Simulation Research And Application Of Geographically Weighted Poisson Regression Model

Hand,foot and mouth disease is an acute infectious disease caused by a group of intestinal diseases that is prevalent worldwide.At present,research on its etiology and transmission mechanism has been relatively complete.However,when exploring the influence of various factors on hand,foot and mouth disease,global models are often used for research.Lack of analysis and modeling based on spatial geographic information,and failed to incorporate the regional and local characteristics of the disease transmission into the analysis process.In addition,the collinearity between the data was not considered in the previous research on hand,foot and mouth disease.As a result,the coefficients estimated by the model are unstable,and cannot reveal the true relationship between various influencing factors and the condition of the disease.The Geographically Weighted Regression(GWR)model is a method to provide a local specific model for the spatial heterogeneity of data.It has been greatly developed in model fusion and optimization,and is widely used in geology,environmental science,ecology,and economics.But when the dependent variable is a count variable,such as the number of patients,It is not appropriate to use traditional GWR,which is suitable for Gaussian distribution data,to fit the model.At this time,it is more appropriate to use a Geographically Weighted Poisson Regression(GWPR)model.As mentioned above,there is inevitably multicollinearity in many variables that affect disease transmission.In addition,the geographical weighting method will also increase the collinearity between the original data.At this time,the use of the Geographically Weighted Poisson Ridge Regression(GWPRR)model can help suppress the influence of multiple collinearity and make the statistical inference results more stable and reliable.Therefore,this article also considers the regional characteristics of the outbreak and spread of the disease and the multicollinearity of the observation data of influencing factors,and studies the estimation and prediction effects of GWR,GWPR and GWPRR.The article designed a systematic simulation experiment,the purpose is to compare the GWR model,the GWPR model and the GWPRR model in more detail when the dependent variable obeys the Poisson distribution and the independent variable has multicollinearity,so as to find out the fitting effect of the model.A model that explores the non-stationarity of the data space under the circumstances.In this paper,a simulation experiment is designed to set the dependent variable as a random number that obeys the poisson distribution,and at the same time set the correlation coefficient of the independent variable to 0,0.5,and 0.9 corresponding to 3 different levels of correlation,and select the average absolute deviation and average standard deviation statistical indicators are compared to evaluate the performance of GWR,GWPR and GWPRR from the aspects of accuracy and stability.The experimental results show that when the response variable obeys the poisson distribution,under different degrees of collinearity,the estimated results of the coefficients and response variables of the GWR model are quite different from the real situation.Compared with the GWPR model and the GWPRR model,when there is no collinearity,the prediction error and stability are not much different;as the collinearity between variables increases,the prediction accuracy and stability of the GWPRR model are significantly better than the GWPR model.Finally,based on the analysis and processing of 6 meteorological index data and 3 economic index data in Xinjiang,this article applies the three models to the analysis of the hand,foot and mouth disease data of 106 counties in Xinjiang in2018,and further verifies the effectiveness in practical applications.The root mean square error and root mean square prediction error of the predicted value of the number of patients show that the prediction error of the GWPR model and the GWPRR model for the number of patients is much smaller than that of the GWR model.The comparative analysis of the estimated coefficients of the three models further proves that for the data set where the dependent variable is the number of patients and the independent variable has multicollinearity,the GWPRR model can more truly reveal the space of the impact of each factor on the number of patients Non-stationarity.