A general class of zero-or-one inflated beta regression models

TL;DR

This paper introduces a flexible regression framework for continuous proportion data that includes zeros and ones, modeling the response with a mixed distribution combining discrete mass points and a beta distribution for the continuous part.

Contribution

It develops a comprehensive class of zero-or-one inflated beta regression models with inference, diagnostics, and model selection tools, extending beta regression to handle boundary values.

Findings

Effective modeling of proportions with zeros and ones.

Demonstrated applicability with real data.

Provides inference and diagnostic procedures.

Abstract

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.