Abstract
Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures.
Highlights
The analysis of percentage data is a common issue in quantitative research
A recent survey conducted by Warton & Hui [2] even found that nearly one third of papers published in Ecology in 2008/09 dealt with the analysis of percentage data
The National Lakes Assessment (NLA) Database Statistical analysis is based on data from the 2007 U.S National
Summary
The analysis of percentage data is a common issue in quantitative research. A recent survey conducted by Warton & Hui [2] even found that nearly one third of papers published in Ecology in 2008/09 dealt with the analysis of percentage data. The analysis of percentage data is a challenging problem. This problem primarily concerns the development of regression models for percentage outcomes, which may be biased and inefficient if the specific nature of percentage outcomes is not taken into account. In order to avoid biased estimators and hypothesis tests, regression techniques that are tailored to the analysis of percentage outcomes are needed
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