Multivariate analysis of covariance with potentially singular covariance matrices and non-normal responses
Multivariate analysis of covariance with potentially singular covariance matrices and non-normal responses
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具有潜在奇异协方差矩阵和非正态响应的协方差多变量分析
DOI：
10.1016/j.jmva.2020.104594
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Bathke
中科院分区：
文献类型：
--
作者：
Zimmermann;Bathke
在应用研究中，在检验几个组的多变量均值之间的差异时，考虑一个或几个协变量通常是明智的。然而，“经典的”参数多变量协方差分析（MANCOVA）检验（例如，Wilks’Lambda）是基于相当严格的假设（误差的均方差和正态性），这可能很难在小样本设置中证明。此外，现有的潜在补救措施（例如，异方差鲁棒性方法）在协方差矩阵为奇异的情况下变得不合适。然而，在生命科学和其他领域经常遇到这种情况，例如，在标准化评估的背景下，对摘要绩效衡量标准及其相应的子量表进行分析。在目前的手稿中，我们考虑一个一般的MANCOVA模型，允许潜在的异方差和甚至奇异协方差矩阵以及非正态误差。我们将异方差一致协方差矩阵估计方法与我们提出的改进的MANCOVA anova型统计（MANCATS）相结合，并应用两种不同的自举方法。我们提供了各自测试过程的渐近有效性的证明以及广泛模拟研究的结果，这些结果表明，特别是参数引导版本的MANCATS在大多数情况下，在I型错误率和功率方面都优于其竞争对手。通过检查标准化成绩测试的实际数据，进一步说明和证实了这些考虑。
In applied research, it is often sensible to account for one or several covariates when testing for differences between multivariate means of several groups. However, the "classical" parametric multivariate analysis of covariance (MANCOVA) tests (e.g., Wilks' Lambda) are based on quite restrictive assumptions (homoscedasticity and normality of the errors), which might be difficult to justify in small sample size settings. Furthermore, existing potential remedies (e.g., heteroskedasticity-robust approaches) become inappropriate in cases where the covariance matrices are singular. Nevertheless, such scenarios are frequently encountered in the life sciences and other fields, when for example, in the context of standardized assessments, a summary performance measure as well as its corresponding subscales are analyzed. In the present manuscript, we consider a general MANCOVA model, allowing for potentially heteroskedastic and even singular covariance matrices as well as non-normal errors. We combine heteroskedasticity-consistent covariance matrix estimation methods with our proposed modified MANCOVA ANOVA-type statistic (MANCATS) and apply two different bootstrap approaches. We provide the proofs of the asymptotic validity of the respective testing procedures as well as the results from an extensive simulation study, which indicate that especially the parametric bootstrap version of the MANCATS outperforms its competitors in most scenarios, both in terms of type I error rates and power. These considerations are further illustrated and substantiated by examining real-life data from standardized achievement tests.
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