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Department of Geography

 

Bayesian spatial modelling of burglaries in Sheffield

Research Team: Robert Haining and Jane Law

Abstract

The observed counts of burglaries are assumed to be independent binomial random variables. The parameter P(i), the probability that any household in i is burgled, is modelled through a logit transformation. Logit(P(i)) was initially expressed as a function of spatially structured and spatially unstructured random effects. Two covariates representing deprivation and population turnover were then included in the model. The result shows that the covariates are statistically significant and the signs are consistent with expectations. A multiplicative decomposition of the odds is into the explained (by the covariates) and unexplained (the random effects) components, which can be mapped.

Illustrations

Image as described adjacent

Multiplicative decomposition of the odds map for burglary in Sheffield by ward. The decomposition is into the explained components due to deprivation (x1), population turnover (x2), spatially structured random effects (v), and unstructured random effects (e).

Further reading

  • Haining, R. (2003). Spatial Data Analysis: Theory and Practice. Cambridge: Cambridge University Press.