PSYCHOMETRIKA—VOL. 71, NO. 1, 161–171 MARCH 2006 DOI: 10.1007/S11336-004-1173-X AN EXTENSION OF MULTIPLE CORRESPONDENCE ANALYSIS FOR IDENTIFYING HETEROGENEOUS SUBGROUPS OF RESPONDENTS HEUNGSUN HWANG HEC MONTR ´ EAL WILLIAM R. DILLON SOUTHERN METHODIST UNIVERSITY YOSHIO T AKANE MCGILL UNIVERSITY An extension of multiple correspondence analysis is proposed that takes into account cluster-level heterogeneity in respondents’ preferences/choices. The method involves combining multiple correspon- dence analysis and k-means in a unified framework. The former is used for uncovering a low-dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents. The proposed method offers an integrated graphical display that provides informa- tion on cluster-based structures inherent in multivariate categorical data as well as the interdependencies among the data. An empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches. Key words: multiple correspondence analysis, k-means, cluster-level respondent heterogeneity, alternating least squares. 1. Introduction Multiple correspondence analysis (MCA) is a popular descriptive technique to explore the relationships among multiple categorical variables (Benz´ ecri, 1973; Gifi, 1990; Greenacre, 1984; Lebart, Morineau, & Warwick, 1984; Nishisato, 1980). It amounts to a nonlinear principal com- ponents analysis that assigns numerical scores to respondents and response categories of dummy- coded categorical variables which results in a graphical map of the interdependencies among the variables. This graphical display is a useful by-product as it aids in communicating the association structures inherent in multivariate categorical data to practitioners and other researchers. The parameters of MCA are estimated by pooling the data across respondents under the implicit assumption that all respondents come from a single, homogenous group. However, it often seems more realistic to assume that respondents come from heterogeneous groups, so that they are different with respect to their attitudes and preferences. Such group- or cluster-level respondent heterogeneity has been discussed from several different theoretical and modeling per- spectives; for example, consumer belief structures have been hypothesized to vary across different market segments according to the expectancy value models (Bagozzi, 1982), and accounting for cluster-level respondent heterogeneity has been shown to be important in modeling consumer brand choice decisions (see Kamakura, Kim, & Lee, 1996). The work reported in this paper was supported by Grant 290439 and Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first and third authors, respectively. We wish to thank Ulf B¨ ockenholt, Paul Green, and Marc Tomiuk for their insightful comments on an earlier version of this paper. We also wish to thank Byunghwa Yang for generously providing us with his data. Requests for reprints should be sent to Heungsun Hwang, Department of Marketing, HEC Montr´ eal, 3000 Chemin de la C ˆ ote Ste Catherine, Montr´ eal, QC, H3T-2A7, Canada. E-mail: heungsun.hwang@hec.ca 161 c  2006 The Psychometric Society