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.

部分线性单指数空间自回归模型 (PLSISARM) 可用于评估协变量对空间相关数据响应的线性和非线性影响。使用由自由结样条近似的非参数函数，我们开发了一种基于贝叶斯采样的方法，该方法可以通过促进有效的马尔可夫链蒙特卡罗方法来执行，以分析 PLSISARM 并设计一个 Gibbs 采样器来探索联合后验分布。为了获得快速收敛的算法，我们改进了带有自由结的贝叶斯样条的移动步骤，以便每次可以重新定位所有结，而不是只有一个结。我们通过对波士顿房价数据集的模拟研究和分析来说明所提出的模型和估计方法的性能。