Research And Application Of Generalized Spatially Varying Coefficient Autoregressive Model

The linear regression model is mainly applied to the case where the dependent variable is a continuous random variable.The GLM can deal with the dependent variable for discrete and continuous random variables.The GWR method assumes that the regression coefficient is a function of the geographic location of the observation point and solves the problem of spatial non-stationarity of spatial research objects.Therefore,for the classical GLM,the GWGLM can detect the non-stationarity of the spatial variables including the discrete variables in spatial distribution and can gain a deeper understanding of the structure and influencing factors of spatial heterogeneity of spatial research objects.Because the existence of the boundary effect will make the estimated distortion of coefficient function in the boundary area,resulting unrealistic analysis of the results.And the local polynomial fitting method has the advantage of automatically correcting the boundary effect.In this paper,we use the local linear GWR method to locally expand the coefficient function in the GWGLM as a linear function of the spatial geographical coordinates,which is called the local linear geographically weighted GLM.This problem is analyzed in detail for the Poisson regression model,which is called the local linear geographically weighted Poisson regression model.And the accuracy of local linear geographically weighted Poisson regression model is investigated by numerical simulation.By plotting the surface graph and calculating the mean of the deviation squared are compared with the corresponding result of the geographically weighted Poisson regression model to illustrate the superiority of the model in reducing the boundary effect and bias of the regression coefficient function estimation.And the above two models are also used to analyze the impact of macroscopic factors of 31 provinces of China in 2012,including the economic level,transportation,social security and health level,and on the spatial variation of HIV/AIDS incidence.It is further explained that the local linear geographically weighted Poisson regression model is superior to the geographically weighted Poisson regression model by fitting the goodness test.Because spatial data has spatial correlation and spatial heterogeneity,only the two properties can be considered at the same time can we better represent the spatial relationship of the data.However,for the discrete spatial data with spatial dependency,the varying coefficient generalized linear model can not be well analyzed.Therefore,this paper introduces the spatial autoregressive process of data into the varying coefficients generalized linear model,and proposes a generalized spatially varying coefficient autoregressive model to deal with the spatial problem of spatial data including discrete variables with spatial dependence and spatial heterogeneity.And for the Poisson regression model is described and analyzed in detail,which is called the spatially varying coefficient Poisson autoregressive model.And the accuracy of the spatially varying coefficient Poisson autoregressive model is investigated by numerical simulation.At the same time,the two models are applied to the above empirical analysis,and by fitting the goodness test to show that the spatially varying coefficient Poisson autoregressive model is more suitable for the analysis of such spatial data.