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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 (http://jeffgill.org/publications/generalized-linear-models-unified-approach-0) 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 https://github.com/smtorres/GLMpack.


T271311

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

 
Prerequisites and Preliminaries

 
Looking Forward

 
 
2. The Exponential Family
Justification

 
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

 
Distributions

 
 
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

 
Summary

 
 
8. Conclusion
Summary

 
Related Topics

 
Classic Reading

 
Final Motivation

 
 
9. References
Key features

NEW TO THIS EDITION:

  • New examples using real data include capital punishment (a count of executions in each state), electoral politics in Scotland (percentage of votes in favor of granting parliament taxation powers), and voting intention in the U.S. Republican presidential primaries (candidate selected from a list).
  • Strengthens material on the exponential family form, including a new discussion on multinomial distribution.
  • Adds more information on how to interpret results and make inferences in the chapter on estimation procedures.
  • A new section on extensions to generalized linear models.

Preview this book

Sample Materials & Chapters

2. The Exponential Family


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