Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

TL;DR

This paper introduces a Bayesian extension of geographically weighted regression (GWR) that handles partial model misspecification across multiple components using a modularized Bayesian framework and spatially weighted KL divergence.

Contribution

It develops a novel Bayesian GWR model within a modularized framework to address partial misspecification in multiple model components, justified by an information risk minimization approach.

Findings

The proposed estimator is consistent under a geographically weighted KL divergence.

The model effectively manages partial misspecification across multiple components.

Optimal spatial weighting is achieved via KL divergence minimization.

Abstract

Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback-Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.