Models for the Interactions

If the statistical analysis of a contingency table is based on one of the log-linear models in chapters 5, 6 and 7, a number of natural models are easily overlooked. Many useful models can thus be expressed as structures in the log-linear interaction parameters. In this chapter a number of such models are discussed. Many of these models can be viewed as attempts to describe the non-zero interactions by a simple structure if the analysis of the data by a log-linear model has failed to give a satisfactory fit to the model. If e.g. the independence hypothesis for a two-way table has been rejected, a residual analysis will often reveal a certain structure in the two-factor interactions.