Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Modelling Count Responses with Overdispersion

  • Received : 2012.08.09
  • Accepted : 2012.09.24
  • Published : 2012.11.30
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Abstract

We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

Keywords

References

  1. Agresti, A. (2002). Categorical Data Analysis, 2nd Ed., Wiley, New York.
  2. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25.
  3. Jowaheer, V. and Sutradhar, B. C. (2002). Analysing longitudinal count data with overdispersion, Biometrika, 89, 389-399 https://doi.org/10.1093/biomet/89.2.389
  4. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, Second Ed., Chapman and Halls, London.
  5. Morel, J. G. and Neerchal, N. K. (2012). Overdispersion Models in SAS, SAS Institute Inc.
  6. Pan, Z. and Lin, D. Y. (2005). Goodness-of-Fit methods for generalized linear mixed models, Biometrics, 61, 1000-1009. https://doi.org/10.1111/j.1541-0420.2005.00365.x
  7. Sutradhar, S. C., Neerchal, N. K. and Morel, J. G. (2007). A goodness-of-fit test for overdispersed binomial or multinomial models, Journal of Statistical Planning and Inference, 138, 1459-1471.
  8. Thall, P. F. and Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion, Biometrics, 46, 657-671. https://doi.org/10.2307/2532086
  9. Waagepetersen, R. (2006). A simulation-based goodness-of-fit test for random effects in generalized linear mixed models, Scandinavian Journal of Statistics, 33, 721-731. https://doi.org/10.1111/j.1467-9469.2006.00504.x
  10. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss- Newton method, Biometrika, 61, 439-447.
  11. Wood, G. R. (2002). Assessing goodness-of-fit for Poisson and negative binomial models with low means, Communications in Statistics, Theory and Methods, 31, 1977-2001. https://doi.org/10.1081/STA-120015014
  12. Xu, W. and Lu, Y. (2009). Goodness-of-fit for longitudinal count data with overdispersion, Communications in Statistics, Theory and Methods, 38, 3745-3754. https://doi.org/10.1080/03610920802618400

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