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Improved testing inferences for beta regressions with parametric mean link function

Author

Listed:
  • Cristine Rauber

    (Universidade Federal de Pernambuco)

  • Francisco Cribari-Neto

    (Universidade Federal de Pernambuco)

  • Fábio M. Bayer

    (Universidade Federal de Santa Maria)

Abstract

Beta regressions are widely used for modeling random variables that assume values in the standard unit interval, (0, 1), such as rates, proportions, and income concentration indices. Parameter estimation is typically performed via maximum likelihood, and hypothesis testing inferences on the model parameters are commonly performed using the likelihood ratio test. Such a test, however, may deliver inaccurate inferences when the sample size is small. It is thus important to develop alternative testing procedures that are more accurate when the sample contains only few observations. In this paper, we consider the beta regression model with parametric mean link function and derive two modified likelihood ratio test statistics for that class of models. We provide simulation evidence that shows that the new tests usually outperform the standard likelihood ratio test in samples of small to moderate sizes. We also present and discuss two empirical applications.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:4:d:10.1007_s10182-020-00376-3
    DOI: 10.1007/s10182-020-00376-3
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    References listed on IDEAS

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    1. Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    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. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
    4. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2011. "Erratum to "Improved point and interval estimation for a beta regression model" [Comput. Statist. Data Anal. 51 (2006) 960-981]," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2445-2445, July.
    5. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    6. 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.
    7. 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.
    8. Fábio Bayer & Francisco Cribari-Neto, 2015. "Bootstrap-based model selection criteria for beta regressions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 776-795, December.
    9. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    10. 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.
    11. 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.
    12. Patrícia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2014. "Bootstrap prediction intervals in beta regressions," Computational Statistics, Springer, vol. 29(5), pages 1263-1277, October.
    13. Hakim-Moulay Dehbi & Mario Cortina-Borja & Marco Geraci, 2016. "Aranda-Ordaz quantile regression for student performance assessment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(1), pages 58-71, January.
    14. Enrico A. Colosimo & Liciana V. A. S. Chalita & Clarice G. B. Demétrio, 2000. "Tests of Proportional Hazards and Proportional Odds Models for Grouped Survival Data," Biometrics, The International Biometric Society, vol. 56(4), pages 1233-1240, December.
    15. Daryl Pregibon, 1980. "Goodness of Link Tests for Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 15-24, March.
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