Modeling Temporal Gradients in Regionally Aggregated California Asthma Hospitalization Data

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Harrison Quick*+ and Sudipto Banerjee and Bradley P Carlin
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: Gaussian process ; Gradients ; Markov chain Monte Carlo ; Spatial process models ; Spatially associated functional data

Abstract

Advances in GIS have led to enormous recent burgeoning of spatial-temporal databases and associated statistical modeling. Here we depart from the rather rich literature in space-time modeling by considering the setting where space is discrete, but time is continuous. Our major objective in this application is to carry out inference on gradients of a temporal process in our dataset of monthly county level asthma hospitalization rates in California, while at the same time accounting for spatial similarities of the temporal process across neighboring counties. Rather than use parametric forms to model time, we opt for a more flexible stochastic process embedded within a dynamic Markov random field framework. Through the cross-covariance function we can ensure that the temporal process realizations are mean square differentiable, and may thus carry out inference on temporal gradients in a posterior predictive fashion. We use this approach to evaluate temporal gradients where we are concerned with temporal changes in the residual and fitted rate curves after accounting for seasonality, spatiotemporal ozone levels, and several spatially-resolved important sociodemographic covariates.