Generalized Linear Models

Abstract

In Chap. 10 we examined nonlinear models with normally-distributed errors. Given these conditions, minimizing the residual sum of squares maximizes the likelihood function. Not all variables of interest to scientists are normally distributed, however. Instead of being continuous and unbounded, many variables are discrete (e.g., number of aphids on a leaf), categorical (e.g., number of men and women who buy or do not buy life insurance in a given year), binary (e.g., employed or unemployed), or restricted to having only non-negative values (e.g., rainfall). Because these variables are not normally-distributed, minimizing the residual sum of squares does not produce maximum likelihood estimates.