J. Japan Statist. Soc., Vol. 31 (No. 1), pp. 15-26, 2001

Property of the RC(M) Association Model and a Summary Measure of Association in the Contingency Table

Nobuoki Eshima, Minoru Tabata and Masaaki Tsujitani

Abstract. The RC(M) association model is designed for analyzing the association in two-way contingency tables. First, the RC(M) association model is discussed through entropy, and it is shown that the entropy in the model is decreased in the direction of the intrinsic association parameter vector, and that the Pearson product-moment correlation coefficients of row and column scores increase in the corresponding intrinsic association parameters. Second, a summary measure of association between two categorical variables in the RC(M) association model is proposed, and the relationship between the association measure and the intrinsic association parameter vector is investigated. Lastly, the present paper applies the discussion to the multivariate normal distribution.

Key words and phrases: Association model, canonical correlation coefficient, contingency table, entropy, multivariate normal distribution, summary measure of association.

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