Spatially Varing Coefficient Processes Models with Application to House Price Data

• Activity Number: 188
• Type: Invited
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Council of Chapters
• Author(s): Alan Gelfand*+
• Affiliation(s): University of Connecticut

Abstract

In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly all of this work the regression coefficients are assumed to be constant over the region. However, in some applications, coefficients are expected to vary at the local or subregion level. Here we focus on the local case. While parametric modeling of the spatial surface for the coefficient is possible, here we argue that it is more natural and flexible to view the surface as a realization from a spatial process. Then, prediction of coefficients at new locations can be supplied.

We show how such modeling can be formalized in the context of Gaussian responses, providing attractive interpretation both in terms of random effects and in terms of explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal settings. The spatial settings generally encourage a Bayesian inferential framework to avoid inappropriate asymptotics. In the present case, these models can only be fitted and the desired inference provided using this framework.