Models for Categorical Response Variables

Abstract

Generalized linear models (GLMs) are a generalization of the classical linear models of regression analysis and analysis of variance, which model the relationship between the expectation of a response variable and unknown predictor variables according to

$$\begin{array}{ll} {\rm E}(y_i) &= x_{i1}\beta_1 + \ldots + x_{ip}\beta_p\\ &= x^{\prime}_i \beta.\\ \end{array}$$

(8.1)

The parameters are estimated according to the principle of least squares and are optimal according to the minimum dispersion theory or, in the case of a normal distribution, are optimal according to the ML theory (cf. Chapter 3).