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Mean and Variance Modeling of Under- and Overdispersed Count Data

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  • Smith, David M.
  • Faddy, Malcolm J.

Abstract

This article describes the R package CountsEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models. These provide a Poisson process based family of flexible models that can handle both underdispersion and overdispersion in observed count data, with the negative binomial and Poisson distributions being special cases. Within CountsEPPM models with mean and variance related to covariates are constructed to match a generalized linear model formulation. Use of the package is illustrated by application to several published datasets.

Suggested Citation

  • Smith, David M. & Faddy, Malcolm J., 2016. "Mean and Variance Modeling of Under- and Overdispersed Count Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i06).
    • Handle: RePEc:jss:jstsof:v:069:i06
    DOI: http://hdl.handle.net/10.18637/jss.v069.i06
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. Tammy Harris & Joseph M. Hilbe & James W. Hardin, 2014. "Modeling count data with generalized distributions," Stata Journal, StataCorp LP, vol. 14(3), pages 562-579, September.
    3. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107611252.
    4. M. J. Faddy & D. M. Smith, 2011. "Analysis of count data with covariate dependence in both mean and variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2683-2694, February.
    5. M. J. Faddy & D. M. Smith, 2005. "Modeling the Dependence between the Number of Trials and the Success Probability in Binary Trials," Biometrics, The International Biometric Society, vol. 61(4), pages 1112-1114, December.
    6. Cribari-Neto, Francisco & Zeileis, Achim, 2010. "Beta Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i02).
    7. M. J. Faddy & D. M. Smith, 2008. "Extended Poisson process modelling of dilution series data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 461-471, September.
    8. Cameron, A Colin & Johansson, Per, 1997. "Count Data Regression Using Series Expansions: With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 203-223, May-June.
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