Research On Regressive Model For Spatial Differentiation

Because of the spatial correlation and spatial heterogeneity of geographical entities,the traditional regression model is global,and it is assumed that there is no correlation between geographic entities,which leads to low accuracy.Based on the residential price,this paper uses the exploratory spatial data analysis method to analyze the spatial autocorrelation and spatial heterogeneity of residential price data,and discusses its temporal and spatial evolution characteristics.Aiming at the problems existing in the traditional regression model,we first try and experiment with the spatial autoregressive model of the distance adjacency matrix instead of the spatial adjacency matrix,which provides a new direction for the selection of the weight of the spatial autoregressive model,and then proposes a geographically weighted autoregressive model which Taking into account spatial correlation and heterogeneity,On this basis,the time factor is incorporated into the model,and the geographically and temporally weighted autoregressive model is built,Therefore,the spatial heterogeneity and temporal characteristics of spatial entities was solved.The main research contents and innovations include:(1)Owing to the spatial autocorrelation and spatial heterogeneity of geographic entities,this paper uses the global Moran index to measure the degree of autocorrelation,and uses the local Moran index to explore the autocorrelation model of local data;And then the semivariogram is used to test the spatial heterogeneity of geographic entities.(2)The traditional spatial autocorrelation model is based on the spatial adjacency matrix,ignoring the influence of the distance factor on the autocorrelation.In this paper,the spatial weight matrix based on inverse distance and Gauss kernel function is taken as an example,and then the possibility of replacing the spatial adjacency matrix by the distance weight matrix is studied.The autoregressive model based on distance reciprocal spatial weight matrix and based on Gaussian weight matrix are improved by 0.08 and 0.11 respectively compared with the traditional spatial autoregressive model.(3)A geographically weighted autoregressive model which taking into account spatial correlation and heterogeneity was built,on the basis of the traditional geography weighting model,the autoregressive term was added.The main contents include the two-step least squares estimation of the model and the CV method to select the optimal spatial bandwidth.The fitting accuracy is improved by 0.16 and 0.07 compared with the traditional spatial autoregressive model and the geographically weighted regression model.(4)The geographically and temporally weighted regressive model is constructed by adding time factors to the geographically weighted regressive model.The main processes were the establishment of spatio-temporal kernel functions and the selection of time and space factors.The variance analysis,regression coefficient analysis and goodness of fit analysis of the experimental results were carried out.The results show that the geographically and temporally weighted regressive model has the best performance in terms of residual sum of squares,mean square error,good fit and so on.