Description
Book SynopsisThis book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou′s book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website.
Trade ReviewThis book provides a thorough and accessible look at an important class of statistical models. It communicates intuition well and shows through numerous examples that understanding how to analyze bounded outcome variables is useful for applied researchers. -- Jeff Harden
The authors are leaders in the world-wide effort to extend and tailor the generalized linear model to variables that are bounded and not normally distributed. The discussion of models for data recorded as proportions is worth the price of admission. -- Paul Johnson
Table of Contents1. Introduction and Overview Overview of this Book The Nature of Bounds on Variables The Generalized Linear Model Examples 2. Models for Singly-Bounded Variables GLMs for singly-bounded variables Model Diagnostics Treatment of Boundary Cases 3. Models for Doubly-Bounded Variables Doubly-Bounded Variables and \Natural" Heteroskedasticity The Beta Distribution: Definition and Properties Modeling Location and Dispersion Estimation and Model Diagnostics Treatment of Cases at the Boundaries 4. Quantile Models for Bounded Variables Introduction Quantile regression Distributions for Doubly-Bounded Variables with Explicit Quantile Functions The CDF-Quantile GLM 5. Censored and Truncated Variables Types of censoring and truncation Tobit models Tobit Model Example Heteroskedastic and Non-Gaussian Tobit Models 6. Extensions and Conclusions Extensions and a General Framework Absolute Bounds and Censoring Multi-Level and Multivariate Models Bayesian Estimation and Modeling Roads Less Traveled and the State of the Art References
