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Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses

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  • Tatiane Fontana Ribeiro
  • Fernando A Peña-Ramírez
  • Renata Rojas Guerra
  • Gauss M Cordeiro

Abstract

In many practical situations, there is an interest in modeling bounded random variables in the interval (0, 1), such as rates, proportions, and indexes. It is important to provide new continuous models to deal with the uncertainty involved by variables of this type. This paper proposes a new quantile regression model based on an alternative parameterization of the unit Burr XII (UBXII) distribution. For the UBXII distribution and its associated regression, we obtain score functions and observed information matrices. We use the maximum likelihood method to estimate the parameters of the regression model, and conduct a Monte Carlo study to evaluate the performance of its estimates in samples of finite size. Furthermore, we present general diagnostic analysis and model selection techniques for the regression model. We empirically show its importance and flexibility through an application to an actual data set, in which the dropout proportion of Brazilian undergraduate animal sciences courses is analyzed. We use a statistical learning method for comparing the proposed model with the beta, Kumaraswamy, and unit-Weibull regressions. The results show that the UBXII regression provides the best fit and the most accurate predictions. Therefore, it is a valuable alternative and competitive to the well-known regressions for modeling double-bounded variables in the unit interval.

Suggested Citation

  • Tatiane Fontana Ribeiro & Fernando A Peña-Ramírez & Renata Rojas Guerra & Gauss M Cordeiro, 2022. "Another unit Burr XII quantile regression model based on the different reparameterization applied to dropout in Brazilian undergraduate courses," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-25, November.
    • Handle: RePEc:plo:pone00:0276695
    DOI: 10.1371/journal.pone.0276695
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    References listed on IDEAS

    as
    1. 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.
    2. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    3. repec:plo:pone00:0218796 is not listed on IDEAS
    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. Eline Sneyers & Kristof De Witte, 2017. "The interaction between dropout, graduation rates and quality ratings in universities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 416-430, April.
    6. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
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    1. Fernando A Peña-Ramírez & Renata R Guerra & Charles Peixoto Mafalda, 2023. "The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses," PLOS ONE, Public Library of Science, vol. 18(11), pages 1-22, November.

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