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Titolo: Generalized Linear Models and Extensions

Autori: Hardin James W., Hilbe Joseph M.

Product Details:

Paperback: 387 pages
Publisher: Stata Press;
2 edition (February 20, 2007)
Language: English

ISBN-10: 1597180149

ISBN-13: 978-1597180146

Product Dimensions: 9.2 x 7.2 x 0.9 inches

Table of contents

Preface (pdf)
Chapter 1—Introduction (pdf)
Author index (pdf)
Subject index (pdf)
Download the datasets used in the book

http://www.stata-press.com/books/glmext.html

http://www.amazon.com/Generalized-Linear-Models-Extensions-Second/dp/1597180149#reader_1597180149

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.

Product Description

 Generalized Linear Models and Extensions, Second Edition provides a comprehensive overview of the nature and scope of generalized linear models (GLMs) and of the major changes to the basic GLM algorithm that allow modeling of data that violate GLM distributional assumptions. Deftly balancing theory and application, the book stands out in its coverage of the derivation of the GLM families and their foremost links, while also guiding readers in the application of the various models to real data. This edition has new sections on discrete response models, including zero-truncated, zero-inflated, censored, and hurdle count models, as well as heterogeneous negative binomial, generalized Poisson, and generalized binomial models. The book also includes a substantially expanded discussion of both proportional-odds and generalized ordered models, making it easy for readers to use these models in their own research.

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. 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, since it lets the authors describe computational algorithms relatively simply. Devoting an entire chapter to each distribution (or family in GLM terms) also allows including 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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Abstract

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, 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.. generalized linear models, logit, probit, Poisson