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首页> 外文期刊>International Journal of Statistics and Applications >Regularized Multiple Regression Methods to Deal with Severe Multicollinearity
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Regularized Multiple Regression Methods to Deal with Severe Multicollinearity

机译：正则化多元回归方法处理严重的多重共线性

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摘要

This study aims to compare the performance of Ordinary Least Square (OLS), Least Absolute Shrinkage and Selection Operator (LASSO), Ridge Regression (RR) and Principal Component Regression (PCR) methods in handling severe multicollinearity among explanatory variables in multiple regression analysis using data simulation. In order to select the best method, a Monte Carlo experiment was carried out, it was set that the simulated data contain severe multicollinearity among all explanatory variables (ρ = 0.99) with different sample sizes (n = 25, 50, 75, 100, 200) and different levels of explanatory variables (p = 4, 6, 8, 10, 20). The performances of the four methods are compared using Average Mean Square Errors (AMSE) and Akaike Information Criterion (AIC). The result shows that PCR has the lowest AMSE among other methods. It indicates that PCR is the most accurate regression coefficients estimator in each sample size and various levels of explanatory variables studied. PCR also performs as the best estimation model since it gives the lowest AIC values compare to OLS, RR, and LASSO.
机译：这项研究旨在比较使用多元回归分析中的解释变量之间的普通最小二乘（OLS），最小绝对收缩和选择算子（LASSO），岭回归（RR）和主成分回归（PCR）方法处理严重多重共线性的性能数据模拟。为了选择最佳方法，我们进行了一次蒙特卡洛实验，设置为在不同样本量（n = 25、50、75、100， 200）和不同级别的解释变量（p = 4、6、8、10、20）。使用平均均方误差（AMSE）和Akaike信息准则（AIC）比较了这四种方法的性能。结果表明，PCR在其他方法中具有最低的AMSE。它表明，PCR是在每个样本量和研究的各种解释变量水平中最准确的回归系数估计量。由于PCR与OLS，RR和LASSO相比具有最低的AIC值，因此它也是最佳的估计模型。

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