Abstract

This paper introduces a new test of harmful multicollinearity based on the ratio of the levels of significance of ordinary least squares and generalized ridge regression estimates of the coefficients. Harmful multicollinearity is the degree of multicollinearity that leads to an incorrect statistical inference. The proposed test is based on a rule that an insignificant regressor will not change to a significant regressor by adding ridge factors to the design matrix; however, insignificant coefficients that have become insignificant because of multicollinearity will change to significant coefficients by using ridge estimation. The simulation results show that the power of the proposed test is high—even for small sample sizes—and converges to one as the sample size increases. In addition, the empirical size of the test is less than the nominal value in most cases, with a tendency to zero in larger samples. Therefore, the proposed test is consistent. The comparison of the proposed test with the main diagnostic measures confirms the success of the test because the diagnostic measures have the wrong nominal sizes in all cases. The application of the test to real-world data shows that it can be helpful for detecting harmful multicollinearity.

摘要

本文介绍了一种基于普通最小二乘显着性水平比和系数的广义岭回归估计的有害多重共线性的新检验。有害多重共线性是导致错误统计推断的多重共线性程度。提议的测试基于这样一个规则，即通过在设计矩阵中添加岭因子，一个不显着的回归变量不会变为显着的回归变量；但是，由于多重共线性而变得不重要的不重要系数将通过使用岭估计变为重要系数。模拟结果表明，即使对于小样本量，所提出的测试的功效也很高，并且随着样本量的增加会收敛到一个。此外，在大多数情况下，检验的经验值小于标称值，在较大样本中趋于为零。因此，建议的测试是一致的。建议的测试与主要诊断措施的比较证实了测试的成功，因为诊断措施在所有情况下都具有错误的标称尺寸。将该检验应用于实际数据表明，它有助于检测有害的多重共线性。