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.

Models for Singly Bounded Variables

In this chapter, we focus on models for variables with nonnegative values, as these are typical of singly bounded variables. However, nearly all of the material in this chapter generalizes to variables with lower or upper bounds that are not zero. We start with the lognormal distribution because of its familiarity to readers, but also because it illustrates how a bound induces dependency between location and dispersion. The chapter then introduces models using the popular gamma and Weibull distributions and provides two examples of their application to real data. The second section describes popular model diagnostic tools and illustrates their use. The final section deals with the often neglected issue of how to treat cases that are on the ...

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