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) 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.