Cluster analysis of learning disabled children

A series of cluster analyses were performed on a sample of 125 learning disabled (LD) children, based on scores on a battery of 26 psychometric measures. The sample was randomly divided in half. Each half was separately subjected to two methods of ordination (principal components analysis and Q-technique components analysis), seven hierarchical clustering algorithms (using up to three of four measures of similarity) and four methods of iterative partitioning. While the data were heterogeneous, cluster solutions varied widely across methods. Results were consistent for both halves, and it was concluded that no reliable LD subgroups could be identified. Hierarchical clustering algorithms and measures of similarity were compared. The most similar methods were Ward's method and within-group average, while Ward's method and average linkage were the most dissimilar methods. Euclidean distance and squared Euclidean distance were found to be the most similar measures, while Euclidean distance and product-moment correlation coefficient were least similar. Iterative partitioning techniques were also evaluated. CLUSTAN (Wishart, 1979, 1982) and BMDPKM were found to be similar, and to generate acceptable partitions when default options were used. SPSSX QUICK CLUSTER was unacceptable, and it was recommended that the program not be used without a partially optimized initial partition. It was strongly recommended that any practical application of cluster analysis use multiple clustering algorithms. Clusters derived from a single method of clustering should not be given much credence in the absence of external confirmation.