Generalized linear models for bounded and limited quantitative variables

Author(s)

• Smithson, Michael
• Shou, Yiyun

Bibliographic Information

Generalized linear models for bounded and limited quantitative variables

Michael Smithson, Yiyun Shou

（Sage publications series, . Quantitative applications in the social sciences ; v. 181）

Sage, c2020

Note

Includes bibliographical references and index

Description and Table of Contents

Description

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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB29322112
• ISBN:
  • 9781544334530
• LCCN: 2019028200
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Los Angeles
• Pages/Volumes: xiii, 117 p.
• Size: 22 cm
• Classification:
  • LCC : QA279
  • DC23 : 519.5
• Subject Headings:
  • LCSH : Linear models (Statistics)
  • LCSH : Random variables
  • LCSH : Functions of bounded variation
  • LCSH : Quantitative research
• Parent Bibliography ID:
  • BA71788007