Model selection for four- and higher-dimensional tables

Abstract

As the number of dimensions of the contingency table increases so does the number of possible hierarchical log-linear models. For example, for three dimensions there are eight models and for four dimensions there are 113 models (Bishop et al, 1975). Obviously we cannot test the fit of all these models so we need a method of selecting terms to be included in our 'best fit' model. There is no best method for selecting a log-linear model just as there is no best method for variable selection in multiple regression. Three methods of model selection are discussed, each in the context of a single data set. The program GLIM is used throughout to fit models.