The Analysis of Multidimensional Contingency Tables: Stepwise Procedures and Direct Estimation Methods for Building Models for Multiple Classifications

For the m-way contingency table, we consider models that describe the possible multiplicative interactions among the m variables of the table, and we show how to select models that fit the data in the table, using methods that are, in part, somewhat analogous to the usual stepwise procedures in regression analysis. (The m variables here are dichotomous or, more generally, polytomous variables.) These methods can be applied to build models for any of the following situations: (a) the m variables are response variables and the mutual relationships among the variables are of interest; (b) one of the variables is a response variable and the other m – 1 variables are factors that may affect the response; (c) m′ of the variables are response variables (1 < m′ < m) and the other m-m′variables are factors that may affect the m′ variables and the mutual relationships among the m′ variables. For illustrative purposes, we analyze a 4-way table (actually, a 3 × 23 table), considering both linear and quadratic interaction effects.