Generalized linear models: General theory

Chapters 1-3 focused on the most common class of models used in applications: linear models. Despite their versatility, linear models do not apply in all situations. In particular, they are not designed to deal with binary or count responses. In Chapter 4, we introduce generalized linear models (GLMs), a generalization of linear models that encompasses a wide variety of incredibly useful models, including logistic regression and Poisson regression.

We’ll start Chapter 4 by introducing exponential dispersion models (Section Chapter 19), a generalization of the Gaussian distribution that serves as the backbone of GLMs. Then we formally define a GLM, demonstrating logistic regression and Poisson regression as special cases (Section Chapter 20). Next, we discuss maximum likelihood inference in GLMs (Section Chapter 21). Finally, we discuss how to carry out statistical inference in GLMs (Section Chapter 22).