Bi-dendrograms for clustering the categories of a multivariate categorical data set

Abstract: The clustering of categories in a multivariate categorical data set is investigated, where the problem separates into that of merging categories of the same variables (i.e., within-variable categories), and combining categories of different variables (i.e., between-variable categories). For the within-variable problem, the objective is to arrive at fewer categories (and, consequently, lower data dimensionality) without affecting the essential features of the data set, thereby simplifying the interpretation of any analysis using the categorical variables. The categories can be of an ordinal or nominal nature, and this property is respected in the clustering, where only adjacent categories of ordinal variables can be combined. For the between-variable problem, the objective is to arrive at asmall number of category clusters that typify the observations in the data set. In this latter problem there is no restriction on which categories can combine, as long as they do not combine within the same variable. In each of these problems, results are given in the form of a pair of dendrograms stacked one on top of the other, called a bi-dendrogram. For the within-variable problem, once all categories within each variable have been merged, the second stage is to cluster the variables themselves. For the between-variable problem, the second stage is to cluster groups of respondents that fall into the response sets arrived at in the first stage of clustering. The approach is illustrated using a sociological survey data set from the International Social Survey Program.