Abstract
Beta regression models have become a popular tool for describing and predicting limited-range continuous data such as rates and proportions. However, these models can be severely affected by outlying observations that the beta distribution does not handle well. A robust alternative to the modeling with the beta distribution is considering the rectangular beta (RB) distribution, which is an extension of the former one. The RB distribution can deal with heavy tails and is therefore more flexible than the beta distribution. Regression modeling where covariates are measured with error is a frequent issue in different areas. This paper derives robust regression modeling for proportions with errors-in-variables using the RB distribution under a new parametrization recently proposed in the literature. We use a Bayesian approach to estimate the model parameters with a specification of prior distributions and a computational implementation carried out via the Gibbs sampling. Monte Carlo simulations allow us to conduct numerical evaluation to detect the statistical performance of the approach considered. Then, an illustration with real-world data is presented to show its potential uses.
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Acknowledgements
The authors would like to thank the Editors and Reviewers for their constructive comments on an earlier version of this manuscript which led to an improved presentation. The authors acknowledge funding supported by Grants: VRID 217.014.027-1 from Universidad de Concepción, Chile (J.I. Figueroa-Zúñiga), DGI-2014-0017/0070 and DGI-2014-0077/0065 from the Dirección de Gestión de la Investigación at PUCP, Peru (C.L. Bayes); and FONDECYT 1200525 from the National Agency for Research and Development (ANID) of the Chilean government (V. Leiva).
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Appendix
Appendix
Next, we present BUGS codes used for fitting the RB regression models with errors-in-variables.
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Figueroa-Zúñiga, J.I., Bayes, C.L., Leiva, V. et al. Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications. Stat Papers 63, 919–942 (2022). https://doi.org/10.1007/s00362-021-01260-1
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DOI: https://doi.org/10.1007/s00362-021-01260-1