Generalized Linear Models and Extensions: Fourth Edition

by James W. Hardin, Joseph M. Hilbe

Overview

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 models. 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, with an emphasis on Stata. The theory consists of showing how the various GLMs are special cases of the exponential family, showing general properties of this family of distributions, and showing the derivation of maximum likelihood (ML) estimators and standard errors. Hardin and Hilbe show how iteratively reweighted least squares, another method of parameter estimation, are a consequence of ML estimation using Fisher scoring.

Product Details

ISBN-13:	9781597182256
Publisher:	Stata Press
Publication date:	04/27/2018
Edition description:	New
Pages:	598
Product dimensions:	7.50(w) x 9.25(h) x (d)

About the Author

James W. Hardin is a professor and the Biostatistics division head in the Department of Epidemiology and Biostatistics at the University of South Carolina. He is also the associate dean for Faculty Affairs and Curriculum of the Arnold School of Public Health at the University of South Carolina.

Joseph M. Hilbe was a professor emeritus at the University of Hawaii and an adjunct professor of sociology and statistics at Arizona State University.

Table of Contents

Foundations of Generalized Linear Models. GLMs. GLM estimation algorithms. Analysis of fit. Continuous Response Models. The Gaussian family. The gamma family. The inverse Gaussian family. The power family and link. Binomial Response Models. The binomial–logit family. The general binomial family. The problem of overdispersion. Count Response Models. The Poisson family. The negative binomial family. Other count-data models. Multinomial Response Models. Unordered-response family. The ordered-response family. Extensions to the GLM. Extending the likelihood. Clustered data. Bivariate and multivariate models. Bayesian GLMs. Stata Software. Programs for Stata. Data synthesis.