Log-Linear Models

Abstract

The three preceding chapters have all used models in which the response variables were probabilities (Chapters 4 and 5) or a linear combination of probabilities (Chapter 6). In this chapter we consider a model in which the response function involves the natural logarithm of the response variable. The particular form of the logarithmic function that we will use is the logit. The logit function is defined as the natural logarithm of π divided by 1 - π:

$$ \log it(\pi ) = \ln \left( {\frac{\pi } {{1 - \pi }}} \right) $$

One rationale for this transformation is presented in this chapter. After performing this transformation, we analyze the logit in the same fashion as the linear functions in Chapters 4, 5, and 6.