Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories

Abstract

Abstract The association models considered in Goodman (1979a) for the analysis of cross-classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach. Both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories, and these scores can be used to partition into relevant components the usual chi-squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification. However, while the usual procedure for testing the statistical significance of chi-squared components is invalid when these components are based on the canonical correlations, a corresponding procedure is valid when these components are obtained with the association models. The components of association obtained with the association mo...