The Flexible Beta Regression Model

This chapter aims to study the performances of a new regression model for continuous variables with bounded support that extends the well-known beta regression model. Under the new regression model, the response variable is assumed to have a flexible beta (FB) distribution, a special mixture of two beta distributions that can be interpreted as the univariate version of the flexible Dirichlet distribution. The chapter introduces the FB distribution, proposes a reparameterization that is designed for this regression context, and enables a very clear interpretation of the new parameters. It defines the FB regression (FBR) model and interprets it as mixture of regression models. The chapter provides details concerning Bayesian inference and the Gibbs sampling algorithm specifically designed for mixture models. It performs an illustrative application on a real data set in order to evaluate the performance of the FBR model and compare it with the BR and beta regression ones.