510
Views
6
CrossRef citations to date
0
Altmetric
Research Article

Bayesian Conway–Maxwell–Poisson regression models for overdispersed and underdispersed counts

ORCID Icon & ORCID Icon
Pages 3094-3105 | Received 07 Aug 2018, Accepted 15 Oct 2019, Published online: 06 Nov 2019

References

  • Andrianatos, I. 2017. On robustness and compatibility of count regression models. Honours Thesis, University of Queensland.
  • Benson, A., and N. Friel. 2017. Bayesian inference, model selection and likelihood estimation using fast rejection sampling: The Conway-Maxwell-Poisson distribution. arXiv:1709.03471.
  • Bonat, W. H., B. Jorgensen, C. C. Kokonendji, J. Hinde, and C. G. B. Demetrio. 2018. Extended Poisson–Tweedie: Properties and regression models for count data. Statistical Modelling: An International Journal 18 (1):24. doi:10.1177/1471082X17715718.
  • Chanialidis, C., L. Evers, T. Neocleous, and A. Nobile. 2017. Efficient Bayesian inference for COM-Poisson regression models. Statistics and Computing 28 (3):595–608. doi:10.1007/s11222-017-9750-x.
  • Consul, P. C., and F. Famoye. 1992. Generalized Poisson regression model. Communications in Statistics—Theory and Methods 21 (1):89–109. doi:10.1080/03610929208830766.
  • Fung, T., A. Alwan, J. Wishart, and A. Huang. 2019. mpcmp: Mean-parametrized Conway-Maxwell-Poisson, R package.
  • Gelman, A., and J. Hill. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge: Cambridge University Press.
  • Guikema, S. D., and J. P. Goffelt. 2008. A flexible count data regression model for risk analysis. Risk Analysis 28 (1):213–23. doi:10.1111/j.1539-6924.2008.01014.x.
  • Hoff, P. D. 2009. A first course in Bayesian statistical methods. New York: Springer Series in Statistics.
  • Huang, A. 2017. Mean-parametrized Conway-Maxwell-Poisson regression models for dispersed counts. Statistical Modelling: An International Journal 17 (6):359–22. doi:10.1177/1471082X17697749.
  • Kadane, J. B., G. Shmueli, T. P. Minka, S. Borle, and P. Boatwright. 2006. Conjugate analysis of the Conway-Maxwell-Poisson distribution. Bayesian Analysis 1 (2):363–74. doi:10.1214/06-BA113.
  • Lord, D., S. D. Guikema, and S. R. Geedipally. 2008. Application of the Conway-Maxwell-Poisson generalized linear model for analyzing motor vehicle crashes. Accident Analysis & Prevention 40 (3):1123–34. doi:10.1016/j.aap.2007.12.003.
  • Marley, J. K., and M. P. Wand. 2010. Non-standard semiparametric regression via BRugs. Journal of Statistical Software 37 (5):1–30. doi:10.18637/jss.v037.i05.
  • Martin, A. D., K. M. Quinn, and J. H. Park. 2011. MCMCpack: Markov Chain Monte Carlo in R. Journal of Statistical Software 42 (9):1–21. http://www.jstatsoft.org/v42/i09/ doi:10.18637/jss.v042.i09.
  • McCullagh, P., and J. A. Nelder. 1989. Generalized linear models. 2nd ed. London: Chapman and Hall.
  • Sáez-Castillo, A. J., and A. Conde-Sánchez. 2013. A hyper-Poisson regression model for overdispersed and underdispersed count data. Computational Statistics & Data Analysis 61:148–57. doi:10.1016/j.csda.2012.12.009.
  • Sellers, K. F., and D. S. Morris. 2017. Underdispersion models: Models that are “under the radar”. Communications in Statistics – Theory and Methods 46 (24):12075–86. doi:10.1080/03610926.2017.1291976.
  • Sellers, K. F., and G. Shmueli. 2010. A flexible regression model for count data. The Annals of Applied Statistics 4 (2):943–61. doi:10.1214/09-AOAS306.
  • Shmueli, G., T. P. Minka, J. B. Kadane, S. Borle, and P. Boatwright. 2005. A useful distribution for fitting discrete data: Revival of the Conway-Maxwell-Poisson distribution. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (1):127–42. doi:10.1111/j.1467-9876.2005.00474.x.
  • Wedderburn, R. W. M. 1974. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton Method. Biometrika 61:439–47. doi:10.2307/2334725.
  • Wilmot, G. E. 1987. The Poisson-Inverse Gaussian distribution as an alternative to the negative binomial. Scandinavian Actuarial Journal 1987 (3–4):113–127.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.