Hierarchical Cluster Analysis Using Intraclass Correlations: A Mixture Model Study

Sixteen hierarchical clustering algorithms were compared on their ability to resolve 20 multivariate normal mixtures (Blashfield, 1976) and 12 multivariate gamma mixtures (Mojena, 1977). The 16 algorithms represented a 4 x 4 (amalgamation rule x similarity measure) design. The amalgamation rules were single, complete, average, and centroid linkage. The similarity measures were Euclidean distance, correlation, and the one-way and two-way intraclass correlations. Accuracy was calculated using both kappa as a function of coverage (Edelbrock, 1979) and Rand's statistic. Comparisons were also made with Ward's minimum variance technique. Conclusions based on kappa and Rand's statistic were identical. A subset of algorithms was found to be highly accurate in solving both types of mixtures. The accurate algorithms were average and centroid linkage using the one-way intraclass correlation and Ward's technique. This suggests that the one-way intraclass correlation may be useful in clustering applications aimed at identifying subtypes differing in profile shape, elevation, and scatter.