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Influence measures in beta regression models through distance between distributions

Author

Listed:
  • J. M. Muñoz-Pichardo

    (Andalusian Center of Prospective)

  • J. L. Moreno-Rebollo

    (University of Seville)

  • R. Pino-Mejías

    (University of Seville)

  • M. D. Cubiles Vega

    (University of Seville)

Abstract

In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frèchet distance (Frèchet in Comptes Rendus hebdomadaires des seances de l’Academie des Sciences de Paris 244:689–692, 1957), and the Rao distance (Rao in Indian J Stat Ser A 9:246–291, 1949). Moreover, a jackknife-after-bootstrap transformation of the diagnostics is also proposed to make clear the decision about cases to be considered as influential. Artificial and real examples are included to illustrate the usefulness of the diagnostics and to compare them to others in the literature.

Suggested Citation

  • J. M. Muñoz-Pichardo & J. L. Moreno-Rebollo & R. Pino-Mejías & M. D. Cubiles Vega, 2019. "Influence measures in beta regression models through distance between distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 163-185, June.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:2:d:10.1007_s10182-018-00332-2
    DOI: 10.1007/s10182-018-00332-2
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    References listed on IDEAS

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    1. Michael Martin & Steven Roberts, 2010. "Jackknife-after-bootstrap regression influence diagnostics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 257-269.
    2. J. Muñoz-Pichardo & J. Moreno-Rebollo & A. Enguix-González & A. Pascual-Acosta, 2008. "Influence measures on profile analysis with elliptical data through Frèchet’s metric," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 111-127, June.
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    5. Andréa Rocha & Alexandre Simas, 2011. "Influence diagnostics in a general class of beta regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 95-119, May.
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