A Bayesian Implementation of the Multiscale Geographically Weighted Regression Model with INLA

• Published in: Annals of the American Association of Geographers Vol. 113; no. 6; pp. 1501 - 1515
• Main Authors: Ma, Zhihua, Huang, Zhelin
• Format: Journal Article
• Language: English
• Published: Washington Routledge 03.07.2023; Taylor & Francis Ltd
• Subjects: Algorithms; Approximation; Bayesian analysis; Bayesian MGWR; Bayesian theory; Coefficients; coeficientes espacialmente variables; Cost analysis; el MGWR bayesiano; Estimates; heterogeneidad espacial; Housing costs; Illustrations; Markov analysis; Markov chains; Monte Carlo simulation; multiscale geographically weighted regression; Nonstationarity; Parameter identification; Probability theory; regresión multiescalar geográficamente ponderada; Regression models; Simulation; Spatial analysis; spatial heterogeneity; spatially varying coefficients; Statistical methods; Uncertainty; 动态空间系数; 多尺度地理加权回归; 空间异质性; 贝叶斯MGWR
• ISSN: 2469-4452; 2469-4460
• DOI: 10.1080/24694452.2023.2187756

The multiscale geographically weighted regression (MGWR) model is an important extension of the classical geographically weighted regression (GWR) model that can be used to explore the spatial nonstationarity of the regression relationship in spatial analysis, but also allows for different scales on conditional relationships between response and different predictors. A Bayesian version of the MGWR model is proposed to obtain estimates of the spatially varying coefficients and the bandwidths simultaneously. The hierarchical form of the Bayesian MGWR model has attractive features, including obtaining posterior estimates of the bandwidths and local parameters simultaneously, and their uncertainty can be easily measured. For Bayesian posterior inference, an efficient algorithm based on integrated nested Laplace approximation is introduced to provide a great alternative of the classical Markov chain Monte Carlo algorithm under the Bayesian framework. The performance of the proposed method is evaluated through simulation study, and it is shown that the proposed approach can correctly identify the differences between scales of parameter surfaces and also obtain precise posterior estimates. Finally, for illustration, this approach is used to analyze monthly housing cost data in the state of Georgia.