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Robust beta regression through the logit transformation

Author

Listed:
  • Yuri S. Maluf

    (University of São Paulo)

  • Silvia L. P. Ferrari

    (University of São Paulo)

  • Francisco F. Queiroz

    (University of São Paulo)

Abstract

Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural sciences. The maximum likelihood estimation is widely used to make inferences for the parameters. Nonetheless, it is well-known that the maximum likelihood-based inference suffers from the lack of robustness in the presence of outliers. Such a case can bring severe bias and misleading conclusions. Recently, robust estimators for beta regression models were presented in the literature. However, these estimators require non-trivial restrictions in the parameter space, which limit their application. This paper develops new robust estimators that overcome this drawback. Their asymptotic and robustness properties are studied, and robust Wald-type tests are introduced. Simulation results evidence the merits of the new robust estimators. Inference and diagnostics using the new estimators are illustrated in an application to health insurance coverage data. The new R package robustbetareg is introduced.

Suggested Citation

  • Yuri S. Maluf & Silvia L. P. Ferrari & Francisco F. Queiroz, 2025. "Robust beta regression through the logit transformation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(1), pages 61-81, January.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:1:d:10.1007_s00184-024-00949-1
    DOI: 10.1007/s00184-024-00949-1
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. La Vecchia, Davide & Camponovo, Lorenzo & Ferrari, Davide, 2015. "Robust heart rate variability analysis by generalized entropy minimization," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 137-151.
    7. Davide Ferrari & Davide La Vecchia, 2012. "On robust estimation via pseudo-additive information," Biometrika, Biometrika Trust, vol. 99(1), pages 238-244.
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