Heteroscedastic CAR Models for Areally Referenced Temporal Processes with an Application to California Asthma Hospitalization Data

• Activity Number: 345
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Harrison Quick*+ and Bradley P. Carlin and Sudipto Banerjee
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: Gaussian process ; Gradients ; Markov chain Monte Carlo ; Spatial process models ; Heteroscedastic CAR

Abstract

Often in regionally aggregated spatial models, a single variance parameter is used to capture variability in the spatial association structure of the model. In real world phenomena, however, spatially-varying factors such as climate and geography may impact the variability in the underlying process. Here, our interest is in modeling monthly asthma hospitalization rates over an 18 year period in the counties of California. Earlier work has accounted for spatiotemporal association using a process-based method that permits inference on the underlying temporal rates of change and has revealed progressively muted transitions into and out of the summer months. We extend these methods to allow for region-specific variance components, introducing a heteroscedastic CAR model that can help avoid over- and under-smoothing in our overall spatiotemporal process and our temporal gradient process. After demonstrating the effectiveness of our model via simulation, we reanalyze the asthma data and compare our findings to previous work. We find the following important differences: a dramatic change in an important covariate, improved fit in outlying counties, and sharp temporal gradients.