Exponential Family of Distributions and Generalized Linear Models

Abstract

For several decades linear models of the form

$$ y = X\beta + e $$

((3.1))

with the assumption that the elements of e are NID(0, σ²) have formed the basis of most analyses of continuous data. For instance the examples in the previous chapter, the comparison of two means (plant growth example) and the relationship between a continuous response variable and a covariate (birthweight example), are both of this form. So, too, are generalizations of these examples to comparisons of more than two means (ANOVA) and the relationship between a continuous response variable and several explanatory variables (multiple regression).