LASSO及其拓展方法在回归分析变量筛选中的应用

Application of LASSO and its extended method in variable selection of regression analysis

多重共线性是影响回归分析结果的一个重要问题,近年来发展的LASSO方法对于筛选解释性较高的变量、处理高维数据和解决多重共线性问题具有强大的优势。该方法是在模型估计中增加了惩罚项,能将一些不必要变量的回归系数压缩为零进而从模型中剔除,达到变量筛选的目的。本文将重点介绍LASSO这一方法,并与最优子集、岭回归、自适应LASSO与弹性网络的结果进行比较,结果显示LASSO与自适应LASSO在解决自变量多重共线性问题以及增强模型解释性、预测精度方面均有较好的表现。

Multicollinearity is an important issue affecting the results of regression analysis.LASSO developed in recent years has great advantages in selecting explanatory variables,processing high-dimensional data,and solving multicollinearity problems.This method adds a penalty term to the model estimation,which can compress the regression coefficients of some unnecessary variables to zero and then remove them from the model to achieve the purpose of variable screening.This paper focuses on the LASSO method and compares it with optimal subsets,ridge regression,adaptive LASSO,and elastic net results.It is found that both LASSO and adaptive LASSO have good performance in solving independent variable multicollinearity problems and enhancing model interpretation and prediction accuracy.