Rank-Based Inference for Multivariate Data in Factorial Designs

Bathke, Arne C.; Harrar, Solomon W.

doi:10.1007/978-3-319-39065-9_7

Cited by 10 publications

(2 citation statements)

References 26 publications

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“…Classical MANOVA tests assume that the number of treatments is fixed and observations in different treatment groups are independent. There has been extension of these tests for large number of treatment groups under general conditions in the parametric [16,18,22] and nonparametric [17,19,23] settings. In the univariate case, the usual F statistic for one-way ANOVA coincides with the regression lack-of-fit test when there are multiple replications for each observed value of the predictor variable [9].…”

Section: Omnibus Testsmentioning

confidence: 99%

Nonparametric Tests for Multivariate Association

Harrar

2022

Symmetry

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Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings.

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Section: Omnibus Testsmentioning

confidence: 99%

Nonparametric Tests for Multivariate Association

Harrar

2022

Symmetry

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“…Among these are the permutation-based nonparametric combination methods discussed, for example, in Pesarin and Salmaso (2010) or Pesarin and Salmaso (2012) (see also Anderson, 2001), and the fully nonparametric rank-based tests presented in , Bathke, Harrar, and Madden (2008), Harrar and Bathke (2008a, b), and Liu, Bathke, and Harrar (2011), and implemented in the R package npmv (Burchett & Ellis, 2015;Ellis, Burchett, Harrar, & Bathke, 2017). However, these methods are currently limited to the one-way layout, or to some particular factorial design situations (Hahn & Salmaso, 2015, Bathke & Harrar, 2016. Thus, they are not applicable to data from complex factorial designs, such as the AD data described in detail below.…”

Section: Introductionmentioning

confidence: 99%

Testing Mean Differences among Groups: Multivariate and Repeated Measures Analysis with Minimal Assumptions

Bathke

Friedrich

Pauly

et al. 2018

Multivariate Behavioral Research

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To date, there is a lack of satisfactory inferential techniques for the analysis of multivariate data in factorial designs, when only minimal assumptions on the data can be made. Presently available methods are limited to very particular study designs or assume either multivariate normality or equal covariance matrices across groups, or they do not allow for an assessment of the interaction effects across within-subjects and between-subjects variables. We propose and methodologically validate a parametric bootstrap approach that does not suffer from any of the above limitations, and thus provides a rather general and comprehensive methodological route to inference for multivariate and repeated measures data. As an example application, we consider data from two different Alzheimer's disease (AD) examination modalities that may be used for precise and early diagnosis, namely, single-photon emission computed tomography (SPECT) and electroencephalogram (EEG). These data violate the assumptions of classical multivariate methods, and indeed classical methods would not have yielded the same conclusions with regards to some of the factors involved.

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Rank-Based Analysis of Multivariate Data in Factorial Designs and Its Implementation in R

Kiefel

Bathke

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Rank-Based Inference for Multivariate Data in Factorial Designs

Cited by 10 publications

References 26 publications

Nonparametric Tests for Multivariate Association

Nonparametric Tests for Multivariate Association

Testing Mean Differences among Groups: Multivariate and Repeated Measures Analysis with Minimal Assumptions

Rank-Based Analysis of Multivariate Data in Factorial Designs and Its Implementation in R

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