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

• Published in: Computational statistics & data analysis Vol. 56; no. 6; pp. 1609 - 1623
• Main Authors: Ospina, Raydonal, Ferrari, Silvia L.P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2012; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Beta; Continuous proportions; Continuous proportions Zero-or-one inflated beta distribution Fractional data Maximum likelihood estimation Diagnostics Residuals; Data processing; Density; Diagnostics; Fractional data; Mathematical analysis; Mathematical models; Maximum likelihood estimation; Parametrization; Regression; Residuals; Statistics; Zero-or-one inflated beta distribution; Zero-or-one inflated beta distribution; Maximum likelihood estimation; Continuous proportions; Diagnostics; Residuals; Fractional data
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.10.005

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.