Glim Syntax and Simultaneous Tests for Graphical Log Linear Models

Within the class of hierarchical log linear models for contingency tables, conditional independence models have a special place and as they are well represented by their independence graphs they are known as graphical models. Standard GLIM model formulae are extended to give a simple representation of these models and rules are given to translate formulae between the standard and extended language. The deviances for all conditional independence models can be computed from the deviances of the elementary graphical models. These computations are employed in a simultaneous test procedure for selecting a parsimonious model from the class of all graphical models. This procedure is illustrated on a contingency table from the sociological literature classified by four response factors.