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Beta distribution misspecification tests with application to Covid-19 mortality rates in the United States

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  • José Jairo Santana-e-Silva
  • Francisco Cribari-Neto
  • Klaus L P Vasconcellos

Abstract

The beta distribution is routinely used to model variables that assume values in the standard unit interval, (0, 1). Several alternative laws have, nonetheless, been proposed in the literature, such as the Kumaraswamy and simplex distributions. A natural and empirically motivated question is: does the beta law provide an adequate representation for a given dataset? We test the null hypothesis that the beta model is correctly specified against the alternative hypothesis that it does not provide an adequate data fit. Our tests are based on the information matrix equality, which only holds when the model is correctly specified. They are thus sensitive to model misspecification. Simulation evidence shows that the tests perform well, especially when coupled with bootstrap resampling. We model state and county Covid-19 mortality rates in the United States. The misspecification tests indicate that the beta law successfully represents Covid-19 death rates when they are computed using either data from prior to the start of the vaccination campaign or data collected when such a campaign was under way. In the latter case, the beta law is only accepted when the negative impact of vaccination reach on death rates is moderate. The beta model is rejected under data heterogeneity, i.e., when mortality rates are computed using information gathered during both time periods.

Suggested Citation

  • José Jairo Santana-e-Silva & Francisco Cribari-Neto & Klaus L P Vasconcellos, 2022. "Beta distribution misspecification tests with application to Covid-19 mortality rates in the United States," PLOS ONE, Public Library of Science, vol. 17(9), pages 1-30, September.
    • Handle: RePEc:plo:pone00:0274781
    DOI: 10.1371/journal.pone.0274781
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    References listed on IDEAS

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    1. Andréa V. Rocha & Francisco Cribari-Neto, 2017. "Erratum to: 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. 26(2), pages 451-459, June.
    2. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    3. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    4. 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.
    5. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    6. K. Chua & S. Ong, 2013. "Test of misspecification with application to negative binomial distribution," Computational Statistics, Springer, vol. 28(3), pages 993-1009, June.
    7. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    8. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    9. 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.
    10. Sulaiman, M.Yusof & Hlaing Oo, W.M & Abd Wahab, Mahdi & Zakaria, Azmi, 1999. "Application of beta distribution model to Malaysian sunshine data," Renewable Energy, Elsevier, vol. 18(4), pages 573-579.
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