Bayesian beta regression for bounded responses with unknown supports

Abstract

A new Bayesian regression framework is presented for the analysis of continuous response data with support restricted to an unknown finite interval. A four-parameter beta distribution is assumed for the response conditioning on covariates, with the mean or mode depending linearly on covariates through a known link function. An informative g-prior is proposed to incorporate the prior distribution for the marginal mean or mode of the response. Byproducts of the Markov chain Monte Carlo sampling for implementing the proposed method lead to model criteria useful for model selection. Goodness-of-fit of the model is assessed using Cox-Snell residual plots. The methodology is illustrated in simulations and demonstrated in two real-life data applications. An R package, betaBayes, is developed for easy implementation of the proposed regression methodology.