Abstract
Abstract This chapter introduces the three components of a generalized linear model (GLM): the linear predictor, the link function, and the probability function. It discusses the exponential dispersion family as a generator model for GLMs in a large sense. It sketches the fitting of a GLM with the iteratively weighted least squares algorithm for maximum likelihood in the frequentist framework. It introduces the main methods for assessing the effects of explanatory variables in frequentist GLMs (the Wald and likelihood ratio tests), the use of deviance as a measure of lack of model fit in GLMs, and the main types of residuals (Pearson, deviance, and randomized quantile) used in GLM model validation. It also discusses Bayesian fitting of GLMs, and some issues involved in defining priors for the GLM parameters.
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