Comparison of permutation methods for the partial correlation and partial Mantel tests
Comparison of permutation methods for the partial correlation and partial Mantel tests
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DOI：
10.1080/00949650008812035
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发表时间：
2000-01-01
影响因子：
1.2
通讯作者：
Legendre, P
中科院分区：
文献类型：
--
作者：
Legendre, P
本研究比较了可用于涉及三个数据向量的部分相关分析和部分Mantel测试的不同排列技术的经验I型误差和功率。偏Mantel检验是一种涉及三个距离矩阵的一阶偏相关分析形式，广泛应用于群体遗传学、生态学、人类学、心理计量学和社会学等领域。比较的方法如下：(1)在其中一个向量（或矩阵）中排列对象；(2)对零模型残差进行置换；(3)将残差向量1（或矩阵A）与残差向量2（或矩阵B）关联；置换残馀向量（或矩阵）之一；(4)对全模型残差进行排序。在偏相关研究中，将结果与参数t检验的结果进行比较，为正态性下提供参考。采用正态和非正态数据、无离群值和有离群值进行了模拟，以测量这些排列方法的I型误差和功率。每种情况有10000次模拟（n = 5时为100000次）；每次使用排列的测试产生999个排列。推荐的测试程序如下：(a)在偏相关分析中，大多数方法在大多数情况下都可以使用。参数t检验不应用于高度偏斜的数据。只有当高度偏斜的数据与协变量中的异常值相结合时，才应避免原始数据的排列。当高度偏斜的数据与小样本量相结合时，不应使用含有残差排列的方法，因为已知残差排列仅具有渐近精确的显著性水平。(b)在局部曼特尔试验中，总是可以使用方法2。除非高度偏斜的数据与小样本量相结合。(c)由于样本量小，在进行部分相关分析或部分曼特尔分析之前，应仔细检查数据。对于高度偏斜的数据，在没有异常值的情况下，原始数据的排列具有正确的I型误差。当高度偏斜的数据与协变量向量或矩阵中的离群值相结合时，仍然建议使用原始数据的排列。(d)绝不应使用方法3。
This study compares empirical type I error and power of different permutation techniques that can be used for partial correlation analysis involving three data vectors and for partial Mantel tests. The partial Mantel test is a form of first-order partial correlation analysis involving three distance matrices which is widely used in such fields as population genetics, ecology, anthropology, psychometry and sociology. The methods compared are the following: (1) permute the objects in one of the vectors (or matrices); (2) permute the residuals of a null model; (3) correlate residualized vector 1 (or matrix A) to residualized vector 2 (or matrix B); permute one of the residualized vectors (or matrices); (4) permute the residuals of a full model. In the partial correlation study, the results were compared to those of the parametric t-test which provides a reference under normality. Simulations were carried out to measure the type I error and power of these permutatio methods, using normal and non-normal data, without and with an outlier. There were 10 000 simulations for each situation (100 000 when n = 5); 999 permutations were produced per test where permutations were used. The recommended testing procedures are the following: (a) In partial correlation analysis, most methods can be used most of the time. The parametric t-test should not be used with highly skewed data. Permutation of the raw data should be avoided only when highly skewed data are combined with outliers in the covariable. Methods implying permutation of residuals, which are known to only have asymptotically exact significance levels, should not be used when highly skewed data are combined with small sample size. (b) In partial Mantel tests, method 2 can always be used. except when highly skewed data are combined with small sample size. (c) With small sample sizes, one should carefully examine the data before partial correlation or partial Mantel analysis. For highly skewed data, permutation of the raw data has correct type I error in the absence of outliers. When highly skewed data are combined with outliers in the covariable vector or matrix, it is still recommended to use the permutation of raw data. (d) Method 3 should never be used.