ABSTRACT

We have thus far discussed some basic types of statistical model estimation, providing code at the end of Chapter 3 to estimate the parameters of traditional linear regression models. These models required the assumption that the observed data were conditionally normal; that is, conditional on the model. The response variable followed the normal distribution. We now extend the linear model to include estimation of parameters of a collection of models that allow a range of conditional distributions — for example, binomial, Poisson, and gamma. These models are referred to as generalized linear models, or GLM. The linear model, being based on the normal probability distribution function (PDF) is a member of the GLM family. However, the normal model is nearly always estimated using the methods described in the last chapter, and we shall not cover it in this chapter.