSS Statistics and Amos (2nd ed.). Thousand Oaks, CA: Sage.
Byrne, B. M. (2010). Structural equation modeling
with Amos: Basic concepts, applications, and
programming (2nd ed.). New York: Routledge.
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A69
Tool support
o EQS:
Byrne, B. M. (2006). Structural equation
modeling with EQS: Basic concepts,
applications, and programming (2nd ed.). New York: Routledge.
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A70
Tool support
o lavaan:
Beaujean, A. A. (2014). Latent variable
modeling using R: A step-by-step guide. New York: Routledge.
http://lavaan.ugent.be/
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A71
Tool support
o LISREL:
Vieira, A. L. (2011). Interactive LISREL in
practice: Getting started with a SIMPLIS
approach. New York: Springer.
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A72
Tool support
o Mplus:
Geiser, C. (2013). Data analysis with Mplus. New York: Guilford.
Wang, J., & Wang, X. (2012). Structural equation
modeling: Applications using Mplus. Chichester, UK: Wiley.
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A73
Tool support
o Stata:
Acock, A. C. (2013). Discovering structural
equation modeling using Stata 13. College Station, TX: Stata Press.
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A74
Statistics
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A75
Continuous
o Theoretically infinite scores
o In practice, range > 15
o Symmetrical distribution
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A76
Likert scale
o Items
o E.g., 1 = disagree, 2 = not sure 3 = agree
o Ordinal, ordered-categorical
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A77
Scales vs. items
o Scale: Σ score, continuous
o Item: Noncontinuous
o Proper method
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A78
Other outcomes
o Dichotomous (binary), k = 2
o Nominal, k > 2
o Logit or probit link function
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A79
Other outcomes
o Agresti, A. (2007). An
introduction to categorical
data analysis. Hoboken, NJ: Wiley.
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A80
Other outcomes
o Count variables
o Poisson distribution
o Mean ≈ variance
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A81
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A82
Covariance
o Continuous only
o Linear only
o covXY = rXY SDX SDY
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A83
rXY = .55, SDX = 3.5, SDY = 2.0
covXY = .55 (3.5) (2.0) = 8.1
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A84
Raw data
Case X W Y
A 3 65 24
B 8 50 20
C 10 40 22
D 15 70 32
E 19 75 27
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A85
Covariance matrix
38.500
42.500 212.500
17.500 51.250 22.000
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A86
Correlation matrix + SDs
1.000
.470 1.000
.601 .750 1 .000
6.205 14.577 4.690
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A87
Raw data not needed
comment spss, y on x, w, matrix input.
matrix data variables=x w y/contents=mean sd n corr
/format=lower nodiagonal.
begin data
11.000 60.000 25.000
6.205 14.577 4.690
5 5 5
.470
.601 .750
end data.
regression matrix=in(*)/variables=x w y/dependent=y
/enter.
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A88
MR
o Y, X1, X2
o 1 1 2 2Y B X B X A= + +
o ˆYYR r=
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A89
Coefficients
B1 = 2.30, B2 = 6.35, A = 10.50
b1 = .65, b2 = .30
Capitalization on chance
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A90
Comparisons
Predictors Samples B b
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A91
MR assumptions
o Y is continuous
o Linear only
o No interactions
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A92
MR assumptions
o r11 = r22 =1.00
o No indirect effects
o No specification error
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A93
No specification error
No irrelevant predictors
No omitted predictors that covary with measured predictors
Correct functional form
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A94
Heartbreak of L.O.V.E
Y = suicide attempts
X1 Therapy
X2 Depression
rY1 = .19 rY2 = .49 r12 = .70
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A95
Heartbreak of L.O.V.E
Y = suicide attempts
X1 Therapy
X2 Depression
rY1 = .19 rY2 = .49 r12 = .70
b1 = −.30 b2 = .70 R = .54
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A96
Results depend on
What is measured (data)
What is not (omitted variables)
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A97
Predictor entry
Rational (e.g., HMR)
Statistical (e.g., stepwise)
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A98
Stepwise flaws
Results are wrong
Will not replicate
Banned
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A99
SEM version
MIs only
Same problems
Think for yourself