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.

Quantile Models for Bounded Variables


A viable strategy for analyzing bounded data is quantile regression. Hao and Naiman (2007) outline three major limitations of linear regression models: (1) providing limited information about the behavior of a dependent variable for values far from the conditional mean, (2) inability to deal with heteroscedasticity, and (3) providing limited information about the distribution shape, such as skewness or bimodality. A quantile regression can estimate any quantile such as the 25th percentile, median, or the 75th percentile. Researchers using this technique often prefer to model several quantiles, because together they can reveal whether the distribution of the dependent variable changes shape for different values of a predictor (e.g., whether the skew covaries with a predictor). Moreover, quantile regression ...

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