Canonical exponential models for analysis of association between two sets of variables

The present paper discusses canonical exponential models for analysis of association between two sets of variables. First, properties of the models are discussed in view of entropy. It is shown that entropy in the models is decreasing in canonical association parameters. Second, the present paper proposes a summary measure of association in the models that is decomposed into canonical association components. The present approach is applied to the RC(M) association model and canonical correlation analysis with the multivariate normal distribution. (C) 2003 Elsevier B.V. All rights reserved.