Generalized Linear Models and Extensions, 3rd Edition

Generalized linear models (GLMs) extend linear regression to models with a non-Gaussian, or even discrete, response. GLM theory is predicated on the exponential family of distributions—a class so rich that it includes the commonly used logit, probit, and Poisson distributions. Although one can fit these models in Stata by using specialized commands (for example, logit for logit models), fitting them as GLMs with Stata’s glm command offers some advantages. For example, model diagnostics may be calculated and interpreted similarly regardless of the assumed distribution. This text thoroughly covers GLMs, both theoretically and computationally. The theory consists of showing how the various GLMs are special cases of the exponential family, general properties of this family of distributions, and the derivation of maximum likelihood (ML) estimators and standard errors. The book shows how iteratively reweighted least squares, another method of parameter estimation, is a consequence of ML estimation via Fisher scoring. The authors also discuss different methods of estimating standard errors, including robust methods, robust methods with clustering, Newey–West, outer product of the gradient, bootstrap, and jackknife.