摘要
检测和解决多元回归分析中的多重共线性问题具有重要意义.本文采用岭回归(RR)和核主成分回归(KCPR)对同一数据进行回归分析,使用方差膨胀因子(VIF)和条件指数(CI)作为共线性诊断的量度,并对回归模型结果进行比较.经过实证分析,发现这两种回归方法都能很好地消除多重共线性,总的来说核主成分回归的对内拟合效果要优于岭回归.但是这两种方法的参数选择的不同对回归模型的好坏都有巨大影响,需要进一步分析判断.
It is of important significance to detect and solve the problem of multiple collinearity in multivariate regression analysis.In this paper we use the Ridge Regression and Kernel Principal Component Regression to analyze the same data,employ the differential expansion factor and conditional index as the measure of collinearity diagnosis,and then compare the results of the regression models.With the empirical analysis it is found that boh the two regression methods can eliminate multiple collinearity well.In general the internal fitting effect of kernel principal component regression is better than that of the ridge regression.However,the choice of parameters of the two methods has a great impact on the quality of the regression model,which needs further analysis and judgment.
作者
姚睿
刘金容
刘培江
王浩华
Yao Rui;Jinrong Liu;Liu Peijiang;Wang Haohua(School of Science,Hainan University,Haikou 570228,China;School of Statistics and Mathematics,Guangdong University of Finance&Economics,Guangzhou 510320,China)
出处
《数学理论与应用》
2019年第1期111-119,共9页
Mathematical Theory and Applications
基金
国家自然科学基金(11901114)
广州市科技创新一般项目(201904010010)
广东省教育厅青年创新人才类项目(182050205909109)
国家自然科学基金资助项目(11761025,11775314,31460420)
海南省自然科学基金资助项目(117011)
海南省教育厅高校科研资助项目(Hnky2017-12)
海南大学青年基金(hdkyxj201719)
海南大学科研启动基金项目(KYQD(ZR)1735).
关键词
多重共线性
岭回归
核主成分回归
实证比较
Multiple collinearity
Ridge regression
Kernel principal component regression
Empirical comparison
