Bayesian analysis of partially linear, single-index, spatial autoregressive models

The partially linear single-index spatial autoregressive models (PLSISARM) can be used to evaluate the linear and nonlinear effects of covariates on the response for spatial dependent data. With the nonparametric function approximated by free-knot splines, we develop a Bayesian sampling-based method which can be performed by facilitating efficient Markov chain Monte Carlo approach to analyze PLSISARM and design a Gibbs sampler to explore the joint posterior distributions. To obtain a rapidly-convergent algorithm, we improve the movement step of Bayesian splines with free-knots so that all the knots can be relocated each time instead of only one knot. We illustrate the performance of the proposed model and estimation method by a simulation study and analysis of a Boston housing price dataset.