Guided and Unguided Methods for the Selection of Models for a Set of T Multidimensional Contingency Tables

The combined use of direct estimation (in saturated models) and indirect testing (of unsaturated models), proposed in [7, 8] for the analysis of a given multidimensional contingency table, is extended here to the analysis of a set of T multidimensional tables (T ≥ 2). For this set of tables, a three-fold classification of models is introduced: (1) models that assume “complete homogeneity” among the tables; (2) models that allow “complete heterogeneity” among the tables; and (3) models that allow “partial heterogeneity.” Stepwise procedures proposed in [8] for model selection are extended. “Guided” and “unguided” selection methods and “multidirectional” methods are introduced. For illustrative purposes, a set of two 4-way tables is analyzed.