ABSTRACT
Generalized linear models (GLMs) broaden the types of outcomes that are allowed. In this chapter the authors consider logistic, Poisson, and negative binomial regression. But they also explore a variant that is relevant to both linear models and generalized linear models: multilevel modeling. Logistic regression, and its close variants, are useful in a variety of settings, from elections through to horse racing. One application of Poisson regression is modeling the outcomes of sports. For instance Burch builds a Poisson model of hockey outcomes, following Baio and Blangiardo who build a Poisson model of football outcomes. One of the restrictions with Poisson regression is the assumption that the mean and the variance are the same. Multilevel modeling goes by a variety of names including “hierarchical”, and “random effects”. While there are sometimes small differences in meaning between disciplines, in general they refer to the same or at least similar ideas.
