为有效探索空间数据间的自相关性与异质性及其非线性关系，本项目扩展经典的空间滞后模型，构建空间滞后变系数模型，将数据的空间属性引入到回归系数和滞后因子中：假定回归系数是各个观测点的函数，反映解释变量在不同区域对响应变量的影响；考虑空间滞后因子为固定常数与随地理位置变化两种情况，探索响应变量的全局及局部滞后性。在贝叶斯框架下，单一的MCMC算法或INLA算法无法胜任该复杂模型参数的估计。本项目结合MCMC和INLA算法，估计该模型参数，分析估计方法的稳健性，构建统计量检验模型空间自相关性。该估计方法继承了MCMC和INLA算法的优点，可实现并行计算，大大缩短计算时间，同时还能保持较高的计算精度，弥补了空间滞后变系数模型估计的空白，对于处理空间数据有着重要的理论价值和现实意义。该模型的理论研究成果可广泛应用于生态环境、生物医学、交通、社会学等领域，更深入揭示空间数据的局部变化响应关系与影响因素。

In order to effectively explore the autocorrelation and heterogeneity between spatial data and its nonlinear relationship, this project extends the classical spatial lag model and constructs a spatial lag variable coefficient model. Introduce the spatial properties of the data into the regression coefficients and lag factors: It is assumed that the regression coefficient is a function of each observation point, reflecting the influence of the explanatory variable on the response variable in different regions; considering the spatial lag factor as a fixed constant and the change of geographical location, the global and local lag of the response variable is explored. Under the Bayesian framework, a single MCMC algorithm or INLA algorithm is not sufficient for the estimation of the complex model parameters. This project combines MCMC and INLA algorithms to estimate the parameters of the model, analyze the robustness of the estimation method, and construct the spatial autocorrelation of the statistical test model. The estimation method inherits the advantages of the MCMC and INLA algorithms, can realize parallel computing, greatly shortens the calculation time, and at the same time maintains high calculation accuracy, and makes up for the blank of spatial hysteresis variable coefficient model estimation, which has important theoretical and practical significance for processing spatial data. The theoretical research results of this model can be widely applied in the fields of ecological environment, biomedicine, transportation, sociology, etc., and reveal the local response relationship of spatial data.