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Bayesian Bell Regression Model for Fitting of Overdispersed Count Data with Application

Author

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  • Ameer Musa Imran Alhseeni

    (Department of Statistics, University of Tabriz, Tabriz 51666-15648, Iran)

  • Hossein Bevrani

    (Department of Statistics, University of Tabriz, Tabriz 51666-15648, Iran
    Department of Statistics, University of Kurdistan, Sanandaj 66177-15175, Iran)

Abstract

The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application. Specifically, we introduce a G-prior distribution for Bayesian inference in BRM, in addition to a flat-normal prior distribution. To compare the performance of the proposed prior distributions, we conduct a simulation study and demonstrate that the G-prior distribution provides superior estimation results for the BRM. Furthermore, we apply the methodology to real data and compare the BRM to the Poisson and negative binomial regression model using various model selection criteria. Our results provide valuable insights into the use of Bayesian methods for estimation and inference of the BRM and highlight the importance of considering the choice of prior distribution in the analysis of count data.

Suggested Citation

  • Ameer Musa Imran Alhseeni & Hossein Bevrani, 2025. "Bayesian Bell Regression Model for Fitting of Overdispersed Count Data with Application," Stats, MDPI, vol. 8(4), pages 1-11, October.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:4:p:95-:d:1768419
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    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. Duncan Lee & Tereza Neocleous, 2010. "Bayesian quantile regression for count data with application to environmental epidemiology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 905-920, November.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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