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Department of Geography


Bayesian spatial modelling of excluded children in Sheffield

Research Team: Robert Haining and Jane Law


The observed counts of children excluded from school by ward in Sheffield refers to a rare event and each is assumed an independent Poisson random variable with mean E(i)R(i) where E(i) is the expected number excluded from school and R(i) is the relative risk of exclusion for area i. The parameter of [R(i)] is modelled as a function of a ward index of deprivation, spatially structured and unstructured random effects. The variable % of single parent families was also included in an initial specification but found not to be significant. The deprivation variable is strongly significant and the parameter yields an odds ratio of 1.22 or a 22% increase in risk for every unit increase in the Townsend index of deprivation. Map decomposition shows for each ward the contribution of each of the three elements of the model to the relative risk of children being excluded from school.


Image as described adjacent

Multiplicative decomposition of the relative risk map for children excluded from school in Sheffield by ward. The decomposition is into the explained components due to deprivation (x1), 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.