Parameter Estimation Of Linear Bayes Hybrid Geographically Weighted Regression Model And Its Application

The hybrid geographic weighted regression model is a more comprehensive spatial analysis method.In order to fully consider the type of the model parameters,it divides the model parameters into global parameters and local parameters to explore the non-stationarity of the spatial relationship.In this dissertation,a hybrid geographic weighted regression model is used.The linear Bayesian estimation and two-step estimation of the hybrid geographically weighted regression model are mainly studied.The two-step estimation of the linear Bayes and the hybrid geographic weighted regression model of the hybrid geographically weighted regression model is used.In actual application and comparison analysis,taking the emission of SO₂ in 31 provinces as an example,the Bayes hybrid geographic-weighted regression model was used to detect and analyze the special nature of space.Firstly,the basic theory of ordinary linear regression model and the method of least squares estimation are expounded.The basic principle and parameter estimation of the hybrid geographic weighted regression model are introduced in detail,and the two parameter estimation methods are compared.In practical applications,due to the least squares parameter estimation in the model estimation there is a certain error,and does not fully consider the specificity of the model.Therefore,the hybrid geographic weighted model was selected and the model parameter estimation was deeply studied.Finally,the linear Bayesian estimation was used to estimate the parameters of the hybrid geographic weighted model.Secondly,the third chapter introduces the linear Bayes estimation method of regression parameters of the model,mainly uses the second-order matrix optimization method to reduce the risk of Bayesian estimation,and deduces the Bayesian hybrid geographic-weighted regression model estimation method.Finally,taking the emissions of SO₂ in 31 provinces as an example,the following analysis was conducted by selecting population density,employment rate,per capita primary industry,per capita secondary industry,per capita tertiary industry,and per capita electricity consumption as variables.?1?Analysis of spatial autocorrelation analysis from global spatial autocorrelation and local spatial autocorrelation.Through the theory of global spatial autocorrelation and local spatial autocorrelation,we further calculated values,plotted scatter plots,and LISA cluster maps.And significance to explain SO₂ emissions due to spatial differences in space,that there is a clear spatial agglomeration and spatial dependence.?2?Secondly,establish a general linear regression model for the SO₂ emissions and the selected six explanatory variables and perform a least-squares estimation.The calculation and analysis of the P value and the goodness of fit and the analysis of the significance of the variables.The linear regression model does not take into account the effects of spatial non-stationarity and geospatial location changes.Therefore,this paper establishes a hybrid geographically weighted regression model of SO₂ emissions and variables and performs two-step estimation and Bayesian estimation of the model parameters..?3?Based on the theoretical knowledge of the hybrid geographically weighted regression model,in the actual application analysis,this paper adopts the two-step method and the linear Bayes estimation method respectively to compare the parameter estimation of the model,and to calculate the P value and draw it.The residual plot was fitted,and the SO₂ emission level map was compared with the residual plot.?4?The final result shows that there are spatial dependence and strong agglomeration of the emission of SO₂ in 31 provinces across the country;the significance and fitting of the linear Bayes hybrid geographically weighted regression model is better than the hybrid geographically weighted regression.The two-step estimation of the model is better than the parameter estimation of the ordinary linear regression model,and the linear Bayes hybrid geographic weighted model can better detect the non-stationarity of the space.The analysis results are consistent with the facts.