Modeling Dispersed Count Data: Evaluating the Conway–Maxwell–Poisson Regression with COVID-19 Mortality Data

Year : 2025 | Volume : 13 | Issue : 03 | Page : 18 26
    By

    Nazmin Akter,

  • Md Rezaul Karim,

  • Sultana Begum,

  1. Lecturer, Department of Social Relations, East West University, Dhaka, Bangladesh
  2. Professor, Department of Statistics and Data Science, Jahangirnagar University, Dhaka, Bangladsh
  3. Assistant Professor, Department of Statistics and Data Science, Jahangir Nagar, Dhaka, Bangladesh

Abstract

Count data are prevalent in diverse fields such as biology, healthcare, psychology, and marketing, characterized by non-negativity and inherent heteroskedasticity, often exhibiting overdispersion or underdispersion. Traditional Poisson regression, which assumes equal mean and variance, is inadequate for such dispersed data. To address this, various generalized linear models (GLMs) and their extensions, including negative binomial (NB) and Conway–Maxwell–Poisson (CMP) regressions, are utilized. This study evaluates the performance of CMP regression compared to Poisson, NB, and generalized Poisson models using COVID-19 death data from Bangladesh. The CMP distribution, a flexible two-parameter generalization of the Poisson distribution, accommodates both overdispersion and underdispersion, enhancing model accuracy. Model comparisons based on the Akaike Information Criterion (AIC) indicate that the CMP model, influenced by temperature and humidity, provides the best fit with the lowest AIC value. The next-best models, NB, and generalized Poisson show significantly higher AIC values, underscoring CMP’s superiority. Results indicate that while NB and CMP regressions provide superior accuracy over the Poisson model, CMP regression demonstrates the best fit in terms of log-likelihood and AIC. This research underscores the CMP distribution’s efficacy and highlights the importance of using appropriate models for dispersed count data. Advances in computational power have enabled the revival and application of CMP regression, offering new insights into discrete data modeling.

Keywords: Negative binomial regression, generalized Poisson regression, Conway–Maxwell–Poisson regression, COVID-19, Bangladesh

[This article belongs to Research & Reviews : Journal of Statistics ]

How to cite this article:
Nazmin Akter, Md Rezaul Karim, Sultana Begum. Modeling Dispersed Count Data: Evaluating the Conway–Maxwell–Poisson Regression with COVID-19 Mortality Data. Research & Reviews : Journal of Statistics. 2025; 13(03):18-26.
How to cite this URL:
Nazmin Akter, Md Rezaul Karim, Sultana Begum. Modeling Dispersed Count Data: Evaluating the Conway–Maxwell–Poisson Regression with COVID-19 Mortality Data. Research & Reviews : Journal of Statistics. 2025; 13(03):18-26. Available from: https://journals.stmjournals.com/rrjost/article=2025/view=211706


References

  1. Barriga GDC, Louzada F. The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic. Stat Methodol. 2014;21:23–34. doi: 10.1016/j.stamet.2013.11.003.
  2. Boatwright P, Borle S. The timing of bid placement and extent of multiple bidding: An empirical investigation using eBay online auctions. Stat Sci. 2006;21(2):194–205.
  3. Borle S, Boatwright P, Kadane JB, Nunes JC, Galit S. The effect of product assortment changes on customer retention. Mark Sci. 2005;24(4):616–22. doi: 10.1287/mksc.1050.0121.
  4. Consul PC. Generalized Poisson distributions: properties and applications. 1989.
  5. Coxe S, West SG, Aiken LS. The analysis of count data: A gentle introduction to Poisson regression and its alternatives. J Pers Assess. 2009;91(2):121–36. doi: 10.1080/00223890802634175. PubMed: 19205933.
  6. Conway R. A queueing model with state dependent service rate. J Ind Eng. 1961;12:132.
  7. Daly F, Gaunt RE. The Conway–Maxwell–Poisson distribution: distributional theory and approximation. arXiv Preprint arXiv:1503.07012. 2015.
  8. Hilbe JM. Modeling count data. Cambridge University Press; 2014. doi: 10.1017/CBO9781139236065.
  9. Harris T, Yang Z, Hardin JW. Modeling underdispersed count data with generalized Poisson regression. STATA J. 2012;12(4):736–47. doi: 10.1177/1536867X1201200412.
  10. Huang A. Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts. Stat Model. 2017;17(6):359–80. doi: 10.1177/1471082X17697749.
  11. Ismail N, Zamani H. Estimation of claim count data using negative binomial, generalized Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. Cas Actuar Soc E-Forum. 2013;41(20):1–28.
  12. Karim R, Akter N. Effects of climate variables on the COVID-19 mortality in Bangladesh. Theor Appl Climatol. 2022;150(3):1463–75. doi: 10.1007/s00704-022-04211-4. PubMed: 36276261.
  13. Lynch HJ, Thorson JT, Shelton AO. Dealing with under- and over-dispersed count data in life history, spatial, and community ecology. Ecology. 2014;95:3173–80. doi: 10.1890/13-1912.1.
  14. O’Hara R, Kotze J. Do not log-transform count data. Nat Prec. 2010. doi: 10.1038/npre.2010.
    1.
  15. Rodríguez G. Models for count data with overdispersion. Addendum to the WWS. Vol. 509; 2013.
  16. Sellers KF, Shmueli G. A flexible regression model for count data. Ann Appl Stat. 2010;4(2):943–61. doi: 10.1214/09-AOAS306.
  17. Shmueli G, Minka TP, Kadane JB, Borle S, Boatwright P. A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution. J R Stat Soc C. 2005;54(1):127–42. doi: 10.1111/j.1467-9876.2005.00474.x.
  18. Scollnik DPM. A damaged generalised Poisson model and its application to reported and unreported accident counts. ASTIN Bull. 2006;36(2):463–87. doi: 10.2143/AST.36.2.2017930.
  19. Wang G. Bayesian regression models for ecological count data in PyMC3. Ecol Inform. 2021;63:101301. doi: 10.1016/j.ecoinf.2021.101301.
Regular Issue Subscription Review Article
Volume 13
Issue 03
Received 06/01/2025
Accepted 18/01/2025
Published 29/05/2025
Publication Time 143 Days
176

Login


My IP

PlumX Metrics