5 - The Log-Linear Model and its Applications

Summary

Introduction

In chapter 3 we presented procedures useful for analysing models of one or more dependent variables assuming several discrete values. These models must be constructed on a case by case basis, reflecting our intuition of the dynamics underlying the phenomena under investigation. The formulation may be that of a continuous latent variable with a threshold determining the value of the qualitative variable, or it may involve assumptions about the number of decision makers and their behaviour. This intuitive understanding of the behaviour we are modelling is essential, but it must be complemented with rigorous statistical methods.

In the first sections of this chapter we shall introduce a series of techniques suitable for studying relationships between qualitative variables – testing for independence and conditional independence, for example. This descriptive approach is useful for specifying the model.

To begin, we assume that our observations correspond to a single setting of the exogenous variable, i.e. the probability associated with each value of the endogenous variable is independent of the observation. The various probabilities are summarized in a contingency table, the number of entries of which being determined by the number of variables.