Modelling small area counts in the presence of overdispersion and spatial autocorrelation
The problems arising when modelling counts of rare events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present or anticipated are considered. Different models are presented for handling inference in this case. The different strategies are implemented using data on offender counts at the enumeration district scale for Sheffield, England and results compared. This example is chosen because previous research suggests that social processes and social composition variables are key to understanding geographical variation in offender counts which will, as a consequence, show evidence of clustering both at the scale of the enumeration district and at larger scales. This in turn leads the analyst to anticipate the presence of overdispersion and spatial autocorrelation. Diagnostic measures are described and different modelling strategies are implemented. The evidence suggests that modelling strategies based on the use of spatial random effects models or models that include spatial filters appear to work well and provide a robust basis for model inference but gaps remain in the methodology that call for further research.
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- Michael Tiefelsdorf & Daniel A Griffith, 2007. "Semiparametric filtering of spatial autocorrelation: the eigenvector approach," Environment and Planning A, Pion Ltd, London, vol. 39(5), pages 1193-1221, May.
- Kawachi, Ichiro & Kennedy, Bruce P. & Wilkinson, Richard G., 1999. "Crime: social disorganization and relative deprivation," Social Science & Medicine, Elsevier, vol. 48(6), pages 719-731, March.
- Griffith, Daniel A., 2002. "A spatial filtering specification for the auto-Poisson model," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 245-251, July.
- Kaiser, Mark S. & Cressie, Noel, 1997. "Modeling Poisson variables with positive spatial dependence," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 423-432, November.
- Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer, vol. 43(1), pages 1-20, March.
- Daniel A. Griffith, 2004. "Distributional properties of georeferenced random variables based on the eigenfunction spatial filter," Journal of Geographical Systems, Springer, vol. 6(3), pages 263-288, October.
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