A Simultaneous Approach to Constrained Multiple Correspondence Analysis and Cluster Analysis For Market Segmentation

EXTENDED ABSTRACT - A common practice for cluster-based market segmentation is to first uncover a low-dimensional representation of variables (e.g., the first few principal components) with data reduction techniques such as principal components analysis, factor analysis, or multidimensional scaling, and to subsequently use cluster analysis to identify a set of segments based on the low-dimensional data (Arimond & Elfessi, 2001; Furse, Punj, & Stewart, 1984; Green, Shaffer, & Patterson, 1988; Sheppard, 1996). This two-step sequential or tandem approach (Arabie & Hubert, 1994) has been advocated for substantive reasons (see Green & Krieger, 1995).

Citation:

Heungsun Hwang, Byunghwa Yang, and Yoshio Takane (2005) ,"A Simultaneous Approach to Constrained Multiple Correspondence Analysis and Cluster Analysis For Market Segmentation", in AP - Asia Pacific Advances in Consumer Research Volume 6, eds. Yong-Uon Ha and Youjae Yi, Duluth, MN : Association for Consumer Research, Pages: 197-199.

Asia Pacific Advances in Consumer Research Volume 6, 2005      Pages 197-199

A SIMULTANEOUS APPROACH TO CONSTRAINED MULTIPLE CORRESPONDENCE ANALYSIS AND CLUSTER ANALYSIS FOR MARKET SEGMENTATION

Heungsun Hwang, HEC Montreal, Canada

Byunghwa Yang, University of Michigan, U.S.A.

Yoshio Takane, McGill University, Canada

EXTENDED ABSTRACT -

A common practice for cluster-based market segmentation is to first uncover a low-dimensional representation of variables (e.g., the first few principal components) with data reduction techniques such as principal components analysis, factor analysis, or multidimensional scaling, and to subsequently use cluster analysis to identify a set of segments based on the low-dimensional data (Arimond & Elfessi, 2001; Furse, Punj, & Stewart, 1984; Green, Shaffer, & Patterson, 1988; Sheppard, 1996). This two-step sequential or tandem approach (Arabie & Hubert, 1994) has been advocated for substantive reasons (see Green & Krieger, 1995).

Despite its popularity, many authors have warned about a critical problem which is inherent to the tandem approach. Specifically, there is no guarantee that the low-dimensional representation of the data obtained in step one are optimal for subsequently identifying segmentation structures because data reduction is carried out with no reference to cluster analysis (Arabie & Hubert, 1994; Chang, 1983; DeSarbo, Jedidi, Cool, & Schendel, 1990; De Soete & Carroll, 1994). This suggests that preliminary data reduction may mask or distort the true segmentation structures in the original data. Green and Krieger (1995) offer empirical examples which support the legitimacy of this concern. Similarly, Vichi and Kiers (2001) present a simulation-based example in which tandem analysis failed to identify correct segments in the context of principal components analysis. Technically, this problem stems from the fact that each step of the tandem approach involves a different optimization criterion (i.e., one criterion for data reduction and another for cluster analysis) and that these criteria are addressed separately.

As a solution to the problem, the combined use of data reduction and cluster analysis in a single framework has been recommended (Bock, 1987; DeSarbo, Howard, & Jedidi, 1991; De Soete & Carroll, 1994; Heiser, 1993; van Burren & Heiser, 1989; Vichi & Kiers, 2001). In essence, this amounts to obtaining a low-dimensional representation of variables and classifying cases into a set of segments simultaneously. More technically, this involves combining the two different optimization criteria into a single one. This simultaneous approach ensures that low-dimensional data are optimally chosen in such a way so as to facilitate the identification of segments.

Nevertheless, in the simultaneous approach, it is not uncommon that the low-dimensional data are often difficult to interpret so that the resultant segments become difficult to characterize. To enhance the interpretability of low-dimensional data, one may utilize additional information or prior knowledge on the data. One can incorporate such additional information in the form of linear constraints (Bockenholt & Bockenholt, 1990; Nishisato, 1984; Takane & Shibayama, 1991; Takane, Yanai, & Mayekawa, 1991; ter Braak, 1988; van Buuren & de Leeuw, 1992; Yanai, 1986, 1998). By imposing constraints on data, one may simplify the interpretations of the obtained solutions because the data to be analyzed are already structured by the constraints (Bockenholt & Bockenholt, 1990). From a more technical perspective, one may obtain more reliable parameter estimates if imposed constraints are consistent with the data (Hwang & Takane, 2002).

In this paper, a new tool for market segmentation is proposed. The method is designed to simultaneously provide a low-dimensional representation of categorical variables and to classify cases into a set of segments. It is also designed to allow one to impose linear constraints on variables so as to facilitate the interpretations of solutions. More specifically, it involves the combination of (1) constrained multiple correspondence analysis (Hwang & Takane, 2002; van Buuren & de Leeuw, 1992) for obtaining a constrained low-dimensional data with (2) the k-means algorithm (MacQueen, 1967) for identifying segments.

In this paper, an optimization criterion that combines the criterion for constrained multiple correspondence analysis and that for the k-means algorithm in a single framework is presented. An alternating least squares algorithm (de Leeuw, Young, & Takane, 1976) is developed to minimize the optimization criterion for parameter estimation. By analyzing data collected on clothing brands and attributes, the authors empirically demonstrate that the method affords a flexible and parsimonious graphical display of segmentation structures inherent in multivariate categorical data. Although the contribution of the proposed method to the segmentation literature is largely technical, its important implications for consumer researchers and practitioners are also discussed.

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