Generalized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. Authors Jeff Gill and Michelle Torres provide 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.
About the Author
Jeff Gill is Distinguished Professor in the Department of Government, Professor in the Depart- ment of Mathematics & Statistics, and a Member of the Center for Behavioral Neuroscience at American University. He is also the inaugural director of the Center for Data Science and Co-Director of the graduate program in Data Science there. In additional to theoretical and methodological work in Bayesian statistics and statistical computing, his applied work centers on studying human beings from social, political, and biomedical perspectives.
Michelle Torres is Assistant Professor in the Department of Political Science at Rice University. Her core research covers political methodology, specifically survey methodology, computer vision, and causal inference. Substantively, she focuses on public opinion, participation, and psycholog- ical traits. She holds a Ph.D. in Political Science and an A.M. in Statistics from Washington University in St. Louis.
Table of Contents
Series Editor's IntroductionAbout the AuthorsAcknowledgements1. Introduction Model Specification Prerequisites and Preliminaries Looking Forward2. The Exponential Family Justification Derivation of the Exponential Family Form Canonical Form Multi-Parameter Models3. Likelihood Theory and the Moments Maximum Likelihood Estimation Calculating the Mean of the Exponential Family Calculating the Variance of the Exponential Family The Variance Function4. Linear Structure and the Link Function The Generalization Distributions5. Estimation Procedures Estimation Techniques Profile Likelihood Confidence Intervals Comments on Estimation6. Residuals and Model Fit Defining Residuals Measuring and Comparing Goodness-of-Fit Asymptotic Properties7. 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 Summary8. Conclusion Summary Related Topics Classic Reading Final Motivation9. References