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.

Extensions and Conclusions

Extensions and a General Framework

In this book, we intended to provide researchers and students with an introduction to methods for analyzing continuous variables with bounds. We have focused on three types of bounds: absolute scale limits, censored scores, and sample truncation. We have limited our introductory treatment to variables that are “pure” examples of each of these types of bounds, data that consist of independent and identically distributed observations, and parameter estimation and model diagnostic techniques oriented around maximum likelihood estimation. Real research projects often present researchers with more complex kinds of data, so in this chapter, we provide some glimpses of that broader territory. The next three sections discuss variables in which absolute bounds coexist with censoring or truncation, ...

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