Geographically Weighted Regression Analysis for Spatial Economics Data: a Bayesian Recourse

TL;DR

This paper introduces a Bayesian approach to geographically weighted regression (GWR), enhancing spatial data analysis with advanced variable selection, bandwidth choice, and model assessment methods, validated through simulations and applied to China's macroeconomic data.

Contribution

The paper develops a Bayesian GWR framework incorporating spike-and-slab priors, range-based bandwidth selection, and modified model criteria, providing a comprehensive alternative to classical GWR.

Findings

Bayesian GWR performs well in simulations with various location scenarios.

Variable selection and estimation are satisfactory across different conditions.

Application to Chinese provincial data yields economically meaningful insights.

Abstract

The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods with both small and large number of location scenarios, and comparison with the classical frequentist GWR is made. The performance of variable selection and estimation of the proposed methodology under different circumstances are satisfactory. We further apply the proposed methodology in analysis of a province-level macroeconomic data of 30 selected provinces in China. The estimation and variable selection results reveal insights about China's economy that are convincing and agree with previous studies and facts.