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Spatial Modeling With Spatially Varying Coefficient Processes.

Alan E Gelfand1, Hyon-Jung Kim2, C F Sirmans3

  • 1Institute of Statistics and Decision Sciences, Duke University, Durham, NC 27708-0251.

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|October 18, 2024
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Summary
This summary is machine-generated.

This study introduces a flexible spatial modeling approach for regression coefficients, moving beyond constant coefficient assumptions. This method enhances understanding of spatially correlated data, particularly in real estate price prediction.

Keywords:
Bayesian frameworkMultivariate spatial processesPredictionSpatio-temporal modelingStationary Gaussian process

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Area of Science:

  • Spatial statistics
  • Geostatistics
  • Econometrics

Background:

  • Traditional regression models assume constant coefficients across a region.
  • Spatial correlation in responses is common in many applications.
  • Local variation in regression coefficients is often overlooked but important.

Purpose of the Study:

  • To propose a flexible statistical framework for modeling spatially varying regression coefficients.
  • To treat coefficient surfaces as realizations from spatial processes.
  • To extend existing spatial regression methodologies.

Main Methods:

  • Modeling coefficient surfaces as spatial processes (e.g., Gaussian processes).
  • Formalization within Gaussian response models.
  • Extensions to generalized linear models and spatio-temporal settings.

Main Results:

  • Demonstrates attractive interpretations in terms of random effects and residual analysis.
  • Provides a more natural and flexible alternative to parametric spatial surfaces.
  • Illustrates application with a dataset on single-family house prices.

Conclusions:

  • Viewing spatially varying coefficients as realizations from spatial processes offers a powerful and flexible modeling approach.
  • The proposed methods are applicable to various regression settings, including spatio-temporal data.
  • This framework enhances the interpretability and explanatory power of spatial regression models.