IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i4p95-d1768419.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/4/95/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/4/95/
    Download Restriction: no
    ---><---

    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, Enero-Abr.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lamarche, Carlos & Shi, Xuan & Young, Derek S., 2024. "Conditional Quantile Functions for Zero-Inflated Longitudinal Count Data," Econometrics and Statistics, Elsevier, vol. 31(C), pages 49-65.
    2. Mahsa Nadifar & Hossein Baghishani & Afshin Fallah, 2023. "A Flexible Generalized Poisson Likelihood for Spatial Counts Constructed by Renewal Theory, Motivated by Groundwater Quality Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(4), pages 726-748, December.
    3. Laurence T Kell & Iago Mosqueira & Henning Winker & Rishi Sharma & Toshihide Kitakado & Massimiliano Cardinale, 2024. "Empirical validation of integrated stock assessment models to ensuring risk equivalence: A pathway to resilient fisheries management," PLOS ONE, Public Library of Science, vol. 19(7), pages 1-21, July.
    4. David Kaplan & Jianshen Chen, 2012. "A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 581-609, July.
    5. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    6. Tommi Härkänen & Anna But & Jari Haukka, 2017. "Non-parametric Bayesian Intensity Model: Exploring Time-to-Event Data on Two Time Scales," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 798-814, September.
    7. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    8. Jesse Elliott & Zemin Bai & Shu-Ching Hsieh & Shannon E Kelly & Li Chen & Becky Skidmore & Said Yousef & Carine Zheng & David J Stewart & George A Wells, 2020. "ALK inhibitors for non-small cell lung cancer: A systematic review and network meta-analysis," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-18, February.
    9. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    10. Hongxiu Li & Horatiu Rus, 2018. "Water Innovation and Water Governance: Adaptive Responses to Regulatory Change and Extreme Weather Events," Working Papers 1801, University of Waterloo, Department of Economics, revised Jan 2018.
    11. Francois Olivier & Laval Guillaume, 2011. "Deviance Information Criteria for Model Selection in Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-25, July.
    12. Wang, Xu & Zhang, Xiaobo & Xie, Zhuan & Huang, Yiping, 2016. "Roads to innovation: Firm-level evidence from China," IFPRI discussion papers 1542, International Food Policy Research Institute (IFPRI).
    13. Ferraz, V.R.S. & Moura, F.A.S., 2012. "Small area estimation using skew normal models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2864-2874.
    14. Preusse, Verena & Wollni, Meike, 2021. "Adoption of sustainable agricultural practices in the context of urbanisation and environmental stress – Evidence from farmers in the rural-urban interface of Bangalore, India," 2021 Annual Meeting, August 1-3, Austin, Texas 312690, Agricultural and Applied Economics Association.
    15. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    16. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    17. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.
    18. Niko Hauzenberger & Florian Huber & Massimiliano Marcellino & Nico Petz, 2025. "Gaussian Process Vector Autoregressions and Macroeconomic Uncertainty," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 43(1), pages 27-43, January.
    19. Quoc-Anh Do & Kieu-Trang Nguyen & Anh N. Tran, 2017. "One Mandarin Benefits the Whole Clan: Hometown Favoritism in an Authoritarian Regime," American Economic Journal: Applied Economics, American Economic Association, vol. 9(4), pages 1-29, October.
    20. Ander Wilson & Jessica Tryner & Christian L'Orange & John Volckens, 2020. "Bayesian nonparametric monotone regression," Environmetrics, John Wiley & Sons, Ltd., vol. 31(8), December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:8:y:2025:i:4:p:95-:d:1768419. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.