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Generalized Linear Models and Extensions, Second Edition

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James W. Hardin and Joseph M. Hilbe
Publisher: Stata Press
Copyright: 2007
ISBN-13: 978-1-59718-014-6
Pages: 387; paperback
James W. Hardin and Joseph M. Hilbe
Publisher: Stata Press
Copyright: 2007
Pages: 387; eBook

Comment from the Stata technical group

Generalized linear models (GLMs) extend standard linear (Gaussian) regression techniques 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 (e.g., logit for logit models), fitting them under the GLM paradigm with Stata’s glm command offers the advantage of having many models under the same roof. 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, are 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. The thorough coverage of model diagnostics includes measures of influence such as Cook’s distance, nine forms of residuals, the Akaike and Bayesian information criteria, and various R2-type measures of explained variability.

After presenting general theory, the text then breaks down each distribution. Each distribution has its own chapter that discusses the computational details of applying the general theory to that particular distribution. Pseudocode plays a valuable role here, because it lets the authors describe computational algorithms relatively simply. Devoting an entire chapter to each distribution (or family in GLM terms) also allows for the inclusion of real-data examples showing how Stata fits such models, as well as presenting certain diagnostics and analytical strategies that are unique to that family. The chapters on binary data and on count (Poisson) data are excellent in this regard. Hardin and Hilbe give ample attention to the problems of overdispersion and zero inflation in count-data models.

The final part of the text concerns extensions of GLMs, which come in three forms. First, some chapters cover multinomial responses, both ordered and unordered. Although strictly not part of GLM, the theory is similar in that one can think of a multinominal response as an extension of a binary response. The examples presented in these chapters often use the authors’ own Stata programs, augmenting official Stata’s capabilities. Second, GLMs may be extended to clustered data through generalized estimating equations (GEEs), and one chapter covers GEE theory and examples. Finally, GLMs may be extended by programming one’s own family and link functions for use with Stata’s official glm command, and the book covers this process.

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