Department of Psychology, University of Oviedo, Oviedo, Spain.
School of Psychology, University of Minho, Braga, Portugal.
Behav Res Methods. 2021 Apr;53(2):669-685. doi: 10.3758/s13428-020-01429-w.
Classical MANOVA tests do not pose any difficulty when the assumptions on which they are based are satisfied, while the modified Brown-Forsythe (MBF) procedure has low sensitivity to the lack of multivariate normality and homogeneity of covariance matrices. Both methods assume complete data for all subjects. In this paper, we present combination rules for the MANOVA and MBF procedures with multiply imputed datasets. These rules are illustrated by pooling the results obtained with a two-factor multivariate design after applying the two approaches to each of the imputed datasets when the covariance matrices were equal (MI-MANOVA) and when the covariance matrices were unequal (MI-MBF). A Monte-Carlo study was carried out to compare the proposed solution, in terms of type I error rates and statistical power, with the MANOVA and MBF approaches without missing data, and with listwise deletion of missing data followed by the MANOVA approach (LD-MANOVA) and listwise deletion followed by the MBF procedure (LD-MBF). Simulations showed that the type I error rates in all analyses on datasets with missing values (with or without imputation) were well controlled. We also found that the MI-MANOVA approach was substantially more powerful than LD-MANOVA. Moreover, the power of the MI-MANOVA was generally comparable to that of its complete data counterpart. Similar results were obtained for the MI-MBF procedure when covariance matrices were unequal. We conclude, based on the current evidence, that the solution presented performs well and could be of practical use. We illustrate the application of combination rules using a real dataset.
当基于经典多元方差分析（MANOVA）的假设得到满足时，其检验并不困难，而修正的 Brown-Forsythe（MBF）程序对多元正态性和协方差矩阵同质性的缺乏具有较低的敏感性。这两种方法都假定所有受试者的数据都是完整的。本文提出了用于 MANOVA 和 MBF 程序的组合规则，这些规则适用于在协方差矩阵相等（MI-MANOVA）和不相等（MI-MBF）的情况下，对每个插补数据集应用两种方法后，对具有两因素多变量设计的结果进行汇总。通过对具有缺失数据的 MANOVA 和 MBF 方法、缺失数据的列表删除 followed by MANOVA 方法（LD-MANOVA）和缺失数据的列表删除 followed by MBF 程序（LD-MBF）进行比较，来评估所提出的解决方案在第一类错误率和统计功效方面的表现。模拟结果表明，所有缺失值数据集（有或无插补）分析的第一类错误率都得到了很好的控制。我们还发现，MI-MANOVA 方法的功效大大高于 LD-MANOVA。此外，MI-MANOVA 的功效通常与完整数据的对应方法相当。当协方差矩阵不相等时，MI-MBF 程序也得到了类似的结果。基于目前的证据，我们得出结论，所提出的解决方案表现良好，可能具有实际用途。我们使用真实数据集说明了组合规则的应用。
