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

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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.

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Acknowledgements

The authors are grateful for the insightful comments and constructive suggestions provided by the associate editor and the anonymous referees. Also, the first author would like to thank the Federal Technology University of Paraná and the Araucária Foundation for the financial support during this research.

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Authors and Affiliations

  1. Departmento Acadêmico de Matemática, Universidade Tecnológica Federal do Paraná, Curitiba, Brazil

    Wesley Bertoli

  2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Wesley Bertoli

  3. Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Katiane S. Conceição, Marinho G. Andrade & Francisco Louzada

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  1. Wesley Bertoli
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  2. Katiane S. Conceição
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  3. Marinho G. Andrade
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  4. Francisco Louzada
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Correspondence to Wesley Bertoli.

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Bertoli, W., Conceição, K.S., Andrade, M.G. et al. On the zero-modified Poisson–Shanker regression model and its application to fetal deaths notification data. Comput Stat 33, 807–836 (2018). https://doi.org/10.1007/s00180-017-0788-1

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  • DOI: https://doi.org/10.1007/s00180-017-0788-1

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