Visualizing class specific heterogeneous tendencies in categorical data

Abstract

In multiple correspondence analysis, both individuals (observations) and categories can be represented in a biplot that jointly depicts the relationships across categories or individuals, as well as the associations between them. Additional information about the individuals can enhance interpretation capacities, such as by including categorical variables for which the interdependencies are not of immediate concern, but that facilitate the interpretation of the plot with respect to relationships between individuals and categories. This article proposes a new method for adding such information, according to a multiple-set cluster correspondence analysis approach that identifies clusters specific to classes, or subsets of the data that correspond to the categories of the additional variables. The proposed method can construct a biplot that depicts heterogeneous tendencies of individual members, as well as their relationships with the original categorical variables. A simulation study to investigate the performance of this proposed method and an application to data regarding road accidents in the United Kingdom confirms the viability of this approach.