Generalized Linear Models for Bounded and Limited Quantitative Variables provides a focused discussion on the theoretical and applied aspects of modeling outcomes with natural boundaries, such as proportions, and outcomes subjected to censoring or truncation. The authors introduce models that use appropriate distributions for various types of bounded outcomes, such as beta regression for outcomes bounded between 0 and 1. They also introduce models such as Tobit models that account for censoring and models that can account for excess observations at boundaries. Researchers and students who have some familiarity with generalized linear models will find this book to be a great resource when they are ready to model bounded and limited dependent variables.
The book’s companion website provides annotated code in Stata, SAS, and R, as well as the datasets needed to reproduce the examples in the book. These resources make it easy for readers to learn not only the theory behind these models but also the practical aspects of fitting the models and interpreting the results.
1.2 The Nature of Bounds on Variables
1.3 The Generalized Linear Model
1.4 Examples
2.2 Model Diagnostics
2.3 Treatment of Boundary Cases
3.2 The Beta Distribution: Definition and Properties
3.3 Modeling Location and Dispersion
3.4 Estimation and Model Diagnostics
3.5 Treatment of Cases at the Boundaries
4.2 Quantile Regression
4.3 Distributions for Doubly Bounded Variables With Explicit Quantile Functions
4.4 The CDF-Quantile GLM
5.2 Tobit Models
5.3 Tobit Model Example
5.4 Heteroscedastic and Non-Gaussian Tobit Models
6.2 Absolute Bounds and Censoring
6.3 Multilevel and Multivariate Models
6.4 Bayesian Estimation and Modeling
6.5 Roads Less Traveled and the State of the Art
