Clustering Nominal data with Equivalent Categories

Abstract

The problem considered in the present paper is how to cluster data of nominal measurement level, where the categories of the variables are equivalent (the variables are replications of each other). One suitable technique to obtain such a clustering is latent class analysis (LCA) with equality restrictions on the conditional probabilities. As an alternative, a less well known technique is introduced: GROUPALS. This is an algorithm for the simultaneous scaling (by multiple correspondence analysis) and clustering of categorical variables. Equality restrictions on the category quantifications were incorporated in the algorithm, to account for equivalent categories. In two simulation studies, the clustering performance was assessed by measuring the recovery of true cluster membership of the individuals. The effect of several systematically varied data features was studied. Restricted LCA obtained good to excellent cluster recovery results. Restricted GROUPALS approximated this optimal performance reasonably well, except when underlying classes were very different in size.