Generalized Linear Models for Categorical and Continuous Limited Dependent Variables

By Michael Smithson, Edgar C. Merkle

© 2013 – Chapman and Hall/CRC

308 pages | 54 B/W Illus.

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Hardback: 9781466551732
pub: 2013-09-04
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About the Book

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.

Reviews

"… 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

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

Exercises

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

Exercises

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

Exercises

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

Exercises

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

Exercises

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

Exercises

Extensions

Extensions and Generalizations

Multilevel Models

Bayesian Estimation

Evaluating Relative Importance of Predictors in GLMs

About the Series

Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General