When multiple hypothesis tests are conducted, the familywise Type I error probability correspondingly increases. Various multiple test procedures (MTPs) have been developed, which generally aim to control the familywise Type I error rate at the desired level. However, although multiplicity is frequently discussed in the ANOVA literature and MTPs are correspondingly employed, the issue has received considerably little attention in the regression literature and it is rare to see MTPs employed empirically. The present aims are three-fold. First, within the eclectic uses of multiple regression, specific situations are delineated wherein adjusting for multiplicity may be most relevant. Second, the performance of ten MTPs amenable to regression is investigated via familywise Type I error control, statistical power, and, where appropriate, false discovery rate, simultaneous confidence interval coverage and width. Although methodologists may anticipate general patterns, the focus is on the magnitude of error inflation and the size of the differences among methods under plausible scenarios. Third, perspectives from across the scientific literature are discussed, which shed light on contextual factors to consider when evaluating whether multiplicity adjustment is advantageous. Results indicated that multiple testing can be problematic, even in nonextreme situations where multiplicity consequences may not be immediately expected. Results pointed toward several effective, balanced, MTPs, particularly those that accommodate correlated parameters. Importantly, the goal is not to universally recommend MTPs for all regression models, but. rather to identify a set of circumstances wherein multiplicity is most relevant, evaluate MTPs, and integrate diverse perspectives that suggest multiplicity adjustment or alternate solutions.

中文翻译：

---

多元回归中的多重性：定义问题、评估解决方案和整合观点。


当进行多个假设检验时，族I型错误概率相应增加。人们已经开发了各种多重测试程序（MTP），其通常旨在将系列 I 类错误率控制在所需水平。然而，尽管方差分析文献中经常讨论多重性，并且相应地采用了 MTP，但这个问题在回归文献中很少受到关注，而且很少看到 MTP 在经验上得到应用。目前的目标有三个。首先，在多元回归的折衷使用中，描述了特定情况，其中对多重性的调整可能是最相关的。其次，通过家庭类型 I 误差控制、统计功效以及适当的错误发现率、同时置信区间覆盖范围和宽度，研究了 10 个适合回归的 MTP 的性能。尽管方法学家可能会预测一般模式，但重点是错误膨胀的程度以及在合理情况下方法之间差异的大小。第三，讨论了整个科学文献的观点，这些观点揭示了在评估多重性调整是否有利时要考虑的背景因素。结果表明，即使在无法立即预期多重后果的非极端情况下，多次测试也可能会出现问题。结果指出了几个有效、平衡的 MTP，特别是那些容纳相关参数的 MTP。重要的是，我们的目标不是普遍推荐所有回归模型的 MTP，但是。 而是确定一组与多重性最相关的情况，评估中期计划，并整合建议多重性调整或替代解决方案的不同观点。