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November 2019 Bayesian approach for the zero-modified Poisson–Lindley regression model
Wesley Bertoli, Katiane S. Conceição, Marinho G. Andrade, Francisco Louzada
Braz. J. Probab. Stat. 33(4): 826-860 (November 2019). DOI: 10.1214/19-BJPS447

Abstract

The primary goal of this paper is to introduce the zero-modified Poisson–Lindley regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero-modification is incorporated by considering that a zero-truncated process produces positive observations and consequently, the proposed model can be fitted without any previous information about the zero-modification present in a given dataset. A fully Bayesian approach based on the g-prior method has been considered for inference concerns. An intensive Monte Carlo simulation study has been conducted to evaluate the performance of the developed methodology and the maximum likelihood estimators. The proposed model was considered for the analysis of a real dataset on the number of bids received by $126$ U.S. firms between 1978–1985, and the impact of choosing different prior distributions for the regression coefficients has been studied. A sensitivity analysis to detect influential points has been performed based on the Kullback–Leibler divergence. A general comparison with some well-known regression models for discrete data has been presented.

Citation

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Wesley Bertoli. Katiane S. Conceição. Marinho G. Andrade. Francisco Louzada. "Bayesian approach for the zero-modified Poisson–Lindley regression model." Braz. J. Probab. Stat. 33 (4) 826 - 860, November 2019. https://doi.org/10.1214/19-BJPS447

Information

Received: 1 April 2018; Accepted: 1 April 2019; Published: November 2019
First available in Project Euclid: 26 August 2019

zbMATH: 07120736
MathSciNet: MR3996319
Digital Object Identifier: 10.1214/19-BJPS447

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 4 • November 2019
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