基于样条函数的时空加权回归模型变量选择

Variable Selection of Geographically and Temporally Weighted Regression Model Based on Spline Function

为了提高时空加权回归模型的预测精度,增强时空加权回归模型的可解释性,选择对因变量具有显著影响的重要变量已成为当今统计分析中一个重要研究课题。首先对时空加权回归模型的系数使用样条函数作出逼近,其次在最小二乘的理论基础上,根据SCAD惩罚理论对时空加权回归模型各变量所对应的系数进行处理,并利用BIC准则来选择调谐参数λ,最终通过迭代算法来选择出对时空加权回归模型有用的变量,剔除掉影响模型准确性的变量,达到精简模型、提高预测精度的目的。

In order to improve the prediction accuracy of geographically and temporally weighted regression model and to enhance the interpretation of geographically and temporally weighted regression model,selecting the important variables that has significant influence on the dependent variables has become an important research topic in the statistical analysis.In this paper,firstly the model＇s coefficients are approximated by using the spline function.Secondly,based on the least square theory,the corresponding coefficients of variables are processed by using the SCAD theory.And then the BIC criterion is used to select the tuning parameterλ.Finally,the useful variables for geographically and temporally weighted regression model are selected by the iterative algorithm.Eliminating the variables that affect the model＇s accuracy and achieving the purpose of improving the accuracy of the model.