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Generalized Linear Models

Generalized Linear Models
A Unified Approach

Second Edition

June 2019 | 176 pages | SAGE Publications, Inc

Generalized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. The Second Edition provides examples using real data from multiple fields in the social sciences such as psychology, education, economics, and political science, including data on voting intentions in the 2016 U.S. Republican presidential primaries. The Second Edition also strengthens material on the exponential family form, including a new discussion on the multinomial distribution; adds more information on how to interpret results and make inferences in the chapter on estimation procedures; and has a new section on extensions to generalized linear models.

Software scripts, supporting documentation, data for the examples, and some extended mathematical derivations are available on the authors’ websites ( as well as through the \texttt{R} package \texttt{GLMpack}. Supporting material (data and code) to replicate the examples in the book can be found in the 'GLMpack' package on CRAN or on the website

Series Editor's Introduction
About the Authors
1. Introduction
Model Specification

Prerequisites and Preliminaries

Looking Forward

2. The Exponential Family

Derivation of the Exponential Family Form

Canonical Form

Multi-Parameter Models

3. Likelihood Theory and the Moments
Maximum Likelihood Estimation

Calculating the Mean of the Exponential Family

Calculating the Variance of the Exponential Family

The Variance Function

4. Linear Structure and the Link Function
The Generalization


5. Estimation Procedures
Estimation Techniques

Profile Likelihood Confidence Intervals

Comments on Estimation

6. Residuals and Model Fit
Defining Residuals

Measuring and Comparing Goodness-of-Fit

Asymptotic Properties

7. Extentions to Generalized Linear Models
Introduction to Extensions

Quasi-Likelihood Estimation

Generalized Linear Mixed Effects Model

Fractional Regression Models

The Tobit Model

A Type-2 Tobit Model with Stochastic Censoring

Zero Inflated Accomodating Models

A Warning About Robust Standard Errors


8. Conclusion

Related Topics

Classic Reading

Final Motivation

9. References

Sample Materials & Chapters

2. The Exponential Family

Jeff Gill

Jeff Gill is a Distinguished Professor of Government, a Professor of Statistics, and a Member of the Center for Behavioral Neuroscience at American University. His research applies Bayesian modeling and data analysis (decision theory, testing, model selection, elicited priors) to questions in general social science quantitative methodology, political behavior and institutions, medical/health data analysis especially physiology, circulation/blood, pediatric traumatic brain injury, and epidemiological measurement/data issues, using computationally intensive tools (Monte Carlo methods, MCMC, stochastic optimization, nonparametrics). More About Author

Michelle Torres

Michelle Torres is Assistant professor in the Department of Political Science at Rice University. She holds a PhD in Political Science and a AM in Statistics from Washington University in St. Louis. Her research interests are in the fields of political methodology, with a special focus on survey methodology, computer vision, causal inference, public opinion, and political communication. More About Author

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ISBN: 9781506387345