4.16 Generalized Linear Models

Generalized linear models (GLMs) all follow the same ‘recipe’:

• use a set of predictors \(X_1\), …, \(X_p\) to predict a response \(Y\)

• model the response \(Y\) as coming from a particular distribution

e.g. Poisson Distribution, for Poisson regression

• transform the mean of the response (via a link function \(\eta\)) so that the transformed mean is a linear function of the predictors

e.g. for Poisson regression, \(log(\lambda(X_1, ..., X_p) = \beta_0 + \beta_1X_1 + ... + \beta_pX_p\)