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

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  • Ospina, Raydonal
  • Ferrari, Silvia L.P.
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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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003628
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1609-1623

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1609-1623

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Continuous proportions; Zero-or-one inflated beta distribution; Fractional data; Maximum likelihood estimation; Diagnostics; Residuals;

    References

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    1. 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.
    2. 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.
    3. Hoff, Ayoe, 2007. "Second stage DEA: Comparison of approaches for modelling the DEA score," European Journal of Operational Research, Elsevier, vol. 181(1), pages 425-435, August.
    4. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2009. "Alternative estimating and testing empirical strategies for fractional regression models," CEFAGE-UE Working Papers 2009_08, University of Evora, CEFAGE-UE (Portugal).
    5. 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.
    6. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    7. D. Mikis Stasinopoulos & Robert A. Rigby, . "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, American Statistical Association, vol. 23(i07).
    8. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    9. 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.
    10. 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.
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    Cited by:
    1. Owen, Sian & Yawson, Alfred, 2013. "Information asymmetry and international strategic alliances," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3890-3903.

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