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.
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.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.