A model for non-parametric spatially varying regression effects

A method for non-parametric regression effects is applied to spatially configured data, using a generalised additive form that allows regression effects to vary over areas. The focus is on discrete outcomes in disease mapping but can be adapted to metric outcomes. Specifically a mixed model is proposed that combines a local general additive model (GAM) element for each area with a spatially filtered GAM effect. Modifications are discussed that allow for the impact of outliers on the spatial regression. The paper uses a Bayesian approach that places random walk priors on the various smooth functions, Gamma priors on inverse scale parameters and Dirichlet priors on mixing parameters. The model is illustrated with applications to lip cancer mortality in Scottish counties, where there is one predictor with regression impact modelled non-parametrically, and suicide deaths in 32 London boroughs, where two predictors are taken to follow a spatial GAM form.