Foundations of Linear and Generalized Linear Models

CHAPTER 1 Introduction to Linear and Generalized Linear Models

This is a book about linear models and generalized linear models. As the names suggest, the linear model is a special case of the generalized linear model. In this first chapter, we define generalized linear models, and in doing so we also introduce the linear model.

Chapters 2 and 3 focus on the linear model. Chapter 2 introduces the least squares method for fitting the model, and Chapter 3 presents statistical inference under the assumption of a normal distribution for the response variable. Chapter 4 presents analogous model-fitting and inferential results for the generalized linear model. This generalization enables us to model non-normal responses, such as categorical data and count data.

The remainder of the book presents the most important generalized linear models. Chapter 5 focuses on models that assume a binomial distribution for the response variable. These apply to binary data, such as “success” and “failure” for possible outcomes in a medical trial or “favor” and “oppose” for possible responses in a sample survey. Chapter 6 extends the models to multicategory responses, assuming a multinomial distribution. Chapter 7 introduces models that assume a Poisson or negative binomial distribution for the response variable. These apply to count data, such as observations in a health survey on the number of respondent visits in the past year to a doctor. Chapter 8 presents ways of weakening distributional assumptions ...