Structuring Interaction in Two-Way Tables by Clustering

Abstract

An agglomerative hierarchical clustering procedure is presented for identifying simultaneously groups of unstructured rows and groups of unstructured columns in an orthogonal two-way table of uncorrelated normally distributed observations wiht common variance, such that the interaction between row and column factors is due only to interactions between those groups, leading to a more parsimonious model than the full model with interactions. The procedure is based on sums of squares for interaction components, but mean squares for interactions are used as proximity measure among rows and among columns in each step. In an independent estimate of the variance is available, a stopping rule is based on an extended F ratio simultaneous test procedure as proposed by Calinski and Corsten (1985, Biometrics 41, 39-48). Otherwise, an approximate procedure including variance estimation is suggested.