Replication as a rule for determining the number of clusters in hierarchical cluster analysis

Abstract

A single higher-order cluster analysis can be used to group cluster mean profiles derived from several preliminary analyses. Replication is confirmed when each higher-order cluster contains one cluster mean profile from each of the several preliminary analyses. This study evaluated the utility of replication as a stopping rule in hierarchical cluster analysis. Replication defined by higher-order clustering identifies the correct number of underlying populations that have distinct density regions in the multivariate measurement space. When increased within-population variance obliterates population distinctions, the replication criterion provides an underestimation of the actual number of latent populations. In the case of no true cluster structure or in the case of only two latent populations, chance replication can occur. Thus, replication suggested by higher-order cluster analysis is not a conservative test for the absence of a cluster structure, but it does provide valid evidence concerning the number of latent populations when several are present. Index terms: cluster analysis, cluster means, hierarchical clustering, replication in cluster analysis, stopping rule in cluster analysis, validity of cluster analysis.