A New Robust Regression Model for Proportions

Abstract

A new regression model for proportions is presented by considering the Beta rectangular distribution proposed by Hahn (2008). This new model includes the Beta regression model introduced by Ferrari and Cribari-Neto (2004) and the variable dispersion Beta regression model introduced by Smithson and Verkuilen (2006) as particular cases. Like Branscum, Johnson, and Thurmond (2007), a Bayesian inference approach is adopted using Markov Chain Monte Carlo (MCMC) algorithms. Simulation studies on the influence of outliers by considering contaminated data under four perturbation patterns to generate outliers were carried out and confirm that the Beta rectangular regression model seems to be a new robust alternative for modeling proportion data and that the Beta regression model shows sensitivity to the estimation of regression coefficients, to the posterior distribution of all parameters and to the model comparison criteria considered. Furthermore, two applications are presented to illustrate the robustness of the Beta rectangular model.