Bayesian Spatial Estimation When Areas Are Few

Spatial modelling when there are few (<20) small areas can be challenging. Bayesian methods can be beneficial in this situation due to the ease of specifying structure and additional information through priors. However, care is needed as there are often fewer neighbours and more edges, which may influence results. Here we investigate Bayesian spatial model specification when there are few areas, first through a simulation study (number of areas ranging from 4 to 2500) and then apply to a case study on dengue fever in 2015 in Makassar, Indonesia (14 areas). Four different Bayesian spatial models namely, an independent model and 3 models based on a CAR (Conditional Autoregressive) prior: the Besag, York & Molli ©, Leroux, and a localised model (augments the CAR prior with a cluster model using piecewise constant intercepts) were applied. Data were generated for the simulation study considering low and high spatial autocorrelation and low and high disease incidence. Model goodness of fit was compared using Deviance Information Criteria. Analysis of variance and Bonferroni’s method were also used to determine which models were significantly different. The simulation study showed models differed in their performance mainly in two situations: 1. When there were at least 25 areas and both the disease rate and spatial autocorrelation was low, and 2. For all area sizes when there was low spatial autocorrelation but a high overall disease rate. Likewise, results from the case study showed that all four models performed similarly. This is probably due to the low number of areas and a low disease incidence.