Spatial Modeling With Spatially Varying Coefficient Processes

By Alan E. Gelfand, Hyon‐Jung Kim, C. F. Sirmans, Sudipto Banerjee. Journal of the American Statistical Association, 2003

681 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/746554301fc69990cead47831552c67eefd259cb

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Citations in the corpus

A Simulation-Based Study of Geographically Weighted Regression as a Method for Investigating Spatially Varying Relationships (2011, background): “Bayesian spatially varying coefficient models (Gelfand et al, 2003) are another alternative to model spatial relationships in a well-established statistical framework.”
Towards Causal Inference for Spatio-Temporal Data: Conflict and Forest Loss in Colombia (2020, methodology): “Our approach may be seen as summarizing the output of a spatially varying regression model [e.g., Gelfand et al., 2003] that is allowed to change arbitrarily from one location to the other (within the model class dictated by ˆ f Y | X ).”
Gaussian predictive process models for large spatial data sets (2008, methodology): “The advantages of such models have been detailed in, for example, Gelfand et al. (2003), who recognized the computational infeasibility of these models with large spatial data sets and resorted to separable covariance structures that restrict the same spatial decay to all the coefficients.”
Maximum likelihood estimation of spatially varying coefficient models for large data with an application to real estate price prediction (2020, methodology): “Gelfand et al. (2003) used a Bayesian SVC model with coefficients defined as Gaussian processes (GP) to model single-family houses in Baton Rouge, Louisiana.”
Bayesian functional ANOVA modeling using Gaussian process prior distributions (2010, background): “The approach we describe here can be linked, for example, to the spatially varying coefficient processes discussed by Gelfand et al. (2003).”
Efficient stabilization of crop yield prediction in the Canadian Prairies (2012, background): “Others have proposed more complex spatially-varying models which rely on Markov chain Monte Carlo for inference (e.g. Gelfand et al., 2003; Banerjee et al., 2004); however, our goal of an online implementation restricts us to models with analytic tractability.”
A Moran coefficient-based mixed effects approach to investigate spatially varying relationships (2016, methodology): “21 The Bayesian spatially varying coefficients (B-SVC) model, based on a 22 geostatistical (Gelfand et al., 2003) or lattice autoregressive approach (Assunçao, 2003), 23 is another form of the spatially varying coefficients model that requires Markov chain 24 Monte Carlo (MCMC).”
Multicollinearity and correlation among local regression coefficients in geographically weighted regression (2005, methodology): “Gelfand et al. (2003) demonstrate a simultaneous approach using a Bayesian framework.”
Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices (2010, background): “An extended model of this study with spatially varying coefficient process is also developed in Gelfand et al. (2003).”
Modeling Network Autocorrelation in Space–Time Migration Flow Data: An Eigenvector Spatial Filtering Approach (2011, background): “effects corresponding to different correlation structures is almost impossible, although this type of specification is common in Bayesian spatial models with spatially structured and spatially unstructured random effects (e.g., Banerjee, Carlin, and Gelfand 2004; Gelfand et al. 2003; Law and Haining”
Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor (2011, result): “model (e.g. Gelfand et al. 2003; Waller et al. 2007) or the local cokriging models of Pereira et al. (2002) for modelling nonstationary relationships; and (c) find ways to generalise (and confirm) our results using both real and simulated data sets, where issues of sample size and configuration ar”
Locally Calibrated Probabilistic Temperature Forecasting Using Geostatistical Model Averaging and Local Bayesian Model Averaging (2011, background): “GMA belongs to the general class of spatially varying-coefficient models (Hastie and Tibshirani 1993; Gelfand et al. 2003, 2005).”