Estimation And Variable Selection Of Spatial And Temporal Weighted Regression Model

The accuracy of model selection plays an important role in the estimation of coefficients,data analysis and statistical decision.In recent years,many scholars put forward different methods for the accurate selection of explanatory variables to make the model better,and have a good effect in the application.However,with the increase of the complexity of the data generation mechanism,a simple variable coefficient model can not meet the characteristics of data change characteristics,so in the model,we need to consider more factors affecting the data changes.According to the spatial and temporal characteristics of the data,the geographically and temporally weighted regression model(GTWR)provides a reasonable explanation for the factors of time and geographical location included in the coefficients of the explanatory variables,the GTWR model can be used to analyze the relationship between variables,and the variation of the coefficient function can clearly reflect the spatial and temporal characteristics of the data distribution.However,like other simple models,it is very important to accurately select the explanatory variables in the GTWR model.In this paper,we study the coefficient representation of GTWR model,the method of variable selection and the empirical study.Based on the principle of least squares,the approximation of the variable coefficient function with time and space is given by using spline basis functions,the good properties of local supporting and unit decomposition of spline basis functions make the derivation of the theoretical methods more effective in the process of variable selection,and the local supporting of spline basis function makes the coefficient estimation more flexible.Based on the least squares objective function,combined with the penalty,not only be the coefficient function estimated but also the corresponding coefficient function are compressed.The important variables are preserved and the irrelevant variables are excluded,finally,we can obtain the exact form of the model.At the same time,in order to prove the rationality of the method,we give the proof of the important theorem and conclusion show that the research method is reasonable.In the simulation of the empirical part,the linear regression model is used to simulate three different variable selection methods under different sample sizes.The results show that the SCAD method most accurate for estimation of coefficient functions on the model with increases in the number of sample estimation,and there has the minimum model error.Next,based on the GTWR model,the air quality of the meteorological data used for the 70 cities in China to do the case analysis from the time and space span,the results of the study show whether it is time or space factors,the influence of explanatory variables on the response variables,showing a certain spatial nonstationarity,and the coefficient estimates at different time points and the area has a good fitting effect.