The Parameter Estimation Of Hierarchical Spatially Varying Coefficient Model With Bayes

The spatial variable coefficient model is a non-stationary method that interprets spatial heterogeneity by allowing coefficients to vary spatially.The GWR method plays a very effective role in dealing with the non-stationarity of the spatially coefficient models and the estimation of model parameters.In this paper,The coefficient function is locally expanded into a quadratic function of the spatial geographic coordinates.Combined with the Bayesian estimation theory of multiple linear regression model,The Gibbs sampling technique is used to traverse all geographical locations to obtain all coefficient functions.called the Local polynomial BGWR estimation method.And through the numerical simulation test to investigate the accuracy of the fitting method.Drawing a surface map,calculating the mean of the square of the deviation and comparing the corresponding results obtained by the Local linear GWR method,The corresponding results are compared to illustrate the superiority of the local polynomial BGWR fitting method in reducing the boundary effects and deviations of the coefficient function estimation.The method is used to empirically analyze the macro factors of the 31 provinces in 2016.Namely the indicators selected by the economy,population and natural environment,and the spatial differences in the impact of 2.5 concentration,and the accuracy of the local polynomial BGWR fitting is further explained by visual analysis of the estimation results.The spatial Hierarchical variable coefficient model is an extension of the spatial variable coefficient model,which is proposed to consider the spatial heterogeneity and the geographically hierarchical data structure,that is,combining the dual weight matrix model to deal with the characteristics of the regional data and the spatial variable coefficient model deals with the characteristics of spatial heterogeneity problems.The model contains two different levels of covariates,and explores the spatial variation of the effects of different levels of space.The difference between the SHVC model and the general SVC model is that the index variable at the location point and the index variable of the region are considered separately.At the same time,define two weight matrices: First,a membership matrix A is designed in the Spatial Hierarchical Variable Coefficient model to merge the hierarchy between the upper hierarchy(region hierarchy)and the lower hierarchy(point hierarchy);Secondly,the SHVC model considers variables other than the coefficient of variation of the point-based variables of the region-based variation coefficient;Finally,considering the adjacency relationship,that is,the adjacency relationship between the interior of the region and the boundary of the adjacent region.the fitting parameters method of the two-dimensional meshing and two-step estimation,the coefficients of each hierarchy are estimated by iteratively,and the model was used to empirically study the rental price of 1117 blocks(low-level location)in 111 streets(high-rise areas)in parts of Beijing,China in 2009.The price of the block land(lower level),choosing the size of the land block,the distance from the nearest subway,the distance from the nearest primary school,the distance from the nearest park,the distance from the nearest river as a low-level indicator,and the population density and crime rate are selected as high-level indicators.Analyzing the spatial difference between the influence factors of high and low factors on land price,visualize the estimation results to further explain the rationality and effectiveness of the model establishment.