Acta Psychologica 46 (1980) 2 5 7 - 2 6 9 Q North-t tol land Publishing Company

THE INTEGRATION OF MOTIVATIONAL INFORMATION: A CONJOINT MEASUREMENT ANALYSIS *

Geert De SOETE ** State University of Ghent, Ghent, Belgium

Accepted June 1980

Within Anderson 's (1974a, b, c, 1978b) informat ion integration theory, tlie integration of motivational informat ion was investigated by means of conjoint measurement techniques. Eighteen university s tudents were asked to judge hypothet ical co-students characterized by three features (intelligence, motivat ion and the extent to which they study) according to their chances to pass. Both rank order data and ratings were obtained. The orderings of most subjects could be represented very well by an additive model. A polynomial regression procedure was applied to determine the shape of the response funct ion for the ratings. As this funct ion was quite linear for all subjects, the ratings could be said to form an interval scale.

In all kinds of circumstances, judgments are being made about people and situations based on a wide variety of information. Both the clini- cian, the counselor and the personnel manager have to sum up the client, respectively the job applicant, by integrating several diagnostic data. But also in the daily interaction, people continuousIy attribute to each other qualities, intentions and abilities inferred from certain per- ceived features. It was originally in connection with the latter area, viz., person perception, that Anderson developed his information integra- tion theory. Soon, his theory was applied successfully to the most diverse areas (Anderson 1974a, b, c, 1978b). In this paper we shall investigate the integration of motivational information by use of con- joint measurement techniques.

* I wish to thank Andr6 Vandierendonck for his encouragement and numerous helpful sugges- tions in preparing the manuscript . Ivan Mervielde is also gratefully acknowledged for his critical remarks on an earlier draft. ** Aspirant of the Belgian 'Nationaal Fonds voor Wetenschappelijk Onderzoek ' . Presently at the L.L. Thurs tone Psychometr ic Laboratory, University of North Carolina. Davie Hall 013 A, Chapel Hill NC 27514, U.S.A.

257

258 G. De Soete / Information integration

Anderson's information integration theory

With his integration theory Anderson (1974a, b ,c , 1978b) wants to describe how several kinds of information are combined to make up a unitary judgment. Two operations are sequentially distinguished: valua- tion and integration. Valuation deals with the internal dimensional representation of each stimulus component (cf Matthai~s et al. 1976). Indeed, each task requires a preliminary ewduation of the meaning and relevance of each piece of stinmlus information (Anderson 1974b). Suppose the stimulus set consists of the cartesian product of three fac- tors A, B and C, which represent three different facets of the stimuli. Valuation of a stimulus (ai, bj, ck) means that scale valtles.f'~ (ai),f2(bj) and f3(ck) (with fl, f2 and f3 real-valued functions) are assigned to the stimulus components. Once the different pieces of information are evaluated, they can be integrated in an overall judgment: the scale values fl(ai), f2(bj) and .[3(ck) are combined by the integration ftmc- tion I in a latent response:

riik = l(f,(ai), f2(bi), fa(ck)) ( 1 )

which results in a manifest response Rij k by means of the response function M:

Ri/k = M(ri/k) (2)

A scheme of these processes is presented in fig. 1 which is a modified version of Anderson's (1970, 1974a, 1977) functional measurement diagram.

STIMULUS PSYCHOLOGICAL LATENT MANIFEST COMPONENTS STIMULUS C O M P O N E N T S R E S P O N S E R E S P O N S E

a i . ~, f l i a i )

b j .) f 2 ( b j )

c k :> f 3 ( c k )

~- r i j k

I N T E G R A T O R

:)' Rij k

VALUATION INTEGRATION RESPONSE FUNCTIONS FUN CT ION FUNCT ION

Fig. 1. A scheme of Andersons ' s informat ion integration theory (this is a modified version of Anderson ' s (1970, 1974a, 1977) funct ional measurement diagram).

G. De Soete / hfformation integration 259

Integration theorists generally take the valuation for granted and concentrate primarily on the integration. Mervielde (1977) explains this by indicating that valuation itself can be seen as a result of an integra- tion operation. Anderson has repeatedly shown how simple algebraic models are apt to describe this process. Especially additive models were successful. Anderson draws a sharp psychological distinction between what he calls a simple adding and an initial impression weighted averaging model. In the common case of constant weights per factor, both models can respectively be written as:

ri i k = w l f a ( a i ) + w2f2(b/) + w 3 ~ 3 ( c k ) (3)

and

rijt = 00Io + ViA(ai) + v2f2(b,) + v3f3(cD (4)

with v0 + vl + v2 + v3 = 1. In eq. (4) I0 stands for the initial impression of the subject. Contrary to the w in (3), the v in (4) are only relative weights. However, it can be proved (cf Sch6nemann et al. 1973) that whenever the data fit the following model:

rijk = ~l(ai) + ~b2(bi) + 4~3(ck) (S)

they also fit eqs. (3) and (4). Consequently, in this paper we do not dis- tinguish between (3) and (4) and we consider the additive model (5) only. Although the additive model has played a dominant role, several kinds of interactive models have, rather sporadically, been found.

Integration models are usually validated by means of functional mea- surement, a methodology developed by Anderson (1970, 1974a, 1977, 1978a) parallel to his integration theory. In most information integra- tion experiments the overt responses consist of ratings, which are analyzed by means of ANOVA. Absence of significant interaction effects is interpreted as evidence for an additive model and for the validity of the assumption that the response scale is an interval scale (cf. Anderson 1977, 1978a; Klitzner and Anderson 1977). If however an interaction is detected, one is never sure whether this is due to the judg- mental process itself, or to the nonlinearity of the response function. In this case, it is safer to assume only a monotonic relationship between the latent and manifest responses and to diagnose the model by relying

260 G. De Soete /hLtbrmation integration

on the ordinal characteristics of the data. This can be done by axiomatic conjoint measurement that provides a number of qualitative tests (axioms) which are necessary and ahnost sufficient conditions for the different combination rules (Krantz e t al. t971; Krantz and Tversky 1971). Once the underlying model is determined in this way, the data can be scaled according to it and the relation between the latent and manifest responses can be empirically investigated by means of poly- nomial regression.

The integration of motivational information

When judging the future performance of a person, people generally have not only an impression of the skills and abilities of the person, but they also know more or less his motivation. How will this motivational infor- mation influence the judgment? Intuitively, the idea of motivation as a multiplier seems appealing. This is for instance apparent from Hull's well known formula:

Reaction Potential = Drive X Habi t .

The idea occurs also explicitly in Heider's (1958) at tr ibution theory:

Performance = Motivation X Ability (1958: 83 ) . {6)

This proposit ion has been empirically verified by Anderson and Butzin (1974), together with two derived formulas:

Motivation = Performance X (Ability) -1 (7)

Ability = Performance × (Motivation)- ' (8)

ANOVAs on the ratings of two different groups of subjects indicated for (7) as well as for (8) rather an additive than a multiplicative model. Only eq. (6) has been confirmed. However, if one considers the averaged ratings with regard to (6), as plotted in the first panel of figs. 1 and 2 of Anderson and Butzin (1974), as ordinal data, one can represent them very well according to an additive model by lneans of ADDALS (de

G. De Socte /Information integration 261

Leeuw e t al. 1976) [11. The stress [2] value for both groups is less than 0.0001.

Similar results have been obtained by Ullrich and Painter (1974). In their experiment students had to judge job applicants according to their ability for filling a managerial position, given their intelligence, experi- ence and achievement motivation. A conjoint measurement analysis of the results revealed an additive model for several subjects. In order to investigate further the role of motivational information we performed the following experiment. University students were asked to judge the chances to pass of a set of hypothetical co-students which were charac- terized by their intelligence (l), motivation (M) and the extent to which they studied (S). Working with three factors instead of two has sub- tantial advantages (Klitzner and Anderson 1977) of which the most important is that a better discrimination between additive and interac- tive models is possible.

Given the findings in person perception and attribution (Anderson 1974b, c, 1978b), we can expect in accordance with the results of Ullrich and Painter (1974), an additive model I + M + S. If however Anderson and Butzin's (1974) proposal

Future Performance = Past Performance + Motivation × Ability (1974: 609)

is valid, a dual-distributive model S + M X I is to be found because the extent to which one studies is a kind of performance, which in turn results from an interaction between ability and motivation. If on the contrary one considers S as a part of the ability to succeed, then a distributive combination rule (I + S) X M must be expected.

The expe r imen t

Method

Su bjec ts

Eighteen first year s tudents , 7 males and 11 females, all enrol led in the Facul ty of Psychological and Educat ional Sciences at the Universi ty of Ghen t , par t ic ipated

[ 1 ] We thank Norman H. Anderson for making this data available to us. [2] The stress is a goodness of fit measure which is the square root of the normalized sum of squared deviations between tile optimally transformed data and the model. ADDALS uses Kruskal's (1965) stress formula two.

262 (;. De Soete /In¢brmation in tegration

vo lun ta r i ly in par t ia l fu l f i lmen t s of cer ta in class r equ i r emen t s . No one was acqua in t ed e i the r wi th con jo in t m e a s u r e m e n t or wi th A n d e r s o n ' s i n f o r m a t i o n in t eg ra t ion theory .

St imul i The s t imul i cons i s ted of desc r ip t ions of h y p o t h e t i c a l first year s tuden t s , wh ich were charac te r i zed by th ree fea tures : in te l l igence (3 levels: IQ = 100, 120, 140), mot iva- t ion (3 levels: no t , weakly, s t rongly m o t i v a t e d ) and the e x t e n t to which they s tud ied (2 levels: s tudies l i t t le, much) . By c o m b i n i n g the th ree variables factor ial ly , 18 s t imul i were ob ta ined . Inc lus ion of an add i t iona l s t imulus (IQ = 125, weakly mo t iva t ed , s tudies l i t t le) for conven ience of design yie lded a to ta l of 19 s t imuli .

Procedure As we i n t e n d e d to ana lyze the j u d g m e n t s n o n m e t r i c a l l y ( ax iom analyses) as well as met r ica l ly ( p o l y n o m i a l regressions) , it was desirable to ga ther no t on ly ra t ings bu t also expl ic i t o rd ina l data , because ties or m i n o r o rder invers ions in the rat ings due to r a n d o m j u d g m e n t a l f l uc tua t ions can cause m a n y v io la t ions against the con jo in t m e a s u r e m e n t axioms. When b o t h r ank order data and ra t ings mus t be o b t a i n e d at the same t ime, it is b e t t e r to ask the subjec t s to o rder the s t imul i first, o the rwise there is a big chance t ha t they will use the i r ra t ings while r a n k o r d e r i n g the s t imuli . In o rder to be able to i n t r o d u c e a n u m b e r of rep l ica t ions per subjec t the s t imul i were a r ranged in a ba lanced i n c o m p l e t e b lock design (Cochran and Cox 1957: plan 11.32), c o m p o s e d of 19 b locks of I0 s t imuli . The subjects were r eques t ed to r a n k o r d e r s t imul i wi th in blocks. In this m a n n e r each s t imulus was judged ten t imes , while each pair of s t imul i was p resen ted five t imes.

The subjects were run in group. Each subjec t received a c o m p u t e r genera ted book le t . On the first page they were i n s t r u c t e d t h a t the purpose of the e x p e r i m e n t was to invest igate h o w well first year s t uden t s in psychologica l and educa t iona l sciences were a l ready able to pred ic t the success of co-s tuden t s at the univers i ty . This mild decep t ion was inspired u p o n Mervielde (1977) . The fo l lowing pages con- t a ined the 19 b locks which had to be r a n k o r d e r e d i n d e p e n d e n t l y accord ing to the chances the descr ibed s tuden t s had to pass at the univers i ty . The order of the b locks as well as t h a t of the s~imuli wi th in each b lock was r a n d o m i z e d per subject . F inal ly the 19 s t imul i were p resen ted again and the subjec ts had to ind ica te on an eleven po in t scale (going f rom 0 to 10) h o w m a n y chances to ten the s t imulus s t uden t s had to pass.

The whole task t o o k on the average 65 m i n u t e s to comple t e . Af t e rwards the sub- jects were asked to fill in a ques t ionna i r e a b o u t the expe r imen t .

R esu Its

Orderings and agreement among subjects One sub jec t did n o t u n d e r s t a n d the task proper ly . His data were d iscarded as t hey were unusable . F o r each of the r ema in ing 17 subjec ts the s tochas t ica l ly d o m i n a n t o rder ing ( C o o m b s and Huang 1970) over the 19 s t imul i was ob ta ined . As each pair

G. De Soete /Information integration 263

of s t imul i is repl ica ted five t imes , a s t imulus x is said to d o m i n a t e s tochas t ica l ly y wheneve r x d o m i n a t e s y in more t han two of the five w i th in -b lock compar i sons of (x, y) . Kendal l ' s ( 1 9 5 5 ) coef f ic ien t of c o n c o r d a n c e a m o n g the subjects is 0 .753. When tes ted against the null h y p o t h e s i s of no ag reement , th is value is highly signifi- can t (X 2 (18) = 230.5 2, p < 0 .001) . However , re jec t ion of this hypo thes i s does no t imply t h a t the re are no individual differences. Indeed, the pairwise Kendal l ( 1 9 5 5 ) tau cor re la t ions be t w een the several order ings range f rom 0 .024 to 0 .959. Conse- quen t ly , the data had to be ana lyzed individual ly .

Consistency and transitivity A first way to assess the cons i s tency a m o n g the j u d g m e n t s of a single subject is to c o m p u t e Durb in ' s ( 1 9 5 1 ) tes t s tat is t ic which u n d e r the null hypo thes i s t ha t each rank ing in each b lock is equal ly l ikely, is a p p r o x i m a t e l y d i s t r ibu ted as a chi-square. Fo r each subject , the X2-value associated wi th the s ta t is t ic is l isted in the first c o l u m n of tab le 1. As the cri t ical value at the 0.001 level is 42 .31 , the null h y p o t h e - sis could be re jec ted for all subjects .

A n o t h e r way of look ing at the cons i s tency is by inspec t ing the s u b s e q u e n t choices on each pair of s t imuli . C o o m b s and Huang ( 1 9 7 0 : 328) no t i ced t ha t wi th five rep l ica t ions of a 5 0 / 5 0 choice on each pair, the d i s t r ibu t ion of the d o m i n a n t s t imulus is a fo lded b inomia l over 3, 4 and 5 wi th a m e a n of 3 .44 and a s t andard devia t ion of 0 .371. A s ignif icant devia t ion f rom chance at the 0.01 level (one- ta i l tes t ) for the average over the ( 1 9 ) = 171 pairs is 3.52 or more . The average con-

Table 1 Consistency and transistivity.

Subject x 2 associated with Consistency Number of circular triads Durbin's statistic

L 162.90 4.988 0 A 161.43 4.971 0 R 162.44 4.965 0 Q 161.11 4.936 0 G 157.96 4.801 1 K 156.75 4.790 0 J 155.39 4.766 2 F 159.00 4.760 0 C 151.65 4.760 2 E 153.46 4.754 1 P 152.18 4.725 4 N 153.58 4.714 3 D 150.78 4.714 4 B 151.28 4.696 4 I 150.59 4.667 0 M 143.75 4.602 5 H 136.01 4.515 7

264 G. De Soete /InJormation inte,gration

s is tency per subjec t is p re sen ted in the second c o l u m n of table 1. For all subjects the h y p o t h e s i s of r a n d o m n e s s could be re jected.

Besides es t imat ing the cons i s t ency of the data, it is also i m p o r t a n t to evaluate the t rans i t iv i ty , because , if t rans iv i t i ty does no t hold , the overall o rder ing con- s t ruc t ed ou t of the wi th in -b lock rankings is of no meaning . The t rans i t iv i ty of the s tochas t ica l ly d o m i n a n t choices per pair can be assessed by c o u n t i n g the n u m b e r of c i rcular t r iads (Kendal l 1955). With 19 s t imul i , the n l a x i m u m n u m b e r is 285, while the expec t ed n u m b e r assuming a 5 0 / 5 0 pairwise choice is 242. The n u m b e r of c i rcular t r iads for each subjec t is given in c o l u m n three of table 1. As is a p p a r e n t f rom table 1, t rans i t iv i ty can be said to ho ld qui te well for all subjects .

Independence Accord ing to Kran tz and Tversky ' s ( 1 9 7 1 ) f lowchar t for the diagnosis of three-fac- to r po lynomia l s in the uns igned case, one has to tes t for i n d e p e n d e n c e in the first place. F a c t o r l is said to be i n d e p e n d e n t of M for a f ixed level of S, if the rank o rde r of I is the same at all levels of M. This can be assessed by c o m p u t i n g Kendal l ' s coef f ic ien t of c o n c o r d a n c e b e t w e e n the r ank orders of I over all levels of M (Walls ten 1976). Moreover , this can be done at each level of S.

These coef f ic ien ts revealed t ha t 14 of the 17 subjec ts sat isf ied the i n d e p e n d e n c e r e q u i r e m e n t perfec t ly . For one subjec t , M, f ac to r M was no t comple t e ly indepen- den t of I. Since the coef f ic ien t of c o n c o r d a n c e , averaged over the levels of S, a m o u n t e d to 0 .939, on ly a small v io la t ion was involved. The two remain ing sub- jects , D and H, v io la ted the ax iom more seriously. The i r lowes t averaged coeffi- c ients of c o n c o r d a n c e were respect ively 0 .074 ( for S i n d e p e n d e n t of M) and 0 .203 ( for 1 i n d e p e n d e n t of M). In cases like these, one has to tes t for sign dependence . This was no t done here because the fac tors had no enough levels to pe r fo rm the o t h e r tes ts requ i red in the s igned case.

Double cancellation The doub le cance l la t ion ax iom could on ly be t es ted for the fac tors I and M, as min imal ly a 3 X 3 ma t r ix is required . In each tes t of the cance l l a t ion cond i t i on , six cells are involved. In all the d i f fe ren t tes ts wh ich are possible in a given 3 X 3 mat r ix , on ly six d i f f e ren t six cell c o m b i n a t i o n s are involved. "The doub le cance l l a t ion could be t es ted at each level of S. C o n s e q u e n t l y , 12 d i f fe ren t six cell c o m b i n a t i o n s could violate the cond i t ion . Only one subjec t , P, failed to sat isfy the doub le cance l l a t ion in one single six cell c o m b i n a t i o n . All o t h e r subjects , inc luding subjec ts D and H, sat isf ied the ax iom perfec t ly .

Join t independence The j o i n t i n d e p e n d e n c e was verif ied nex t . Fac to r s I and M are said to be j o in t ly

i n d e p e n d e n t of S, if the r ank order over all c o m b i n a t i o n s o f / a n d M is the same at all levels of S. The ag reemen t b e t w e e n those r ank orders can again be expressed by Kenda l l ' s coef f ic ien t of conco r dance . These coef f ic ien ts were ca lcu la ted for the d i f fe ren t j o i n t i n d e p e n d e n c e tests. A l t h o u g h mos t subjects showed some m i n o r v io la t ions , the results were very similar to those of the i n d e p e n d e n c e analyses: ser ious v io la t ions occu r red on ly wi th subjec ts D and H.

G. De Soete / Information integration

Table 2 Goodness of fit for ADDALS scalings and results of regression analyses.

265

Subject Kendall tau Stress r 2 F-ratio *

L 1.000 0.000 0.956 347.21 A 1.000 0.000 0.983 967.39 R 0.987 0.000 0.782 57.48 Q 1.000 0.000 0.961 349.26 G 0.951 0.002 0.786 58.85 K 0.974 0.000 0.912 166.68 J 0.941 0.002 0.742 46.11 F 0.922 0.049 0.843 85.77 C 0.980 0.000 0.838 82.71 E 0.937 0.004 0.842 85.52 P 0.907 0.000 0.893 134.19 N 0.931 0.054 0.847 88.54 D 0.951 0.000 0.847 88.27 B 0.964 0.001 0.848 89.33 I 0.948 0.017 0.890 130.04 M 0.927 0.002 0.854 93.39 H 0.864 0.002 0.738 45.15

* All F-ratios have one degree of freedom for the numerator and 16 for the denominator, ex- cept for subject A who forgot to rate one stimulus, so that the dffor the denominator for this subject become 15.

All F's are highly significant (p < 0.001).

Model characterization Fi f t een of the 17 subjects satisfied the i ndependence , double cancel la t ion and jo in t i n d e p e n d e n c e axioms very well. Consequen t ly , their j udgmen t s could best be descr ibed by the addit ive mode l 1 + M + S. A discussion of the resurts for subjects D and H is p o s t p o n e d for a while.

Because an addit ive combina t ion rule seems appropr ia te for most subjects , we have scaled each stochast ical ly dominan t order ing according to this mode l by means of the ADDALS algor i thm (de Leeuw et al. 1976) [3]. Some goodness of fit mea- sures for the additive represen ta t ions are repor ted in table 2. The first co lumn con- rains the Kendall tau correlat ions be tween the rank order data and the scale values, while the second column lists the stress values. The squared stress (see f o o t n o t e 2) is up to a normal iza t ion factor the loss func t ion min imized by the algori thm. As is evident f rom table 2, all. r epresen ta t ions are qui te sat isfactory, even for subjects D and H.

The normal ized scale values associated wi th the levels o f the three factors are

[3] The maximum number of iterations allowed was set to 30, while the minimum stress improvement required for continuation was set to 0.0001.

266 G. De Soete /hz¢brmation in tegration

Table 3 Normalized AI)DALS scale values.

Sub- I 1 12 I3 S1 $2 M1 M2 M3 ject

L -0.216 0.006 0.222 -0.999 0.999 -0.672 0.006 0.677 A -0.187 0.005 0.192 --0.288 0.288 1.188 0.025 1.162 R --0.760 -0,029 0.788 -0.909 0,909 0.272 0.001 0.271 Q --0.942 0,017 0.959 -0,744 0.744 0.215 0.017 0.198 G -0.669 0.074 0.744 --0.710 0.710 0,662 ---0.074 0.736 K -0,409 0.000 0.409 -1.005 1.005 -0.510 0,101 0.611 J -0.369 0.178 0.192 0.276 0.276 -1.138 0.023 1.161 F -0.978 0.291 0.687 -0.548 0.548 0.679 0.028 0.651 C -0.369 0.038 0.331 1.009 1.009 0.529 -0.121 0.649 E -0.802 0.009 0.793 - 0.803 0.803 -0.290 0.250 0.540 P 0.707 -0.001 0.708 0.707 0.707 0.706 --0.001 0.707 N 1.002 -0.097 1.099 -0.267 0.267 0.508 0.098 0.606 D 1.167 0.045 1.122 0.000 0.000 0.409 0.045 0.455 B 0.375 -0.058 0.433 0.401 0.401 0.983 - 0.178 1.161 I -0.914 0.036 0.950 0.576 0.576 0.413 0.206 0.619 M -0.787 0.045 0.832 0.812 0.812 0.256 0.239 0.495 tt 0.000 0.001 0.001 0.004 -0.004 -1.203 0.042 1.245

presen ted in table 3. In order to allow for bo th wi thin-subject and be tween-subjec t compar isons , no t only the sum of scale values per factor but also the tota l sum of squared scale values was made cons tan t for each subject . By inspect ing the range of the scale values per factor , one can see tha t a l though all subjects except D and H, took account of the three variables, the relative impor t ance of each factor varied f rom subject to subject . This f inding just if ies our emphasis on analyzing the data at the individual level.

F r o m the scale values of subjects H and D, it can be inferred tha t these individ- uals only d i f fe ren t ia ted the stimuli on the basis o f respect ively one and two factors (mot iva t ion and intel l igence). This has given rise to r an d o m order inversions which caused the many axiom violat ions of these subjects. As in these cases one can hardly speak of an imp!icit combina t ion rule, these subjects canno t be said to dis- conf i rm a t heo ry which predic ts an addit ive model .

Validation o f the rating scale The scale values ob ta ined by ADDALS can be regarded as es t imates of the la tent responses . As out l ined in the first sect ion, the la tent responses are t r ans fo rmed by the response func t ion in to manifes t responses . If this func t ion is linear, the mani- fest responses , i.e., the ratings, can be said to form an interval scale. We have appl ied a s tepwise po lynomia l regression p rocedure to de te rmine the shape of this func t ion . For all subjects a linear regression accoun ted for a substant ia l part o f the variance of the scale values, as is apparen t f rom the squared corre la t ion coeff ic ients

G. De Soete / Information integration 267

p resen ted in the th i rd c o l u m n of table 2. The last c o l u m n of t h a t tab le gives the F- ra t ios associa ted w i th the best l inear fit. In no case add i t i on of h igher o rder poly- nomia l te rms , up to the th i rd degree, improved the fit s ignif icant ly. Since the l inear i ty of the response f u n c t i o n has been assessed by this p rocedure , the ra t ings could be cons idered as in terval data .

As a f inal check of the val idi ty of ou r two main conclus ions , viz., the appropr i - a teness of the addi t ive mode l and the l inear i ty of the response scale, a r epea ted measures A N O V A was p e r f o r m e d on the rat ings [4] . If b o t h our asser t ions were t rue , s ignif icant main effects and nons ign i f i can t i n t e r ac t i on effects of the s t imulus fac tors were to be ob t a ined , unless of course the a s sumpt ions unde r ly ing the me th - od were t oo seriously violated. The A N O V A resul ts were exac t ly as expec ted . The main effects of S, 34 and I were highly s ignif icant (resp. F ( 1 , 1 6 ) = 24 .44 , F ( 2 , 1 6 ) = 16.54, F ( 2 , 1 6 ) = 29.91, all p < 0 .001) , whereas n o n e of the F-values associated wi th the i n t e r ac t i on t e rms a p p r o a c h e d significance. These resul ts provide add i t iona l evidence for the val id i ty of our conclus ions!

Discussion and conclusions

Conjoint measurement techniques have proved to be quite useful for determining the appropriate model. Although this approach lacks an adequate error theory, this did not cause any particular difficulty in interpreting the results of the axiom analyses. The judgments of all sub- jects who differentiated the stimuli on the basis of the three factors, could adequately be represented by an additive model. A question put forward by a referee in connection with this result concerns the power of the present 3 × 3 × 2 design to reject the additive model. Indeed, as in most conjoint measurement applications, the design was minimal, since only such a small design allows for testing the consistency and transitivity at the individual level in a meaningful way. This advantage of the 3 × 3 × 2 design is of course worthless when the design lacks enough power to validate the proposed models. Fortunately, previous experimental applications of conjoint measurement w h e r e the very same design was used show it to have the required power (cf. Coombs and Huang 1970; Ullrich and Painter 1974).

Our conclusion to an additive model contrasts with the intuitive idea of motivation as a multiplier and suggests that at least Belgian students integrate motivational information in a very similar manner as other

[4] The one missing rating (cf. table 2) was estimated by means of linear regression using the latent responses as obtained by ADDALS.

268 G. De Soete / b~formation integratioJt

kinds of information are processed (Anderson 1974b, c). The discrep- ancy between the present results and those of Anderson and Butzin (1974) may possibly be attributed to cultural differences, as a recent replication of the Anderson and Butzin study in India, conducted by Singh et al. (1979), evidences.

Anderson and his colleagues have very often tried to prove the linearity of the response ftmction by heavily relying on ANOVA tech- niques (e.g., Anderson 1977, 1978a; Klitzner and Anderson 1977). We, on the contrary, have assessed this linearity and consequently the validity of the response scale, by relying only on the ordinal character- istics of the data for the model diagnosis and without making prelim- inary distributional assumptions. This can be very useful for fttrther research in the area.

Although some methodologically innovative methods have been applied, we have only been able to prove the descript i l ,e validity of the additive model. Le. the model is only an as i f model. What a person really does when making a judgment that is like an addition, is not known! Much more research will be needed to answer this question!

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