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.