Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach

Spatial data not only enables smart cities to visualize, analyze, and interpret data related to location and space, but also helps departments make more informed decisions. We apply a Bayesian quantile regression (BQR) of the partially linear varying coefficient spatial autoregressive (PLVCSAR) mode...

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Main Authors: Rongshang Chen, Zhiyong Chen
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Entropy
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Online Access:https://www.mdpi.com/1099-4300/27/7/715
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author Rongshang Chen
Zhiyong Chen
author_facet Rongshang Chen
Zhiyong Chen
author_sort Rongshang Chen
collection DOAJ
description Spatial data not only enables smart cities to visualize, analyze, and interpret data related to location and space, but also helps departments make more informed decisions. We apply a Bayesian quantile regression (BQR) of the partially linear varying coefficient spatial autoregressive (PLVCSAR) model for spatial data to improve the prediction of performance. It can be used to capture the response of covariates to linear and nonlinear effects at different quantile points. Through an approximation of the nonparametric functions with free-knot splines, we develop a Bayesian sampling approach that can be applied by the Markov chain Monte Carlo (MCMC) approach and design an efficient Metropolis–Hastings within the Gibbs sampling algorithm to explore the joint posterior distributions. Computational efficiency is achieved through a modified reversible-jump MCMC algorithm incorporating adaptive movement steps to accelerate chain convergence. The simulation results demonstrate that our estimator exhibits robustness to alternative spatial weight matrices and outperforms both quantile regression (QR) and instrumental variable quantile regression (IVQR) in a finite sample at different quantiles. The effectiveness of the proposed model and estimation method is demonstrated by the use of real data from the Boston median house price.
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spelling doaj-art-25accd8fbb294dcbb1dc1d79d798c1de2025-08-20T03:36:14ZengMDPI AGEntropy1099-43002025-07-0127771510.3390/e27070715Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression ApproachRongshang Chen0Zhiyong Chen1School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, ChinaSpatial data not only enables smart cities to visualize, analyze, and interpret data related to location and space, but also helps departments make more informed decisions. We apply a Bayesian quantile regression (BQR) of the partially linear varying coefficient spatial autoregressive (PLVCSAR) model for spatial data to improve the prediction of performance. It can be used to capture the response of covariates to linear and nonlinear effects at different quantile points. Through an approximation of the nonparametric functions with free-knot splines, we develop a Bayesian sampling approach that can be applied by the Markov chain Monte Carlo (MCMC) approach and design an efficient Metropolis–Hastings within the Gibbs sampling algorithm to explore the joint posterior distributions. Computational efficiency is achieved through a modified reversible-jump MCMC algorithm incorporating adaptive movement steps to accelerate chain convergence. The simulation results demonstrate that our estimator exhibits robustness to alternative spatial weight matrices and outperforms both quantile regression (QR) and instrumental variable quantile regression (IVQR) in a finite sample at different quantiles. The effectiveness of the proposed model and estimation method is demonstrated by the use of real data from the Boston median house price.https://www.mdpi.com/1099-4300/27/7/715spatial autoregressive modelspartially linear varying coefficientquantile regressionMarkov chain Monte Carlo approachGibbs sampling
spellingShingle Rongshang Chen
Zhiyong Chen
Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
Entropy
spatial autoregressive models
partially linear varying coefficient
quantile regression
Markov chain Monte Carlo approach
Gibbs sampling
title Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
title_full Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
title_fullStr Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
title_full_unstemmed Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
title_short Modeling Spatial Data with Heteroscedasticity Using PLVCSAR Model: A Bayesian Quantile Regression Approach
title_sort modeling spatial data with heteroscedasticity using plvcsar model a bayesian quantile regression approach
topic spatial autoregressive models
partially linear varying coefficient
quantile regression
Markov chain Monte Carlo approach
Gibbs sampling
url https://www.mdpi.com/1099-4300/27/7/715
work_keys_str_mv AT rongshangchen modelingspatialdatawithheteroscedasticityusingplvcsarmodelabayesianquantileregressionapproach
AT zhiyongchen modelingspatialdatawithheteroscedasticityusingplvcsarmodelabayesianquantileregressionapproach