An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model
An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model
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DOI：
10.1080/00949659908811936
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发表时间：
1999-01-01
影响因子：
1.2
通讯作者：
Legendre, P
中科院分区：
文献类型：
--
作者：
Anderson, MJ;Legendre, P
本研究比较了经验I型错误和权力的不同排列技术的一个单一的偏回归系数的显着性检验在多元回归模型，使用模拟。比较的方法是原始数据值的排列，两种替代方法，提出了减少模型下的残差排列，和全模型下的残差排列。模拟中还包括正态理论t检验。我们研究了（1）样本量，（2）预测变量之间的共线性程度，（3）协变量参数的大小，（4）增加的随机误差的分布和（5）协变量中存在离群值对这些方法的影响。我们发现，两种方法已被确定为等价的配方下的约化模型的置换实际上是非常不同的。其中一种方法导致了持续膨胀的1型错误。此外，当协变量包含极端离群值时，原始数据的排列导致不稳定（通常是膨胀的）1型错误。三种排列方法（原始数据排列、简化模型排列和全模型排列）的功效无显著差异，但当误差为非正态时，所有方法的功效均大于正态理论t检验。简化模型置换法在偏回归系数的检验中具有最一致和最可靠的结果。然而，需要模拟合理的极端情况，以便将方法与正态理论t检验区分开来。原始数据的置换、简化模型下的置换和完整模型下的置换通常是渐进等效的。
This study compared empirical type I error and power of different permutation techniques for the test of significance of a single partial regression coefficient in a multiple regression model, using simulations. The methods compared were permutation of raw data values, two alternative methods proposed for permutation of residuals under the reduced model, and permutation of residuals under the full model. The normal-theory t-test was also included in simulations. We investigated effects of (1) the sample size, (2) the degree of collinearity between the predictor variables, (3) the size of the covariable's parameter, (4) the distribution of the added random error and (5) the presence of an outlier in the covariable on these methods. We found that two methods that had been identified as equivalent formulations of permutation under the reduced model were actually quite different. One of these methods resulted in consistently inflated type 1 error. In addition, when the covariable contained an extreme outlier, permutation of raw data resulted in unstable (often inflated) type 1 error. There were no significant differences in power among the three permutation methods (raw data permutation, reduced-model permutation and full-model permutation), but all had greater power than the normal-theory t-test when errors were non-normal. The reduced model permutation method had the most consistent and reliable results of the methods investigated here for the test of a partial regression coefficient. However, reasonably extreme situations needed to be simulated in order to distinguish methods from the normal-theory t-test and from one another. Permutation of raw data, permutation under the reduced model, and permutation under the full model are generally asymptotically equivalent.