Abstract
BackgroundThere is an expanding literature on different representations of spatial random effects for different types of spatial correlation structure within the conditional autoregressive class of priors for Bayesian spatial models. However, little is known about the impact of these different priors when the number of areas is small. This paper aimed to investigate this problem both in the context of a case study of spatial analysis of dengue fever and more generally through a simulation study.MethodsBoth the simulation study and the case study considered count data aggregated to a small area level in a region. Five different conditional autoregressive priors for a simple Bayesian Poisson model were considered: independent, Besag-York-Mollié, Leroux, and two variants of a localised clustering model. Data were simulated with eight different sizes of areal grids, ranging from 4 to 2500 areas, and two different levels of both spatial autocorrelation and disease counts. Model goodness-of-fit measures and model estimates were compared. A case study involving dengue fever cases in 14 local areas in Makassar, Indonesia, was also considered.ResultsThe simulation study showed that model performance varied under different scenarios. When areas had low autocorrelation and high counts, and the number of areas was at most 25, the BYM, Leroux and localised G = 2 models performed similarly and better than the independent and localised G = 3 models. However, when the number of areas were at least 100, all models performed differently, and the Leroux model performed the best. Overall, the Leroux model performed the best for every scenario especially when there were at least 16 areas. Based on the case study, the comparative performance of spatial models may also vary for a small number of areas, especially when the data have a relatively large mean and variance over areas. In this case, the localised model with G = 3 was a better choice.ConclusionDetecting spatial patterns can be difficult when there are very few areas. Understanding the characteristics of the data and the relative influence of alternative conditional autoregressive priors is essential in selecting an appropriate Bayesian spatial model.
Highlights
There is an expanding literature on different representations of spatial random effects for different types of spatial correlation structure within the conditional autoregressive class of priors for Bayesian spatial models
The authors found that the BYM model was the best among all the models considered based on the deviance information criterion (DIC) values
We investigate the relative performance of Bayesian spatial models when there are few areas via a simulation study
Summary
There is an expanding literature on different representations of spatial random effects for different types of spatial correlation structure within the conditional autoregressive class of priors for Bayesian spatial models. Aswi et al Int J Health Geogr (2020) 19:39 conditional autoregressive (ICAR) model [8], the Besag, York & Mollié (BYM) model [8], the Cressie model [9], the Leroux model [10], locally adaptive [11] and localised models [12]. Several of these models have been compared using simulated data. The authors found that the BYM model was the best among all the models considered based on the deviance information criterion (DIC) values
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