Comparing multilevel and multiscale convolution models for small area aggregated health data

In spatial epidemiology, data are often arrayed hierarchically. The classification of individuals into smaller units, which in turn are grouped into larger units, can induce contextual effects. On the other hand, a scaling effect can occur due to the aggregation of data from smaller units into larger units. In this paper, we propose a shared multilevel model to address the contextual effects. In addition, we consider a shared multiscale model to adjust for both scale and contextual effects simultaneously. We also study convolution and independent multiscale models, which are special cases of shared multilevel and shared multiscale models, respectively. We compare the performance of the models by applying them to real and simulated data sets. We found that the shared multiscale model was the best model across a range of simulated and real scenarios as measured by the deviance information criterion (DIC) and the Watanabe Akaike information criterion (WAIC).