ABSTRACT
The linear regression approach of Part IV suggests a presentation of statistical models in menu form, with a set of possible distributions for the response variable, a set of transformations to facilitate the use of those distributions, and the ability to include information in the form of linear predictors. In a linear model, the expected value of the data y is a linear function of parameters β and predictors X: E(y|X, β)=Xβ. In a generalized linear model, the expected value of y is a nonlinear function of the linear predictor: E(y|X, β)=g−1(Xβ). Robust (Chapter 17) and mixture models (Chapter 18) generalize these by adding a latent (unobserved) mixture parameter for each data point.
