IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i6p1609-1623.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003628
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    4. 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.
    5. 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.
    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. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    8. 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.
    9. 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.
    10. 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.
    11. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    12. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    3. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    4. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    5. S. Turkan & G. Özel, 2014. "Modeling destructive earthquake casualties based on a comparative study for Turkey," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 72(2), pages 1093-1110, June.
    6. Raffaele Brancati & Emanuela Marrocu & Manuel Romagnoli & Stefano Usai, 2018. "Innovation activities and learning processes in the crisis: evidence from Italian export in manufacturing and services," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 27(1), pages 107-130.
    7. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, vol. 2(3), pages 1-22, September.
    8. 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).
    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.
    10. 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.
    11. Marisa Bucheli & Cecilia Olivieri, 2017. "Gendered Effects of the Personal Income Tax: Evidence from a Schedular System with Individual Filing in a Developing Country," Documentos de Trabajo (working papers) 0217, Department of Economics - dECON.
    12. Latouche, Karine & Rouviere, Elodie, 2011. "Brokers vs. Retailers: Evidence from the French Imports Industry of Fresh Produce," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114398, European Association of Agricultural Economists.
    13. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    14. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    15. Claus Michelsen & Peter Boenisch & Benny Geys, 2014. "(De)Centralization and voter turnout: theory and evidence from German municipalities," Public Choice, Springer, vol. 159(3), pages 469-483, June.
    16. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    17. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    18. Li-Chu Chien, 2011. "Diagnostic plots in beta-regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1607-1622, July.
    19. Maria Simona Andreano & Roberto Benedetti & Federica Piersimoni & Giovanni Savio, 2021. "Mapping Poverty of Latin American and Caribbean Countries from Heaven Through Night-Light Satellite Images," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 533-562, August.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1609-1623. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.