A general class of zero-or-one inflated beta regression models
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.
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- Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
- Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011.
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- Espinheira, Patricia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
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- Seung-Hoon Yoo, 2004. "A Note on an Approximation of the Mobile Communications Expenditures Distribution Function Using a Mixture Model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 747-752.
- Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
- Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
- Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
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