An Exposition of Tri-Mode Factor Analysis For Segmenting Target Audience Reactions

ABSTRACT - This paper presents three-mode factor analysis as an alternative technique to help answer the problems of comparing test commercials against each other and to provide a more accurate profile of target audiences' reactions to the commercials. The technique yields simultaneous factor analyses or reductions over at least three classifications of input data. The potential of three-mode factor analysis for providing substantial insight into complex data as illustrated here appears promising.


Terry G. Vavra and Edwin C. Hackleman (1980) ,"An Exposition of Tri-Mode Factor Analysis For Segmenting Target Audience Reactions", in NA - Advances in Consumer Research Volume 07, eds. Jerry C. Olson, Ann Abor, MI : Association for Consumer Research, Pages: 788-791.

Advances in Consumer Research Volume 7, 1980     Pages 788-791


Terry G. Vavra,  Kenyon and Eckhardt, Inc.

Edwin C. Hackleman, The University of Connecticut


This paper presents three-mode factor analysis as an alternative technique to help answer the problems of comparing test commercials against each other and to provide a more accurate profile of target audiences' reactions to the commercials. The technique yields simultaneous factor analyses or reductions over at least three classifications of input data. The potential of three-mode factor analysis for providing substantial insight into complex data as illustrated here appears promising.


Classical factor analysis has often constrained the researcher because it operates on a data matrix of only two dimensions. The "canned" computer program usually labels these dimensions "subjects" and "measures." The two-way table is sometimes inadequate for the social scientist who is almost always interested in studying subjects, tests, and occasions. Cattell [1952] has suggested the concept of the data cube as being more compatible with the real world. His data cube possesses a dimension or "mode" of data classification for subjects, a dimension for tests and a dimension for occasions or objects.

Tucker [1963, 1964, 1966] has extended the mathematics of factor analysis to the three-dimensional data of the data cube. His model seeks to answer the problems encountered with data or more than two dimensions and the challenge of theoreticians such as Harris [1963] and Roff [1971] who have argued for adaptations of multivariate methods to longitudinal studies. In several articles Tucker [1967, 1972] and his colleagues (Levin [1965], Snyder [1963], Hoffman and Tucker [1964], and Mills and Tucker [1964], have demonstrated the distinct advantage of the technique in assimilating data collected over a number of concepts or occasions. The three-mode analysis preserves all the original information in the data by operating on data cubes and also displays relationships upon which previous researchers using similar data had only been able to speculate.

The Three-Mode Factor Analysis Model

In reducing the rank of a data cube, three-mode factor analysis attempts to find: 1. The relevant latent factors representing the major interdependencies in the data for each mode; 2. The interrelationships between the factors of each mode.

The data cube (Figure 1) hold entries, Xijk which can be approximated by Xijk, allowing for the discrepancy of fitting a model to observed data. The approximation will contain unique X and common X variances:

Xijk =  Xuijk + Xcijk    (1)

The three-mode model, in summation form may be represented as:

Xcijk  = Sm Sp Sq aim bjp ckq gmpq    (2)

where a, b and c are observational modes of original dimension i, j and k and of derivational dimension m, p q representing the relationships within each individual mode. g is a "core matrix" of dimension m by p by q which represents the relationships between modes.

A, B and C are three, reduced-rank matrices which describe observed entities of each mode (subjects, descriptions, and products). Hence, the analysis will produce a factor structure describing each response pattern utilized by the original subjects (factors of the subject space). Factors will also be constructed which account for shared meaning of the evaluative scales (factors of the questionnaire scale space). Likewise, the commercial space will be reduced to a few commercial factors (factors of the commercials space) which tend to cluster similar perceived commercials.

The mathematics of the model involve an approximation achieved by truncating each observational mode, retaining only those elements which significantly contribute to the sum of squares of that mode. The procedure to attain a least squares fit for the three mode-model is being investigated by Tucker [1966], Snyder [1968] and others, and entails a complex series of approximation.



An Empirical Example

A collection of commercials was secured featuring a chocolate flavoring mix for milk; the primary consumers (though not necessarily the buyers) for the product are children. Two fundamental appeals were employed in the advertising for the product. Attempts to sell the product to mothers emphasized nutritional and energy-related values, whereas commercials directed towards children stressed taste and fun [Exhibit I]. Therefore, the test commercials were well-suited to the possible benefits of tri-mode factor analysis, for in each case there were a priori clusters of commercials and market segments.

The advertising agency's staff believed it was addressing segments in various ways through each subcluster of commercials.-However, were the commercials in each segment actually being received favorably by the audience to whom they were addressed? Secondly, how did audience segments perceive commercials directed at other audience segments? It was possible that ads directed at children might be poorly received by mothers - destroying some goodwill; and, those ads directed at mothers might be annoying to the children - the heavy users of the product.

A fourth-grade class of 31 school children and a group of 16 young mothers from a church group were used as subjects. To accommodate lack of experience with a semantic differential for the children, a star scale was employed to allow gradational agreement. Every possible attempt was made to reduce words used to the most familiar word in a grade-school vocabulary which still retained the denotative meaning. The completed test was eventually critiqued by three elementary school teachers who were unanimous in their acceptance of the instrument for the majority of their pupils. The same form of the questionnaire was administered to both the children and the mothers.



Initially, responses to the two general reaction questions were tabulated, and a "popularity" score was derived from the subjects' scores. Children rated the commercials from letter grade F to A, and the mothers scored them 1 to 100 when compared against "all TV commercials ever seen." Also, five factual recall questions were answered, and these were averaged over all 47 respondents.


The commercials are rank-ordered by scores for both measures as shown in Table 1. Examining the recall scores shows a surprising reversal performance-wise of the commercials, for popularity would seem to be inversely correlated with factual recall. While commercial D enjoys the highest recall scores, commercial B (the second most popular commercial) is second to last in associated recall. F, the most popular commercial, is third in recall, whereas A, another unpopular take, is second in recall. A and D featured the same female actress returning from the supermarket talking about the product. These results tend to parallel the difficulty agencies have encountered in the past when trying to use traditional methods of measuring advertising effectiveness.

The Commercials Mode

Next, three-mode factor analysis was employed on the data cube, and the first factor structure is that attributable to the commercials. A plot of the eigenvalues revealed a sharp break at the third, and these three accounted for 74.4% of the total variance (Table 2). The three-eigenvalue solution was rotated by the Varimax criterion to produce a pattern of distinct loadings.

Factor I relates six commercials, most of which are explicitly aimed at young, preschool children. They either featured preschool actors or were cartoons directed at younger-aged children. Commercials B and G were targeted for older children, closer to the age of the subjects. Factor II commercials were aimed at mothers since the actor played a shopper giving the illusion of personal conversation. Factor III clustered commercials representing a "fantasy" approach, since both possessed exaggerated characters, one involving Commercial I, a live-action, comedic espionage agent who doubled as an escape artist and the other involving commercial C, an advisory bird talking to housewives about the merits of the product.



The Variables Mode

Stage 2 of the tri-mode analysis yielded four factors in the variable (scales) space, also rotated by the Varimax procedure. These clusters seem reasonable in composition, since the first factor includes such evaluative scales as well-known, trustworthy, best, and honest, together with evaluative reactions towards the product (tastes good, easy to use, fun, etc.) and the communicator (well-known, safe, etc.). An interesting implication stems from the negative association of evaluation and factual recall (the higher the evaluation, the less likely the recall of facts describing the commercial. This finding parallel's Haskin's [1964] disenchantment with the efficiency of factual recall in measuring relevant reactions to advertising.

Factor II uncovers an interest-emotion variable with high loadings on such scales as turns me on, enjoyable, funny, and emotional. Factor III appears to be a reality-utility factor, related to the reality of the message (real, unbelievable) and the judgment of the message's usefulness (helps me, useful). Factor IV concentrates on product attributes (new, cools me off, it's a food). (see Table 3) of the comparative magnitude of cell values in each plane of the matrix.





The Subject Mode

Two retained subject factors accounted for 54.7% of the variance, and these were also rotated using the Varimax procedure. The first subject factor shown in Table 4 clearly represents the child's view of the commercials, whereas the second factor represents the mother's view. The workability of an orthogonal relationship between the subject clusters suggests complete independency of the children's reactions from the mothers', although the mothers and children involved here were not in the same family. (See Table 4)



The Core Matrix

The final aspect of the three mode analysis is an interpretation of the core matrix, which relates the three individual factor analyses to each other. The transformed core matrix (incorporating the transformation applied individually to each mode of the data) is presented in Table 5. Cell entries in the core matrix were simplified by translating them into symbols, indicative of the comparative magnitude of cell values in each plane of the matrix.



Each frontal plan of the core matrix illustrates the utilization by each variable cluster to react to each cluster of commercials. Since each frontal plane represents a different subject-type, one can examine by subject type the performance of each of the clusters of commercials. The advertiser would have expected the adult commercials to have been most favorably received by the mothers (the second frontal plane). The children would have been expected to have liked the commercials clustered in the adult-fantasy cluster and for commercials G and F.

The plane of the core matrix representing the children's reactions suggests the largest positive associations occur in the column representing the evaluative scales. Considering their responses to the three commercial clusters on the evaluative scales, the children reacted most positively to the cluster of commercials composed primarily of appeals to young children (a score of 15.4 compared to 10.6 and 10.9). It is enlightening to observe that none of these young appeal commercials performed strongly in either the popularity or recall polls (Table 1).

The children's reactions were strongest on the evaluative factor, but the young appeal commercials also stimulated positive reactions on the interest and emotion scales as well. The commercials in cluster one neither elicited strong reactions of realism (a score of 1.6), nor of product attributes (a score of .8). Although descriptions and enjoyment of the product were stressed in the preschool commercials, they did not communicate product attributes and benefits.

The children were rather blase in their reactions to the other two clusters of commercials. The only reaction the adult-factual commercials engendered was a rather positive reaction (10.6) on the evaluative scales. The adult-fantasy commercials elicited a positive utilization of the evaluative scales (10.9), but in addition were judged negatively on the realism scales, thus confirming the labeling of this third cluster as the fantasy commercials. Another interesting finding is that none of the commercial types was successful in communicating product information to the children. There was no sizable usage of the fourth variable factor, the product attributes cluster, by the children.

The reactions of the mothers, the second subject type, are indicated by the second frontal plane of the core matrix. The mothers' reactions were not at all what might have been anticipated, for their only positive responses on the variable factors were on the product attribute scales, elicited by commercials of the first and third commercials clusters. These commercials were more successful than the commercials of cluster two in generating perception of the product as "new" and "a food". The rest of the mothers' reactions were negative, the strongest negative reaction being on the interest and emotion scales in response to both the young children's commercials and the adult-fantasy commercials. The adult-factual commercials were rated indifferently in interest and emotion, and the mothers reacted negatively to all three commercial types on the evaluation scales. Concerning their judgments of realism, both the young children's commercials and the adult-fantasy commercials were perceived negative. The mothers were indifferent (-1.2) when judging the adult-factual commercials on realism.


The tri-mode factor analysis promises a significant improvement over traditional unidimensional advertising effectiveness measures. Each cluster of commercials showed striking similarity to the way in which the ad agency might have sorted them, for each cluster was differentially received by the two subject types. The children subject cluster preferred those commercials aimed at children, whereas the mother subject cluster, although generally negative towards all commercials, reacted most positively to those targeted for adults.

Comparing the tri-mode analysis to traditional verbal response measures isolates some fascinating discrepancies. Popularity wise, children preferred one commercial but recalled the most facts from a far-less preferred one. The tri-mode analysis, on the other hand, does yield that neither of these commercials is the most effective for children. The strongest commercial in the young appeal cluster emerges most effective for this target audience. Although the mothers professed a strong affinity for one of the test commercials using traditional measures, the tri-mode analysis rejects this one in favor of another which clustered in an adult-factor dimensions. The additional insight afforded by the multivariate analysis is indeed striking.


Cattell, R. B. Factor Analysis: An Introduction and Manual for the Psychologist and Social Scientist. New York: Harper and Row. 1952.

Harris, C. W. (Ed.) Problems in Measuring Change. Madison: The University of Wisconsin Press, 1963.

Haskins, J. B. "Factual Recall as a Measure of Advertising Effectiveness," Journal of Advertising Research, Vol. 4, No. 1, (March 1964), pp. 2-8.

Hoffman, E. L. and Tucker, L. R. "Three-Way Factor Analysis of a Multi-trait-Multimethod Matrix," Technical Report, Department of Psychology, University of Illinois, 1964 (multilithed).

Levin, J. "Three-Mode Factor Analysis," Psychological Bulletin, Vol. 64, No. 6 (1965), pp. 442-452.

Mills, D. H. and Tucker, L. R. "A Three-Mode Factor Analysis of Clinical Judgment of Schizophrenicity," Technical Report, Department of Psychology, University of Illinois, 1964 (multilithed).

Roff, M. "Time as a Factor in Multivariate Analysis," Multivariate Behavioral Research, 6 (January 1971), pp. 3-6.

Snyder, F. W. A Unique Variance Model for Three-Mode Factor Analysis. Urbana, Illinois: Department of Psychology Technical Reports, University of Illinois, 1968.

Tucker, L. R. "Implications of Factor Analysis of Three-Way Matrices for Measurement of Change," in C. W. Harris (Ed.). Problems in Measuring Change. Madison: University of Wisconsin Press, 1963, pp. 122-137.

Tucker, L. R. "The Extension of Factor Analysis to Three-Dimensional Matrices," in N. Fredericksen and

H. Gulliksen (Eds.). Contributions to Mathematical Psychology. New York: Holt, Rinehart & Winston, 1964.

Tucker, L. R. "Three-Mode Factor Analysis of Parker-Fleishman Complex Tracking Behavior Data," Multivariate Behavioral Research, Vol. 2, No. 2 (April, 1967), pp. 139-152.

Tucker, L. R. "Some Mathematical Notes on Three-Mode Factor Analysis," Psychometrika, Vol. 31, No. 3 (September, 1966), pp. 279-311.

Tucker, L. R. "Relations Between Multidimensional Scaling and Three-Mode Factor Analysis," Psychometrika, Vol. 37, No. 1 (March, 1972), pp. 3-27.



Terry G. Vavra,   Kenyon and Eckhardt, Inc.
Edwin C. Hackleman, The University of Connecticut


NA - Advances in Consumer Research Volume 07 | 1980

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