# The integration of motivational information: A conjoint measurement analysis

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<ul><li><p>Acta Psychologica 46 (1980) 257-269 Q North-ttolland Publishing Company </p><p>THE INTEGRATION OF MOTIVATIONAL INFORMATION: A CONJOINT MEASUREMENT ANALYSIS * </p><p>Geert De SOETE ** State University of Ghent, Ghent, Belgium </p><p>Accepted June 1980 </p><p>Within Anderson's (1974a, b, c, 1978b) information integration theory, tlie integration of motivational information was investigated by means of conjoint measurement techniques. Eighteen university students were asked to judge hypothetical co-students characterized by three features (intelligence, motivation 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 function for the ratings. As this function was quite linear for all subjects, the ratings could be said to form an interval scale. </p><p>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. </p><p>* 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. Thurstone Psychometric Laboratory, University of North Carolina. Davie Hall 013 A, Chapel Hill NC 27514, U.S.A. </p><p>257 </p></li><li><p>258 G. De Soete / Information integration </p><p>Anderson's information integration theory </p><p>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: </p><p>riik = l(f,(ai), f2(bi), fa(ck)) ( 1 ) </p><p>which results in a manifest response Rij k by means of the response function M: </p><p>Ri/k = M(ri/k) (2) </p><p>A scheme of these processes is presented in fig. 1 which is a modified version of Anderson's (1970, 1974a, 1977) functional measurement diagram. </p><p>STIMULUS PSYCHOLOGICAL LATENT MANIFEST COMPONENTS STIMULUS COMPONENTS RESPONSE RESPONSE </p><p>a i . ~, f l i a i ) </p><p>b j .) f2 (b j ) </p><p>c k :> f3 (ck ) </p><p>~- r i j k </p><p>I N T E G R A T O R </p><p>:)' Rij k </p><p>VALUATION INTEGRATION RESPONSE FUNCTIONS FUN CT ION FUNCT ION </p><p>Fig. 1. A scheme of Andersons's information integration theory (this is a modified version of Anderson's (1970, 1974a, 1977) functional measurement diagram). </p></li><li><p>G. De Soete / hfformation integration 259 </p><p>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: </p><p>ri i k = w l fa (a i ) + w2f2(b/) + w3~3(ck) (3) </p><p>and </p><p>rijt = 00Io + ViA(ai) + v2f2(b,) + v3f3(cD (4) </p><p>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: </p><p>rijk = ~l(ai) + ~b2(bi) + 4~3(ck) (S) </p><p>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. </p><p>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 </p></li><li><p>260 G. De Soete /hLtbrmation integration </p><p>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 et 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. </p><p>The integration of motivational information </p><p>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: </p><p>Reaction Potential = Drive X Habit . </p><p>The idea occurs also explicitly in Heider's (1958) attribution theory: </p><p>Performance = Motivation X Ability (1958: 83). {6) </p><p>This proposition has been empirically verified by Anderson and Butzin (1974), together with two derived formulas: </p><p>Motivation = Performance X (Ability) -1 (7) </p><p>Ability = Performance (Motivation)-' (8) </p><p>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 </p></li><li><p>G. De Socte /Information integration 261 </p><p>Leeuw et al. 1976) [11. The stress [2] value for both groups is less than 0.0001. </p><p>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. </p><p>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 </p><p>Future Performance = Past Performance + Motivation Ability (1974: 609) </p><p>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. </p><p>The exper iment </p><p>Method </p><p>Su bjec ts Eighteen first year students, 7 males and 11 females, all enrolled in the Faculty of Psychological and Educational Sciences at the University of Ghent, participated </p><p>[ 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. </p></li><li><p>262 (;. De Soete /Inbrmation in tegration </p><p>voluntar i ly in partial fu l f i lments of certain class requirements. No one was acquainted either with conjo int measurement or with Anderson's in format ion integrat ion theory. </p><p>Stimuli The st imuli consisted of descr ipt ions of hypothet ica l first year students, which were character ized by three features: intel l igence (3 levels: IQ = 100, 120, 140), motiva- t ion (3 levels: not, weakly, strongly mot ivated) and the extent to which they studied (2 levels: studies little, much). By combin ing the three variables factorially, 18 stimuli were obtained. Inclusion of an addit ional st imulus (IQ = 125, weakly mot ivated, studies l ittle) for convenience of design yielded a total of 19 stimuli. </p><p>Procedure As we intended to analyze the judgments nonmetr ica l ly (axiom analyses) as well as metrical ly (po lynomia l regressions), it was desirable to gather not only ratings but also explicit ordinal data, because ties or minor order inversions in the ratings due to random judgmenta l f luctuat ions can cause many violat ions against the conjo int measurement axioms. When both rank order data and ratings must be obta ined at the same time, it is better to ask the subjects to order the stimuli first, otherwise there is a big chance that they will use their ratings while rankorder ing the stimuli. In order to be able to int roduce a number of repl ications per subject the stimuli were arranged in a balanced incomplete block design (Cochran and Cox 1957: plan 11.32), composed of 19 blocks of I0 stimuli. The subjects were requested to rankorder stimuli within blocks. In this manner each st imulus was judged ten t imes, while each pair of st imuli was presented five times. </p><p>The subjects were run in group. Each subject received a computer generated booklet . On the first page they were instructed that the purpose of the exper iment was to investigate how well first year students in psychological and educat ional sciences were already able to predict the success of co-students at the university. This mild decept ion was inspired upon Mervielde (1977). The fol lowing pages con- ta ined the 19 blocks which had to be rankordered independent ly according to the chances the described students had to pass at the university. The order of the blocks as well as that of the s~imuli within each block was randomized per subject. Final ly the 19 stimuli were presented again and the subjects had to indicate on an eleven point scale (going from 0 to 10) how many chances to ten the st imulus students had to pass. </p><p>The whole task took on the average 65 minutes to complete. Afterwards the sub- jects were asked to fill in a quest ionnaire about the exper iment. </p><p>R esu Its </p><p>Orderings and agreement among subjects One subject did not understand the task properly. His data were discarded as they were unusable. For each of the remaining 17 subjects the stochastical ly dominant ordering (Coombs and Huang 1970) over the 19 stimuli was obtained. As each pair </p></li><li><p>G. De Soete /Information integration 263 </p><p>of stimuli is repl icated five t imes, a st imulus x is said to dominate stochastical ly y whenever x dominates y in more than two of the five with in-b lock comparisons of (x, y). Kendal l 's (1955) coeff ic ient of concordance among the subjects is 0.753. When tested against the null hypothes is of no agreement, this value is highly signifi- cant (X 2 (18) = 230.5 2, p < 0.001). However, reject ion of this hypothesis does not imply that there are no individual differences. Indeed, the pairwise Kendall (1955) tau correlations between the several orderings range from 0.024 to 0.959. Conse- quent ly, the data had to be analyzed individually. </p><p>Consistency and transitivity A first way to assess the consistency among the judgments of a single subject is to compute Durbin 's (1951) test statistic which under the null hypothesis that each ranking in each block is equally likely, is approximately distr ibuted as a chi-square. For each subject, the X2-value associated with the statistic is l isted in the first co lumn of table 1. As the critical value at the 0.001 level is 42.31, the null hypothe- sis could be rejected for all subjects. </p><p>Another way of looking at the consistency is by inspecting the subsequent choices on each pair of stimuli. Coombs and Huang (1970: 328) not iced that with five repl ications of a 50/50 choice on each pair, the distr ibut ion of the dominant st imulus is a folded binomial over 3, 4 and 5 with a mean of 3.44 and a standard deviation of 0.371. A signif icant deviation f rom chance at the 0.01 level (one-tail test) for the average over the (19)= 171 pairs is 3.52 or more. The average con- </p><p>Table 1 Consistency and transistivity. </p><p>Subject x 2 associated with Consistency Number of circular triads...</p></li></ul>