Nonparametric MANOVA in meaningful effects
Nonparametric MANOVA in meaningful effects
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DOI：
10.1007/s10463-019-00717-3
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发表时间：
2020-08-01
影响因子：
1
通讯作者：
Pauly, Markus
中科院分区：
文献类型：
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作者：
Dobler, Dennis;Friedrich, Sarah;Pauly, Markus
多变量方差分析（MANOVA）是一种功能强大的和通用的方法来推断和量化度量多变量多因素数据中的主效应和交互效应。然而，它对单位的变化既不稳健，对有序数据也没有意义。因此，我们提出了一种新的非参数MANOVA。与现有的基于秩的程序相反，我们推断出的假设，制定有意义的曼-惠特尼型的影响，而不是分布函数。检验是基于多元秩效应估计的二次型，临界值由自举技术获得。新开发的程序提供了渐近准确和一致的推断一般模型，如非参数的Beynolds-Fisher问题和多变量的一，二，和更高的方式交叉布局。在小样本的计算机模拟证实了有序和度量数据协方差异质性的可靠性的方法。最后，通过对一个真实的数据实例的分析，说明了结果的适用性和正确解释。
Multivariate analysis of variance (MANOVA) is a powerful and versatile method to infer and quantify main and interaction effects in metric multivariate multi-factor data. It is, however, neither robust against change in units nor meaningful for ordinal data. Thus, we propose a novel nonparametric MANOVA. Contrary to existing rank-based procedures, we infer hypotheses formulated in terms of meaningful Mann-Whitney-type effects in lieu of distribution functions. The tests are based on a quadratic form in multivariate rank effect estimators, and critical values are obtained by bootstrap techniques. The newly developed procedures provide asymptotically exact and consistent inference for general models such as the nonparametric Behrens-Fisher problem and multivariate one-, two-, and higher-way crossed layouts. Computer simulations in small samples confirm the reliability of the developed method for ordinal and metric data with covariance heterogeneity. Finally, an analysis of a real data example illustrates the applicability and correct interpretation of the results.