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

Author

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

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.

Suggested Citation

  • Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1609-1623
    DOI: 10.1016/j.csda.2011.10.005
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(04), pages 325-346, January.
    6. 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.
    7. 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.
    8. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    9. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
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    3. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, Open Access Journal, vol. 2(3), pages 1-22, September.
    4. Tian, Guo-Liang & Ma, Huijuan & Zhou, Yong & Deng, Dianliang, 2015. "Generalized endpoint-inflated binomial model," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 97-114.
    5. 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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    12. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    13. Martijn J. Burger & Evert J. Meijers & Marloes M. Hoogerbrugge & Jaume Masip Tresserra, 2015. "Borrowed Size, Agglomeration Shadows and Cultural Amenities in North-West Europe," European Planning Studies, Taylor & Francis Journals, vol. 23(6), pages 1090-1109, June.
    14. Zhao, Weihua & Lian, Heng & Zhang, Riquan & Lai, Peng, 2016. "Estimation and variable selection for proportional response data with partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 40-56.
    15. Xiong, Qizhou, 2015. "Censored Fractional Response Model: Estimating Heterogeneous Relative Risk Aversion of European Households," IWH Discussion Papers 11/2015, Halle Institute for Economic Research (IWH).
    16. Dionne, Georges & Desjardins, Denise, 2017. "Reinsurance Demand and Liquidity Creation," Working Papers 17-3, HEC Montreal, Canada Research Chair in Risk Management.
    17. Ece Yagman & Malcolm Keswell, 2015. "Accents, Race and Discrimination: Evidence from a Trust Game," SALDRU Working Papers 158, Southern Africa Labour and Development Research Unit, University of Cape Town.
    18. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.

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