Models for Categorical Response Variables

Abstract

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

$$ \begin{gathered} E(y_i ) = x_{i1} \beta _1 + ... + x_{ip} \beta _p \hfill \\ = x'_i \beta . \hfill \\ \end{gathered} $$

(10.0)

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