On some similarities between canonical correlation models and latent class models for two-way contingency tables

Abstract

SUMMARY Relationships between parameters of canonical correlations models and latent class models for two-way contingency tables are explored. It is found that under certain conditions, canonical models and latent models are equivalent. As a result, a new interpretation of canonical variables in contingency tables is proposed. Let P be an I x J probability matrix describing the joint distribution of two categorical random variables, X and Y, having I and J categories, respectively. In canonical analysis, e.g. Fisher (1940), Williams (1952) and Lancaster (1958), P is decomposed into a sum of R 2, which is discussed in ? 3.