Summary: Statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables. Three basic classes of models are considered: (a) models that assume complete homogeneity across tables, (b) models that allow partial homogeneity across tables, and (c) models that allow complete heterogeneity.
Methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of differences among the tables in the estimated parameters. To illustrate the wide applicability of these models and methods, we present analyses of two quite different sets of data.