ABSTRACT
Following on from Chapter 7, this chapter presents a number of Bayesian spatial hierarchical models for modelling a set of small area parameters based on the idea of local information borrowing (Strategy 4). Local information borrowing is based on the property of spatial dependence. Data values close together in geographical space tend to be more alike than data values that are further apart in geographical space. Imposing this dependence property of data on parameters helps further strengthen and improve parameter estimation. To implement the process of local information borrowing, models incorporating spatial dependency need to be constructed. Various spatial models for localized information sharing are presented, all of them involving some form of the conditional autoregressive (CAR) modelling structure. The intrinsic conditional autoregressive (ICAR) and the proper CAR (pCAR) models are described. Locally adaptive spatial smoothing models which allow the elements in the spatial weights matrix to be estimated using data are described, as is the Besag-York-Mollié (BYM) model, which combines an exchangeable model (Strategy 3) with the ICAR model, so that borrowing information is carried out both globally and locally. Using the Newcastle household-level income data, this chapter provides insights into the application of these different modelling options.
