Grouping and Association in Contingency Tables: An Exploratory Canonical Correlation Approach

Abstract The criteria of homogeneity and structure were proposed by Goodman (1981a) for determining whether certain rows or columns of a contingency table should be grouped. A data-based procedure (using the canonical form of bivariate distributions) is presented in this article to guide exploratory analysis to determine which rows or columns of a table may be grouped. This procedure facilitates the application of the homogeneity criterion. Relationships between the proposed method of grouping and the structural criterion are discussed as well as simultaneous inference for grouped tables. The grouping method is extended to multiway tables. The use of canonical forms as a model exploratory tool is addressed. Examples are discussed in detail.