Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

Abstract

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.