# Chapter 5: Generalized Linear Models: Structure

• Peter K. Dunn
• Gordon K. Smyth
Chapter
Part of the Springer Texts in Statistics book series (STS)

## Abstract

Chapters ] and  considered linear regression models. These models assume constant variance, which demonstrably is not true for all data, as shown in Chap. . Generalized linear models (glms) assume the responses come from a distribution that belongs to a more general family of distributions, and also permit more general systematic components. We first review the two components of a glm (Sect. 5.2) then discuss in greater detail the family of distributions upon which the random component is based (Sect. 5.3), including writing the probability functions in the useful dispersion model form (Sect. 5.4). The systematic component of the glm is then considered in greater detail (Sect. 5.5). Having discussed the two components of the glm, glms are then formally defined (Sect. 5.6), and the important concept of the deviance function is introduced (Sect. 5.7). Finally, using a glm is compared to using a regression model after transforming the response (Sect. 5.8).

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