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

  • Authors:

  • Raydonal Ospina;Silvia L. P. Ferrari

  • Affiliations:

  • Departamento de Estatística/CCEN, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE 50740-540, Brazil;Departamento de Estatística/IME, Universidade de São Paulo, Rua do Matão 1010, São Paulo/SP 05508-090, Brazil

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2012

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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.