Data Analysis and Related Applications, Volume 1

8The State of the Art in Flexible Regression Models for Univariate Bounded Responses

Modeling bounded continuous responses, such as proportions and rates, is a relevant problem in methodological and applied statistics. A further issue is observed if the response takes values at the boundary of the support. Given that standard models are unsuitable, a successful and relatively recent branch of research favors modeling the response variable according to distributions that are well-defined on the restricted support. A popular and well-researched choice is the beta regression model and its augmented version. More flexible alternatives than the beta regression model, among which are the flexible beta and the variance inflated beta, have been tailored for data with outlying observations, latent structures and heavy tails. These models are based on special mixtures of beta distributions and their augmented versions to handle the presence of values at the boundary of the support. The aim of this chapter is to provide a comprehensive review of these models and to briefly describe the FlexReg package, a newly available tool on CRAN that offers an efficient and easy-to-use implementation of regression models for bounded responses. Two real data applications are performed to show the relevance of correctly modeling the bounded response and to make comparisons between models. Inferential issues are dealt with by the (Bayesian) Hamiltonian Monte Carlo algorithm.

8.1. Introduction

The development ...