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On the use of corrections for overdispersion

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  • J. K. Lindsey

Abstract

In studying fluctuations in the size of a blackgrouse (Tetrao tetrix) population, an autoregressive model using climatic conditions appears to follow the change quite well. However, the deviance of the model is considerably larger than its number of degrees of freedom. A widely used statistical rule of thumb holds that overdispersion is present in such situations, but model selection based on a direct likelihood approach can produce opposing results. Two further examples, of binomial and of Poisson data, have models with deviances that are almost twice the degrees of freedom and yet various overdispersion models do not fit better than the standard model for independent data. This can arise because the rule of thumb only considers a point estimate of dispersion, without regard for any measure of its precision. A reasonable criterion for detecting overdispersion is that the deviance be at least twice the number of degrees of freedom, the familiar Akaike information criterion, but the actual presence of overdispersion should then be checked by some appropriate modelling procedure.

Suggested Citation

  • J. K. Lindsey, 1999. "On the use of corrections for overdispersion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 553-561.
    • Handle: RePEc:bla:jorssc:v:48:y:1999:i:4:p:553-561
    DOI: 10.1111/1467-9876.00171
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    1. Weber, Bryan, 2014. "Can safe ride programs reduce urban crime?," Regional Science and Urban Economics, Elsevier, vol. 48(C), pages 1-11.
    2. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    3. Nigel Yoccoz & Kjell Erikstad & Jan Bustnes & Sveinn Hanssen & Torkild Tveraa, 2002. "Costs of reproduction in common eiders ( Somateria mollissima ): An assessment of relationships between reproductive effort and future survival and reproduction based on observational and experimental," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 57-64.
    4. Tomoki Nakaya & A. Fotheringham & Kazumasa Hanaoka & Graham Clarke & Dimitris Ballas & Keiji Yano, 2007. "Combining microsimulation and spatial interaction models for retail location analysis," Journal of Geographical Systems, Springer, vol. 9(4), pages 345-369, December.
    5. Adrián Quintero-Sarmiento & Edilberto Cepeda-Cuervo & Vicente Núñez-Antón, 2012. "Estimating infant mortality in Colombia: some overdispersion modelling approaches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1011-1036, October.

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