Clustering and Scaling: Grouping Variables in Burt Matrices

Abstract

Although clustering and scaling are different techniques, it has been shown that in the case of a two-way cross-table, cluster analysis and correspondence analysis provide similar solutions (Greenacre 1988a, 1993; Lebart 1994). In this paper we extend this approach to the multiple case. Instead of analyzing two variables we use a set of variables. When scaling the data we apply joint correspondence analysis which is the generalization of simple correspondence analysis (Greenacre 1988b, 1993). The suggested clustering process is hierarchical whereby the similarity matrix consists of standardized χ²-values computed from the subtables of the Burt matrix. As an example we use 25 variables of cultural competences taken from the German General Social Survey 1986 (ALLBUS).