Models for Categorical Response Variables

Abstract

Generalized linear models are a generalization of the classical linearmodels of the regression analysis and analysis of variance, whichmodel the relationship between the expectation of a response variableand unknown predictor variables according to \begin{gathered}E(y_i ) = x_{i1} β_1 + ... + x_{ip} β_p \hfill \\ = x'_iβ. \hfill \\ \end{gathered} (10.0) The parameters are estimatedaccording to the principle of least squares and are optimal accordingto minimum dispersion theory, or in case of a normal distribution,are optimal according to the ML theory (cf. Chapter 3).