This 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.
Spis treści
1. 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
O autorze
Dr Yiyun Shou is a research fellow in the Research School of Psychology at The Australian National University. She received her Ph D degree in psychology in 2015, and was recently awarded an Australian Research Council Discovery Early Career Award (2018 – 2021). She is active in research in the areas of understanding measurement issues in psychology and developing new quantitative methods. She also conducts extensive research in judgment and decision making under uncertainty, and cross-cultural psychological assessments. She has publications in a number of respected international outlets for measurement and quantitative psychology such as Journal of Statistical Software, British Journal of Mathematical and Statistical Psychology, Psychometrika and Psychological Assessment.
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