MUlTIMODi FACTOR ANALYSIS OF INTERPERSONAL PERCEPTIONS

Data resulting from the Interpersonal perceptions of 88 students who were heterogeneous with respect to race and sex were subjected to i variety of analyses, including Tucker's three-mode factor analysis procedure. Ss responded on Semantic and Behavioral Differential scales to complex person stimuli designated In terms of race, sex, and other characteristics which formed a factorial design. The data were reduced to a two-way classification of scales-by-stiaull, using 3s' mean group responses, and conventional factor analyses of scales were performed. Analyses of variance were carried out to determine the relative weights of the stimulus factors in determining the responses of the var'.oun groups of Ss on the scale factors. Final'.y, the three modes of the date classified in terms of scales-by-stlnuli-bysubjects were subjected to Tucker's three-mode factor analysis. After obtaining principal axis factors for the three modes, the scale and subject mode factors were rotated by Variinax and the stimulus mode factors were transformed by means of discriminant function analysis. Counter-rotations of the three modes yielded a core matrix linking the scale factors to the stimulus factors. Although not all of the subject types were clearly interpretable in the present study, this type of analysis, with some modifications, would appear to have great potential value In treating complex Interpersonal perception data. Mi' .tiraode Factor Analysis of Interpersonal Perception ' 2 3 Earl E. Davla and Nadlne Natkar Orobstoln University of Illinois INTRODUCTION The present report describes the treatment by means of both conventional and multlmode factor analytic techniques of data pertaining to the social perceptions of subjects who may be considered to be culturally heterogeneous with respect to each other. A group of people Is usually said to be culturally heterogeneous when certain background characteristics of Its members cause them to differ systematically with respect to their attitudes^, values, norms of behavior, etc. The typical background characteristics which are thought of as being associated with such differences are national-geographic origin, language, rellflon, or similar ethnic characteristics. However, a broader view of culture would define any group as culturally heterogeneous to the extent that its members differed In any characteristics which would lead to or be associated with different ways of thinking about and evaluating relevant aspects of reality. Thus, a group may be considered culturally heterogeneous if its members differ with respect to any of a wide range of characteristics such as social class, occupation, sex, race, religion, aget degree of urbanization, etc. -assuming that these differences are, in fact, related to different ways of thinking about and evaluating relevant aspects of reality. This study was supported by ARPA Order No. 454, Contract Nrl77-472, Nonr 1834(36) with the Advanced Research Projects Agency and the Office of Naval Research to study "Communication, Cooperation and Negotiation in Culturally Heterogeneous Groups" (F.E. Fiedler, L.U. Stolurow, and H.C. Triandis, Principal Investigators). The authors are Indebted to Ping Koo for her expert aid in programming the analyses; to E. Thomanek and Mary Rudsinski for assistance in processing the data; and to H,C. Triandis find L.R. Tucker for their invaluable advice am' patience. 2 Now at the Graduate Faculty of the New School for Social Research. 3 Now with the Department of Welfare of the City of Chicago. In the present study subjects who differed with respect to rece (Negrowhite) and sex (nele-feaale) responded to imaginary social stimuli which «ere designated in ten» of various combination* of race, sex, and other a char&cterlsticr. Whether the subjects' differences In race and sex mean that they constitute a "culturally heterogeneous" group, In the sense indicated above, Is an ««rpirlcal question, the determination of which was one of the purposes of this study. The criterion will be whether or not these (Sifferencec are related to different ways of thinking about and evaluating relevant aspects of reality, and In particular to different interperjonal perceptions when the stlmuM involved are described in terms of ethnic and other social characteristics which have been found to be Important determinants of Interpersonal perception in much previous reaearch. Hie responses along different dimensions, by subjects belonging to different categories, to stimuli designated by various combinations of socially relevant characteristics, constitute a three-way classification of data. The procedures of conventional factor analysis are applicable only to data which form a two-way classification, for example, to matrices of subjects by responses. The treatment of the present data matrix, which is a three-way classification of responses by stimuJ.i by subjects, by means of conventional factor analytic procedures is only possible if the data are reduced in some way to a two-way classification. For example, semantic differential data are typically reduced to a concept by scale matrix, obtaining means of groups of subjects (Osgood, Suet, and Tannenbaum, 1957). The problems involved in reducing semantic differential data in this manner are discussed in detail by Osgood (1962). Behavioral differential data are also usually reduced to a two-way classification in the same manner (Triandls, 1964). Some of the methodological problems Involved in factoring 3 semantic and behavioral diflarentlal reaponses obtained froa nembera of different sub-cultures are discussed by Davis (1966). The mathematical problems of the simultaneous analysis of all three modes of data which form a three-way classification and of examining the relationrllp among the corresponding factors has been solved by L. R. Tucker (196iu, 1965). A major purpose of the present study was to explore the application of three-mode factor analysis to data representing a three-way classification of responses by stimuli by subjects> The present data ware collected earlier by the second author (Natker, 1964) and were first subjected to conventional factor analysis ay reducing th« data in the usual way. Also, analyses of variance were performed in order to examine the relative importance of various stimulus pernon characteristics in the determination of the variance on eat:factor. Some of ther« factor analytic and analysis of variance results will be presented here in order to familarlf» the reader with the data. Finally, the results of the three-mode factor analysis of the data will be presented and discussed.