典型相关分析的置换推断
Permutation Inference for Canonical Correlation Analysis
AI总结：
针对典型相关分析（CCA）中直接对残差进行置换检验导致错误率膨胀的问题，本文提出基于低维基底的残差转换与逐步估计方差去除两种解决方案，并提供了完整的CCA置换推断算法及不保守的多重检验方法。
摘要：
典型相关分析（CCA）已成为群体神经影像学的重要工具，可用于研究多种影像与非影像测量之间的关联。由于其他变量通常是不直接感兴趣的变异来源，先前的研究在去除了这些效应的模型残差上使用 CCA，然后直接进行置换推断。我们证明，这种简单的置换检验会导致错误率膨胀。原因在于残差化在观测值之间引入了依赖性，从而违反了可交换性假设。然而，即使不存在干扰变量，针对 CCA 的简单置换检验也会导致除第一个之外的所有典型相关出现错误率过高的情况。原因在于简单的置换方案并未忽略先前典型变量已经解释的变异性。在此，我们针对这两个问题提出了解决方案：对于干扰变量的情况，我们证明将残差转换到满足可交换性的低维基底上，可以得到有效的置换检验；对于更一般的情况（无论有无干扰变量），我们提出以逐步方式估计典型相关，在每次迭代中去除已解释的方差，同时处理两侧不同数量的变量。我们还讨论了如何解决检验的多重性问题，提出了一种不保守的容许检验，并为 CCA 的置换推断提供了完整的算法。
英文摘要：
Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.
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