General Applications of Hierarchical Grouping Using the HIER-GRP Computer Program

摘要

HIER-GRP is a computer program which hierarchically groups a set of regression equations so as to minimize the overall loss of predictive efficiency at each stage of clustering, as measured by the decrease in the overall squared multiple correlation coefficient. HIER-GRP has been used extensively for grouping regression equations which satisfy the proportionally condition (each equation having the same predictor means and covariance matrix). This technical paper describes procedures for using HIER-GRP, without modification, to perform grouping in more general situations. A simple method is shown for reformulating the grouping problem for the columns of any matrix in terms of a proportional regression clustering problem. Applications include (a) grouping prediction systems which are not proportional, (b) grouping raters on similarity of response profiles, (c) grouping jobs (or technical schools) to minimize loss of differential classification effectiveness, and (d) grouping columns of any standard transportation problem to minimize interaction between columns within a cluster.