Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics
Robust nonparametric tests of general linear model coefficients: A comparison of permutation methods and test statistics
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DOI：
10.1016/j.neuroimage.2019.116030
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发表时间：
2019-11-01
期刊：
影响因子：
5.7
通讯作者：
Helwig, Nathaniel E.
中科院分区：
文献类型：
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作者：
Helwig, Nathaniel E.
神经影像学研究中的统计推断通常涉及检验一般线性模型中回归系数的显著性。在许多应用中，研究人员假设一个形式为Y = alpha + X beta + Z gamma + Z的模型，其中Y是观察到的大脑信号，X和Z包含被认为与大脑信号相关的解释变量。目标是测试零假设H-0：beta = 0，其中滋扰参数gamma包括在模型中。针对这个问题，已经提出了几种非参数（置换）方法，每种方法都使用F比的某种变体作为检验统计量。然而，最近的研究表明，当e项是异方差的（即，具有非恒定方差），这可能由于各种原因而发生。本研究比较了经典的F检验统计量的鲁棒W（Wald）检验统计量使用八种不同的排列方法。结果表明，当误差为同方差时，使用F比的排列检验可以得到准确的结果，但当误差为异方差时，假阳性率较高。相反，使用W检验统计量的排列检验在误差为同方差时产生有效结果，在误差为异方差时产生渐近有效结果。在具有同方差误差的情况下，与F统计量相比，使用W统计量的排列检验的功效略有降低，但随着样本量n的增加，差异消失。因此，建议在神经影像学研究中对回归系数进行稳健的非参数假设检验。
Statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model. In many applications, the researcher assumes a model of the form Y = alpha + X beta + Z gamma + epsilon, where Y is the observed brain signal, and X and Z contain explanatory variables that are thought to be related to the brain signal. The goal is to test the null hypothesis H-0 : beta = 0 with the nuisance parameters gamma included in the model. Several nonparametric (permutation) methods have been proposed for this problem, and each method uses some variant of the F ratio as the test statistic. However, recent research suggests that the F ratio can produce invalid permutation tests of H-0 : beta = 0 when the e terms are heteroscedastic (i.e., have non-constant variance), which can occur for a variety of reasons. This study compares the classic F test statistic to the robust W (Wald) test statistic using eight different permutation methods. The results reveal that permutation tests using the F ratio can produce accurate results when the errors are homoscedastic, but high false positive rates when the errors are heteroscedastic. In contrast, permutation tests using the W test statistic produced valid results when the errors were homoscedastic, and asymptotically valid results when the errors were heteroscedastic. In the situation with homoscedastic errors, permutation tests using the W statistic showed slightly reduced power compared to the F statistic, but the difference disappeared as the sample size n increased. Consequently, the W test statistic is recommended for robust nonparametric hypothesis tests of regression coefficients in neuroimaging research.