Bayesian analysis for zero-or-one inflated proportion data using quantile regression

In this paper, we propose the use of Bayesian quantile regression for the analysis of proportion data. We also consider the case when the data present a zero-or-one inflation using a two-part model approach. For the latter scheme, we assume that the response variable is generated by a mixed discrete–continuous distribution with a point mass at zero or one. Quantile regression is then used to explain the conditional distribution of the continuous part between zero and one, while the mixture probability is also modelled as a function of the covariates. We check the performance of these models with two simulation studies. We illustrate the method with data about the proportion of households with access to electricity in Brazil.