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On the zero-modified Poisson–Shanker regression model and its application to fetal deaths notification data

Author

Listed:
  • Wesley Bertoli

    (Universidade Tecnológica Federal do Paraná
    Universidade de São Paulo, São Carlos)

  • Katiane S. Conceição

    (Universidade de São Paulo)

  • Marinho G. Andrade

    (Universidade de São Paulo)

  • Francisco Louzada

    (Universidade de São Paulo)

Abstract

In this paper, we propose the zero-modified Poisson–Shanker regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero modification has been incorporated using the zero-truncated Poisson–Shanker distribution. The zero-modified Poisson–Shanker distribution has been written as a hurdle model using a simple reparameterization of the probability function which leads to the fact that the proposed model can be fitted without any previous information about the zero modification present in a given dataset. The standard Bayesian procedures have been considered for estimation and inference. A simulation study has been presented to illustrate the performance of the developed methodology. The usefulness of the proposed model has been evaluated using a real dataset on fetal deaths notification data in Bahia State, Brazil. A sensitivity study to detect points which can influence the parameter estimates has been performed using Kullback–Leibler divergence measure. The randomized quantile residuals have been considered for the model validation issue. General comparison of the proposed model with some well-known discrete distributions has been provided.

Suggested Citation

  • Wesley Bertoli & Katiane S. Conceição & Marinho G. Andrade & Francisco Louzada, 2018. "On the zero-modified Poisson–Shanker regression model and its application to fetal deaths notification data," Computational Statistics, Springer, vol. 33(2), pages 807-836, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0788-1
    DOI: 10.1007/s00180-017-0788-1
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    References listed on IDEAS

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    1. Allen McDowell, 2003. "From the help desk: hurdle models," Stata Journal, StataCorp LP, vol. 3(2), pages 178-184, June.
    2. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    3. J.L. Bazán & F. Torres‐Avilés & A.K. Suzuki & F. Louzada, 2017. "Power and reversal power links for binary regressions: An application for motor insurance policyholders," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(1), pages 22-34, January.
    4. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    5. Hyunsoon Cho & Joseph G. Ibrahim & Debajyoti Sinha & Hongtu Zhu, 2009. "Bayesian Case Influence Diagnostics for Survival Models," Biometrics, The International Biometric Society, vol. 65(1), pages 116-124, March.
    6. Gurmu, Shiferaw & Trivedi, Pravin K, 1996. "Excess Zeros in Count Models for Recreational Trips," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 469-477, October.
    7. Angers, Jean-Francois & Biswas, Atanu, 2003. "A Bayesian analysis of zero-inflated generalized Poisson model," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 37-46, February.
    8. Alok K. Bohara & Randall G. Krieg, 1996. "A Zero-inflated Poisson Model of Migration Frequency," International Regional Science Review, , vol. 19(3), pages 211-222, July.
    9. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
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