Оглавление
Michael Smithson. Generalized Linear Models for Bounded and Limited Quantitative Variables
Quantitative Applications in the Social Sciences
GENERALIZED LINEAR MODELS FOR BOUNDED AND LIMITED QUANTITATIVE VARIABLES
CONTENTS
Series Editor’s Introduction
About the Authors
Acknowledgments
Companion Website for this Book
Chapter 1. Introduction and Overview. 1.1 Overview of This Book
1.2 The Nature of Bounds on Variables
1.3 The Generalized Linear Model. 1.3.1 Definitions and Concepts
1.3.2 Estimation
1.3.3 Evaluating and Comparing Models
1.4 Examples
1.4.1 Absolute Bounds Example
1.4.2 Censoring Bounds Example
Chapter 2. Models for Singly Bounded Variables
2.1 GLMs for Singly Bounded Variables. 2.1.1 Alternative Distribution Models
2.1.2 Time Required to Start a Business by Nation
2.1.3 Performance in a Stroop Task Experiment
2.2 Model Diagnostics
2.3 Treatment of Boundary Cases
2.3.1 Ambulance Arrival Times
Chapter 3. Models for Doubly Bounded Variables. 3.1 Doubly Bounded Variables and “Natural” Heteroscedasticity
3.2 The Beta Distribution: Definition and Properties
3.3 Modeling Location and Dispersion. 3.3.1 Location and Dispersion Submodels in the Beta GLM
3.3.2 Example 1: Measuring Speakers’ Grammaticality Judgments
3.3.3 Example 2: Probability Judgment in Moral Dilemmas
3.4 Estimation and Model Diagnostics. 3.4.1 Maximum Likelihood Estimation and Estimator Bias
3.4.2 Model Fit, Comparison, and Effect Sizes
3.4.3 Residuals and Influence Statistics
3.5 Treatment of Cases at the Boundaries. 3.5.1 Rescaling from [0, 1] to (0, 1): Methods and Issues
3.5.2 Hurdle and Boundary-Inflated Models
Chapter 4. Quantile Models for Bounded Variables. 4.1 Introduction
4.2 Quantile Regression
4.2.1 Example: Depressive Symptoms among Chinese University Students
4.3 Distributions for Doubly Bounded Variables with Explicit Quantile Functions
4.3.1 The CDF-Quantile Family
4.4 The CDF-Quantile GLM
4.4.1 Example
4.4.1.1 Example Comparing CDF-Quantile with Beta Regression
4.4.2 Residuals and Influence Measures
4.4.3 Guidelines, Unresolved Problems, and Extensions
Chapter 5. Censored and Truncated Variables
5.1 Types of Censoring and Truncation
5.2 Tobit Models
5.3 Tobit Model Example
5.4 Heteroscedastic and Non-Gaussian Tobit Models
CHAPTER 6. Extensions and Conclusions. 6.1 Extensions and a General Framework
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
6.5.1 State of the Art
References
Index
