Generalized Linear Model - Overview

Overview

In a generalized linear model (GLM), each outcome of the dependent variables, Y, is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial and Poisson distributions, among others. The mean, μ, of the distribution depends on the independent variables, X, through:

where E(Y) is the expected value of Y; Xβ is the linear predictor, a linear combination of unknown parameters, β; g is the link function.

In this framework, the variance is typically a function, V, of the mean:

It is convenient if V follows from the exponential family distribution, but it may simply be that the variance is a function of the predicted value.

The unknown parameters, β, are typically estimated with maximum likelihood, maximum quasi-likelihood, or Bayesian techniques.