Simultaneous Two-Way Clustering of Multiple Correspondence Analysis

A 2-way clustering approach to multiple correspondence analysis is proposed to account for cluster-level heterogeneity of both respondents and variable categories in multivariate categorical data. Specifically, in the proposed method, multiple correspondence analysis is combined with k-means in a unified framework in which k-means is applied twice to partition the object scores of respondents and the weights of variable categories. In this way, joint clusters that relate a subgroup of respondents exclusively to a subset of variable categories are obtained. The proposed method provides a low-dimensional map of displaying variable category points and the centroids of joint clusters simultaneously. In addition, it offers joint-cluster memberships of variable categories as well as respondents. A Monte Carlo study is conducted to assess the parameter recovery capability of the proposed method based on synthetic data. An empirical application concerning Korean consumers' preferences toward various underwear brands and attributes is presented to demonstrate the effectiveness of the proposed method as compared with 2 relevant extant approaches.