| Spatial regression model is a statistical method used to analyze spatial data,including spatial lag model,geographically weighted regression model,and so on.Existing spatial regression models cannot simultaneously consider the heterogeneity,autocorrelation and time-scale effects of spatial data.Therefore,considering the various characteristics of spatial data is conducive to more objective and accurate fitting spatial regression models.The main research contents of this paper are summarized as follows:(1)A spatial lag-geographically weighted regression model is proposed.This model is based on the mixed geographically weighted regression model,introducing spatial autocorrelation terms within the bandwidth range,taking into account the autocorrelation and heterogeneity of data,then,two parameter estimation methods for a spatial lag-mixed geographically weighted regression model are proposed,namely Moran’s I estimation method and determinant estimation method.Finally,through simulation experiments,the effectiveness of the two methods for a spatial lag-mixed geographical weighted regression model is demonstrated.(2)A spatial lag-mixed geographically and temporally weighted regression model is established.For solving the geographically and temporally non-stationary nature of spatial regression models,the model interprets the regression coefficients in a mixed geographically weighted regression model as a function of spatial location and observation time.And this paper proposes a three-step estimation method based on expanding the parameter estimation of extend mixed geographically weighted regression models.This method provides geographical and temporal distance and geographically and temporally weighted function,then estimates the parameters using determinant estimation method.Simulation experiments indicate that both the parameter estimation methods and the model are effective and robustness.(3)A functional spatial lag-geographically weighted regression model is provided,and in order to better consider the prior information of the model parameters,it is assumed that the model parameters obey sparse priors.Based on hierarchical Bayesian model and iterative inverse solver,constant parameters and variable parameters estimation methods of the functional spatial laggeographically weighted regression model are given.And through simulation experiments,the reliability of the model is verified using mean square error and mean relative error. |
