Spatial Modeling With Spatially Varying Coefficient Processes

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...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2003-06, Vol.98 (462), p.387-396
Main Authors: Gelfand, Alan E, Kim, Hyon-Jung, Sirmans, C. F, Banerjee, Sudipto
Format: Article
Language:English
Subjects:
Bayesian framework
Bayesian method
Coefficients
Exact sciences and technology
Generalized linear models
Inference
Inference from stochastic processes
time series analysis
Linear inference, regression
Mathematical foundations
Mathematics
Modeling
Multivariate spatial processes
Parametric models
Perceptual localization
Prediction
Predictive modeling
Probability and statistics
Regression analysis
Sciences and techniques of general use
Spatial analysis
Spatial models
Spatio-temporal modeling
Stationary gaussian process
Statistical analysis
Statistical methods
Statistics
Studies
Theory and Methods
Three dimensional modeling
Two dimensional modeling
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Summary: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 subregional level. Here we focus on the local case. Although 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. We show how such modeling can be formalized in the context of Gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal setting. We illustrate both static and dynamic modeling with a dataset that attempts to explain (log) selling price of single-family houses.
ISSN:0162-1459
1537-274X
DOI:10.1198/016214503000170