Abstract
ABSTRACTTo 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.
Highlights
Almost all interesting data sets are multivariate, that is, they involve more than one variable
Wald-type test statistic (WTS) is the Wald-type statistic approximated by a χ2-distribution, PBS denotes the asymptotic model-based “parametric” bootstrap
We examine whether mean differences in EEG- or single-photon emission computed tomography (SPECT)-features between significant deficits (SCC), mild cognitive impairment (MCI), and Alzheimer’s disease (AD) patients can be discovered using the new inferential method, when the features are considered as multivariate responses
Summary
Almost all interesting data sets are multivariate, that is, they involve more than one variable. Upon reviewing the literature on inference methods for multivariate data, there are very few approaches which do not assume at least one of either multivariate normality or covariance matrix equality across groups (or even both) Among these are the permutation-based nonparametric combination methods discussed, for example, in Pesarin and Salmaso (2010) or Pesarin and Salmaso (2012) (see Anderson, 2001), and the fully nonparametric rank-based tests presented in Bathke and Harrar (2008), 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).
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