Generalized Linear Models for Categorical and Continuous Limited Dependent Variables  book cover
1st Edition

Generalized Linear Models for Categorical and Continuous Limited Dependent Variables

ISBN 9781466551732
Published September 5, 2013 by Chapman and Hall/CRC
312 Pages 54 B/W Illustrations

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Book Description

Generalized Linear Models for Categorical and Continuous Limited Dependent Variables is designed for graduate students and researchers in the behavioral, social, health, and medical sciences. It incorporates examples of truncated counts, censored continuous variables, and doubly bounded continuous variables, such as percentages.

The book provides broad, but unified, coverage, and the authors integrate the concepts and ideas shared across models and types of data, especially regarding conceptual links between discrete and continuous limited dependent variables. The authors argue that these dependent variables are, if anything, more common throughout the human sciences than the kind that suit linear regression. They cover special cases or extensions of models, estimation methods, model diagnostics, and, of course, software. They also discuss bounded continuous variables, boundary-inflated models, and methods for modeling heteroscedasticity.

Wherever possible, the authors have illustrated concepts, models, and techniques with real or realistic datasets and demonstrations in R and Stata, and each chapter includes several exercises at the end. The illustrations and exercises help readers build conceptual understanding and fluency in using these techniques. At several points the authors bring together material that has been previously scattered across the literature in journal articles, software package documentation files, and blogs. These features help students learn to choose the appropriate models for their purpose.

Table of Contents

Introduction and Overview
The Nature of Limited Dependent Variables
Overview of GLMs
Estimation Methods and Model Evaluation
Organization of This Book

Discrete Variables
Binary Variables
Logistic Regression
The Binomial GLM
Estimation Methods and Issues
Analyses in R and Stata
Nominal Polytomous Variables
Multinomial Logit Model
Conditional Logit and Choice Models
Multinomial Processing Tree Models
Estimation Methods and Model Evaluation
Analyses in R and Stata
Ordinal Categorical Variables
Modeling Ordinal Variables: Common Practice versus Best Practice
Ordinal Model Alternatives
Cumulative Models
Adjacent Models
Stage Models
Estimation Methods and Issues
Analyses in R and Stata

Count Variables
Distributions for Count Data
Poisson Regression Models
Negative Binomial Models
Truncated and Censored Models
Zero-Inflated and Hurdle Models
Estimation Methods and Issues
Analyses in R and Stata
Continuous Variables
Doubly Bounded Continuous Variables
Doubly Bounded versus Censored
The beta GLM
Modeling Location and Dispersion
Estimation Methods and Issues
Zero- and One-Inflated Models
Finite Mixture Models
Analyses in R and Stata
Censoring and Truncation
Models for Censored and Truncated Variables
Non-Gaussian Censored Regression
Estimation Methods, Model Comparison, and Diagnostics
Extensions of Censored Regression Models
Analyses in R and Stata
Extensions and Generalizations
Multilevel Models
Bayesian Estimation
Evaluating Relative Importance of Predictors in GLMs

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Michael Smithson, Edgar C. Merkle


"… a very useful contribution for anyone who needs modern extensions of statistical modeling tools. I was also impressed with the elegant way in which the authors went about the demanding task of explaining complex methods to readers."
International Statistical Review, 2015

"What new perspective or emphasis could be brought to this crowded market? This contribution from Smithson and Merkle is distinctive in several respects. It is geared toward a social-science audience … The authors cover an impressive amount of ground … in one book, the authors cover many different models for a wide array of discrete and limited dependent variables (LDVs). … a valuable resource for graduate students and practitioners in psychology, political science, international relations, anthropology, sociology, education, and communication … . The Beta GLM and some of the models for censored and truncated responses are much newer and more exotic than say, logistic regression or count models, making Smithson and Merkle’s book a welcome addition even for seasoned practitioners … ."
Journal of the American Statistical Association, June 2015