COMMENTS Tests of Multiplicative Models in Psychology: A Case Study Using the Unified Theory of Implicit Attitudes, Stereotypes, Self-Esteem, and Self-Concept Hart Blanton University of North Carolina at Chapel Hill James Jaccard University at Albany, State University of New York Theories that posit multiplicative relationships between variables are common in psychology. A. G. Greenwald et al. (2002) recently presented a theory that explicated relationships between group identi- fication, group attitudes, and self-esteem. Their theory posits a multiplicative relationship between concepts when predicting a criterion variable. Greenwald et al. suggested analytic strategies to test their multiplicative model that researchers might assume are appropriate for testing multiplicative models more generally. The theory and analytic strategies of Greenwald et al. are used as a case study to show the strong measurement assumptions that underlie certain tests of multiplicative models. It is shown that the approach used by Greenwald et al. can lead to declarations of theoretical support when the theory is wrong as well as rejection of the theory when the theory is correct. A simple strategy for testing multiplicative models that makes weaker measurement assumptions than the strategy proposed by Greenwald et al. is suggested and discussed. Keywords: regression, interactions, cross-products, implicit association test Numerous theories in psychology posit multiplicative relation- ships between variables. For example, in educational as well as organizational psychology, performance on a task is thought to be a function of ability times motivation (e.g., Anderson & Butzin, 1974; Gupta & Singh, 1981). In cognitive psychology, it has been suggested that decisions are a function of subjective probabilities times utilities (Edwards & Fasolo, 2000). In social psychology, attitudes are thought to be a function of expectancies times values (Ajzen & Fishbein, 1981). In psycholinguistics, the perceived truth value of a compound statement is said to be a multiplicative function of the truth value of the component parts of that statement (e.g., Oden, 1978). Given the presence of multiplicative models in diverse areas of psychology, it is useful to consider the challenges of testing such models, especially in the context of correlational designs that use multiple regression. These tests often are linked to the analysis of interactions. The present article considers the rela- tionship between interaction analysis in multiple regression and the evaluation of models with simple multiplicative relationships. Greenwald et al. (2002) recently presented a theory of attitudes, stereotypes, self-esteem, and self-concept that explicated dynamic relationships between group identification, group attitudes, and self-esteem. Using fundamental concepts from connectionistic frameworks in cognitive psychology and consistency theories in social psychology, these authors derived a set of principles that led them to postulate relationships between the traditional psycholog- ical constructs of self-esteem (SE), group identity (GI) and atti- tudes toward a group (AG). Greenwald et al. argued that any one of these constructs should be a simple multiplicative function of the other two. They characterized this multiplicative function as an interaction and tested the model using the following equations: SE = a 1 + b 1  GI  AG + e (1) GI = a 2 + b 2  SE AG + e (2) AG = a 3 + b 3  SE GI  + e. (3) Greenwald et al. (2002) argued that the model is supported if regression analyses for the above equations yield strong correla- tions and statistically significant and positive regression coeffi- cients. They suggested an additional set of statistical analyses for their theory based on augmenting the “interaction” model with the component parts of the product term, using equations of the following form: SE = a 4 + b 4 GI + b 5 AG + b 6  GI  AG + e (4) GI = a 5 + b 7 SE + b 8 AG + b 9  SE AG + e (5) AG = a 6 + b 10 SE + b 11 GI + b 12  SE GI  + e. (6) Greenwald et al. viewed the regression coefficients for the com- ponent parts as representing the “effects” of the two predictors on the criterion and the coefficient for the product term as represent- Hart Blanton, Department of Psychology, University of North Carolina at Chapel Hill; James Jaccard, Department of Psychology, University at Albany, State University of New York. James Jaccard is now at the Psychology Department, Florida Interna- tional University. Correspondence concerning this article should be addressed to Hart Blanton who is now at the Department of Psychology, 4235 TAMU, Texas A&M University, College Station, TX 77843-4235. E-mail: hblanton@gmail.com Psychological Review Copyright 2006 by the American Psychological Association 2006, Vol. 113, No. 1, 155–169 0033-295X/06/$12.00 DOI: 10.1037/0033-295X.113.1.155 155