A Course in Statistics with R

Chapter 17Generalized Linear Models

Package(s): gdata, RSADBE

Dataset(s): chdage, lowbwt, sat, Disease, BS, caesareans

17.1 Introduction

In Chapter 16 we discussed many useful statistical methods for analysis of categorical data, which may be nominal or ordinal data. The related regression problems were deliberately not touched upon there, the reason for omission being that the topic is more appropriate here. We will see in the next section that the linear regression methods of Chapter 12 are not appropriate for explaining the relationship between the regressors and discrete regressands. The statistical models, which are more suitable for addressing this problem, are known as the generalized linear models, which we abbreviate to GLM.

In this chapter, we will consider the three families of the GLM: logistic, probit, and log-linear models. The logistic regression model will be covered in more detail, and the applications of the others will be clearly brought out in the rest of this chapter.

We first begin with the problem of using the linear regression model for count/discrete data in Section 17.2. The exponential family continues to provide excellent theoretical properties for GLMs and the relationship will be brought out in Section 17.3. The important logistic regression model will be introduced in Section 17.4. The statistical inference aspects of the logistic regression model is developed and illustrated in Section 17.5. Similar to the linear regression model, we will consider ...