Resumen
Quantile modeling has been seen as an alternative and useful complement to ordinary regression mainly focusing on the mean. To directly apply quantile modeling to areal data the discrete conditional quantile function of the data can be an issue. Although jittering by adding a small number from a uniform distribution to impose pseudo-continuity has been proposed, the approach can have a great influence on responses with small values. Thus we proposed an alternative to model the quantiles of relative risk for spatiotemporal areal health data within a Bayesian framework using the log-Laplace distribution. A simulation study was conducted to assess the performance of the proposed method and examine whether the model could robustly estimate quantiles of spatiotemporal count data. To perform a test with a real data example, we evaluated the potential application of clustering under the proposed log-Laplace and mean regression. The data were obtained from the total number of emergency room discharges for respiratory conditions, both infectious and non-infectious diseases, in the U.S. state of South Carolina in 2009. From both simulation and case studies, the proposed quantile modeling demonstrated potential for broad applicability in various areas of spatial health studies including anomaly detection.