Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications

Jorge I. Figueroa-Zúñiga, Cristian L. Bayes, Víctor Leiva, Shuangzhe Liu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalStatistical Papers
DOIs
StateAccepted/In press - 2021
Externally publishedYes

Keywords

  • Bayesian statistics
  • Measurement errors
  • Monte Carlo simulation
  • Regression analysis
  • Statistical software

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