
11Introduction
1.6 Link Functions
In this book, we focus on logit, probit, and complementary log log (cloglog) versions of
ordered regression models. Using a generalized linear modeling framework (McCullagh
and Nelder 1989), these three model types represent different choices of “link functions”
(g[μ]) that relate the linear predictor (η) to the expected value or probability of interest (μ):
η = g(μ) (1.11)
In order to estimate the model, it is necessary to assume that the outcome is the realiza-
tion of a random variable based on a probability distribution. To specify a model, one must
select a particular probability distribution for the random ...