Spatially Variable Coefficient Poisson Regression Model And Its Variable Selection

The spatial variable coefficient model is a powerful tool for exploring spatial dependence structure and spatial heterogeneity.The recently developed spatial variable coefficient Lasso(GWL)method is not related to spatial regression.The selection of local variables under the premise of stability improves the model's adaptability to multicollinear spatial data.In view of the inability of GWL to feed back shrinkage parameters,the coarser coefficient surface estimation and the bias of Lasso,this paper proposes an optimized method based on GWL and adaptive Lasso Spatial variable coefficient Lasso(OGWL)and spatial variable coefficient adaptive Lasso(GWAL)methods perform coefficient shrinkage estimation and local model selection.Based on generalized cross-validation,smooth parameters and spatial distance weighting are selected to construct a weight matrix,and coordinate descent method is used to obtain Lasso and adaptive Lasso solution.The GWL,OGWL and GWAL methods were used to calculate the root mean square of the coefficient and the standard error of the response variable and draw the coefficient surface graph.The results showed that:(1)The standard deviation of the coefficient and the standard deviation of the response variable are both In terms of square root estimation accuracy:The estimatio2n accuracy of GWAL is higher than that of OGWL,and OGWL is higher than GWL;(2)In terms of the fitting effect of coefficient surface:When the coefficient surface is more complicated,the coefficient surface fitted by the GWAL and OGWL method is better than that of the GWL method.Close to the real surface,while the GWAL method compresses the value of the coefficient close to zero to zero,while the GWL method has an insignificant compression effect.Therefore,GWAL and OGWL can make the coefficient estimates more effective in areas where the independent variable has an insignificant influence on the dependent variable.At the same time,in view of the problem that GWL cannot feedback the shrinkage parameter that controls the degree of compression of the estimated function,both OGWL and GWAL have improved,and the shrinkage parameter ?can be fed back.OGWL and GWAL are estimation methods for processing continuous response variables.Geographically weighted Poisson regression models(GWPR)are commonly used to analyze discrete data with spatial heterogeneity.For the processing of discrete count data and the identification of important variables,this paper proposes spatial variable coefficient Poisson Lasso(GWPL)method is used for coefficient shrinkage estimation and local model selection.Based on cross-validation,smooth parameters and spatial distance weighting are selected to construct a weight matrix,and the coordinate descent method is used to obtain the Lasso solution.Through statistical simulation,the GWR,GWPR and GWPL methods are used to calculate the standard error root mean square and the mean value of the absolute deviation of the coefficient and draw the coefficient surface graph.The results are compared and found:(1)In terms of the estimation accuracy of the coefficients:the GWPL method has the highest estimation accuracy,GWPR second,and GWR the lowest;(2)In terms of the coefficient surface fitting effect:the coefficient surface boundary estimated by the GWR method is far from the real surface.GWPR and GWPL can approximate the reduction coefficient surface,and GWPL can compress the value nearly zero to zero.Therefore,When the GWR method explores the heterogeneity of the regression relationship,it may distort the true heterogeneity,and there is a risk of getting wrong conclusions;GWPL,which combines the compression effect of Lasso and the spatially variable coefficient Poisson regression model,is used in the independent variable to the factor.In areas where the variable influence is not significant,Lasso can compress the coefficient estimate to zero.In practical applications,it is helpful to identify the explanatory variable that has a weak influence on a certain spatial area.At the same time,GWPL can feed back the shrinkage parameter that controls the degree of compression of the estimated function ?.This paper is based on the spatial variable coefficient Poisson Lasso(GWPL),geographically weighted Poisson regression(GWPR)and the spatial variable coefficient adaptive Lasso(GWAL)methods.The spatial variation characteristics of the impact of seven macro factors involved in four aspects of economic level,transportation,social security,and health level on the incidence of hepatitis B in 31 regions of the country.GWAL was used to analyze the count-type discrete data,and the empirical results found and selected The seven explanatory variables of GWPL had no effect on the incidence of hepatitis B in 18 of the 31 regions,and the results were contrary to common sense.Therefore,the GWAL method of processing continuous data is unreliable for the statistical discrete data analysis results.GWPL has a compression effect,It can identify explanatory variables that have a weaker impact on a certain spatial region,which reflects the practical value of the spatial variable coefficient Poisson Lasso method.