Classifying Variables on the Basis of Disaggregate Correlations

A clustering algorithm will be introduced in this article that is agglomerative hierarchical in nature and based on disaggregate correlations, and that may be used for classifying variables. The effect of aggregating data prevents the use of ordinary correlations as similarity measures between composite variables or between composite and single variables. This is because the magnitude of such correlations varies with the number of variables included in a composite. A mathematical formulation of this effect provides the opportunity to disaggregate correlations, so that they may be used as similarity measures at any stage during cluster analysis. The cluster algorithm based on disaggregate correlations tends to maximize the average intercorrelations among the variables within clusters. Results of an investigation using random data with an internal structure and an empirical example verify the utility of this approach for classification.