Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.