Generalized linear models for bounded and limited quantitative variables / Michael Smithson, Yiyun Shou.

Format:

Book

Author/Creator:

Smithson, Michael, author.

Shou, Yiyun, author.

Series:

Quantitative applications in the social sciences

Language:

English

Subjects (All):

Linear models (Statistics).

Random variables.

Functions of bounded variation.

Quantitative research.

Physical Description:

xiii, 117 pages : illustrations ; 22 cm.

Place of Publication:

Thousand Oaks, California : SAGE, [2020]

Summary:

"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 at www.sagepub.com/smithsonshou"-- Provided by publisher.

Contents:

Introduction and overview

Overview of this book

The nature of bounds on variables

The generalized linear model

Examples

Models for singly bounded variables

GLMs for singly bounded variables

Model diagnostics

Treatment of boundary cases

Models for doubly bounded variables

Doubly bounded variables and "natural" heteroscedasticity

The beta distribution : definition and properties

Modeling location and dispersion

Estimation and model diagnostics

Treatment of cases at the boundaries

Quantile models for bounded variables

Introduction

Quantile regression

Distributions for doubly bounded variables with explicit quantile functions

The CDF-quantile GLM

Censored and truncated variables

Types of censoring and truncation

Tobit models

Tobit model example

Heteroscedastic and non-gaussian tobit models

Extensions and conclusions

Absolute bounds and censoring

Multilevel and multivariate models

Bayesian estimation and modeling

Roads less traveled and the state of the art.

Notes:

Includes bibliographical references and index.

ISBN:

9781544334530

1544334532

OCLC:

1126346947