Replication as a Rule for Determining the Number of Clusters in Hierarchial Cluster Analysis

摘要

A single higher-order cluster analysis can beused to group cluster mean profiles derived fromseveral preliminary analyses. Replication is confirmedwhen each higher-order cluster contains one clustermean profile from each of the several preliminaryanalyses. This study evaluated the utility ofreplication as a stopping rule in hierarchical clusteranalysis. Replication defined by higher-orderclustering identifies the correct number of underlyingpopulations that have distinct density regionsin the multivariate measurement space. Whenincreased within-population variance obliteratespopulation distinctions, the replication criterionprovides an underestimation of the actual numberof latent populations. In the case of no truecluster structure or in the case of only two latentpopulations, chance replication can occur. Thus,replication suggested by higher-order clusteranalysis is not a conservative test for the absenceof a cluster structure, but it does provide validevidence concerning the number of latent populationswhen several are present. Index terms:cluster analysis, cluster means, hierarchical clustering,replication in cluster analysis, stopping rulein cluster analysis, validity of cluster analysis.