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.

Censored and Truncated Variables

We define and discuss varieties of truncation and censoring in this chapter, including fixed versus random threshold models and sample selection models. We elaborate Tobit models because they are the most well known, and we focus on the most common type of Tobit model with brief introductions to the more complex and less commonplace types. Model estimation, evaluation, and diagnostics are covered. Our main example is a double-censoring model (i.e., where both the lower and upper bounds of a scale are censored scores). After discussing issues of nonnormality and heteroscedasticity for Tobit models, we extend this example by fitting a non-Gaussian heteroscedastic model.

Types of Censoring and Truncation

We introduced censoring and truncation in Chapter 1, where we distinguished among different ...

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