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

Ameer Musa Imran Alhseeni and Hossein Bevrani ()
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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

Stats, 2025, vol. 8, issue 4, 1-11

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.

Keywords: Bayesian estimation; Bell regression model; G-prior distribution; log-marginal pseudo-likelihood; deviance information criterion (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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