IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0274781.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0274781
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0274781&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0274781?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
    ---><---

    References listed on IDEAS

    as
    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. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    3. K. Chua & S. Ong, 2013. "Test of misspecification with application to negative binomial distribution," Computational Statistics, Springer, vol. 28(3), pages 993-1009, June.
    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. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    6. 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.
    7. 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.
    8. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antoine Burg & Christophe Dutang, 2026. "Closed-form estimators for multivariate regressions models -a single categorical variable approach," Post-Print hal-05539060, HAL.
    2. Antoine Burg & Christophe Dutang, 2026. "Closed-form estimators for multivariate regressions models: a single categorical variable approach," Computational Statistics, Springer, vol. 41(3), pages 1-23, April.

    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. Dirk Hoorelbeke, 2004. "Bootstrap correcting the score test," Econometric Society 2004 North American Summer Meetings 228, Econometric Society.
    2. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    3. repec:ebl:ecbull:v:3:y:2008:i:5:p:1-7 is not listed on IDEAS
    4. Guilherme Pumi & Taiane Schaedler Prass & Cleiton Guollo Taufemback, 2024. "Publisher Correction: Unit-Weibull 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. 33(1), pages 358-359, March.
    5. Cribari-Neto, Francisco & Scher, Vinícius T. & Bayer, Fábio M., 2023. "Beta autoregressive moving average model selection with application to modeling and forecasting stored hydroelectric energy," International Journal of Forecasting, Elsevier, vol. 39(1), pages 98-109.
    6. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    7. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    8. Daisuke Nagakura, 2008. "A note on the relationship between the information matrx test and a score test for parameter constancy," Economics Bulletin, AccessEcon, vol. 3(5), pages 1-7.
    9. 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.
    10. Scher, Vinícius T. & Cribari-Neto, Francisco & Bayer, Fábio M., 2024. "Generalized βARMA model for double bounded time series forecasting," International Journal of Forecasting, Elsevier, vol. 40(2), pages 721-734.
    11. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    12. 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.
    13. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    14. Stomberg, Christopher & White, Halbert, 2000. "Bootstrapping the Information Matrix Test," University of California at San Diego, Economics Working Paper Series qt158451cr, Department of Economics, UC San Diego.
    15. Daphna Harel & Russell J. Steele, 2018. "An Information Matrix Test for the Collapsing of Categories Under the Partial Credit Model," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 721-750, December.
    16. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2025. "Information matrix tests for multinomial logit models," Economics Letters, Elsevier, vol. 247(C).
    17. Guillermo Martínez-Flórez & Roger Tovar-Falón & Víctor Leiva & Cecilia Castro, 2024. "Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    18. Dries P.J. Kuijper & Jakub W. Bubnicki & Marcin Churski & Bjorn Mols & Pim van Hooft, 2015. "Context dependence of risk effects: wolves and tree logs create patches of fear in an old-growth forest," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(6), pages 1558-1568.
    19. 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.
    20. 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.
    21. Melchior, Cristiane & Zanini, Roselaine Ruviaro & Guerra, Renata Rojas & Rockenbach, Dinei A., 2021. "Forecasting Brazilian mortality rates due to occupational accidents using autoregressive moving average approaches," International Journal of Forecasting, Elsevier, vol. 37(2), pages 825-837.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0274781. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.