Inference for low- and high-dimensional multigroup repeated measures designs with unequal covariance matrices

Martin Happ, Solomon W. Harrar, Arne C. Bathke

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We propose tests for main and simple treatment effects, time effects, as well as treatment by time interactions in possibly high-dimensional multigroup repeated measures designs. The proposed inference procedures extend the work by Brunner et al. (2012) from two to several treatment groups and remain valid for unbalanced data and under unequal covariance matrices. In addition to showing consistency when sample size and dimension tend to infinity at the same rate, we provide finite sample approximations and evaluate their performance in a simulation study, demonstrating better maintenance of the nominal α-level than the popular Box-Greenhouse–Geisser and Huynh–Feldt methods, and a gain in power for informatively increasing dimension. Application is illustrated using electroencephalography (EEG) data from a neurological study involving patients with Alzheimer's disease and other cognitive impairments.

Original languageEnglish
Pages (from-to)810-830
Number of pages21
JournalBiometrical Journal
Issue number4
StatePublished - Jul 1 2016

Bibliographical note

Funding Information:
We would like to thank Wolfgang Staffen and Yvonne H?ller (Department of Neurology, Christian Doppler Klinik, Paracelsus Medical University, Salzburg, Austria) for providing the EEG data example. Thanks also go to Edgar Brunner (Department of Medical Statistics, University of G?ttingen, Germany) and the anonymous reviewers who have made very helpful suggestions. The theoretical part of the manuscript was mostly developed during a visit of Solomon W. Harrar at Salzburg University, and the host institution, as well as his home institution, University of Kentucky, generously helped in facilitating this visit. This publication was also made possible by a grant from the National Institute of General Medical Sciences (5 U54 GM104944) from the National Institutes of Health.

Publisher Copyright:
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


  • Box epsilon
  • Large dimension
  • Longitudinal data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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