Resampling-Based Analysis of Multivariate Data and Repeated Measures Designs with the R Package MANOVA.RM

“Focusing on metric data and mean-based procedures, MANOVA and RM models are typically inferred by means of “classical” procedures such as Wilks’ Lambda, Lawley-Hotelling, Roy’s largest root (Davis, 2002; Johnson and Wichern, 2007; Anderson, 2001) or (generalized) linear mixed models with generalized estimating equatio…”

“…rank-based methods for null hypotheses formulated in distribution functions are implemented within the packages npmv for oneand two-way MANOVA (Burchett et al., 2017) and nparLD for several repeated measures designs The R Journal Vol. XX/YY, AAAA 20ZZ ISSN 2073-4859 (Noguchi et al., 2012).”

“…the The R Journal Vol. XX/YY, AAAA 20ZZ ISSN 2073-4859 well-established ANOVA-type statistic (ATS) QN = NX ′ •TX• (3) by Brunner (2001) is implemented together with the enhanced F-approximation of the statistic proposed in Brunner et al. (1997, 2002) and implemented in the SAS PROC Mixed procedure.”

“…the The R Journal Vol. XX/YY, AAAA 20ZZ ISSN 2073-4859 well-established ANOVA-type statistic (ATS) QN = NX ′ •TX• (3) by Brunner (2001) is implemented together with the enhanced F-approximation of the statistic proposed in Brunner et al. (1997, 2002) and implemented in the SAS PROC Mixed procedure.”

“, 2018) and ffmanova (Øyvind Langsrud and Mevik, 2019) contain interesting permutation and rotation tests, which, however, require certain invariances resulting in model restrictions (see, e.g., the discussion in Huang et al., 2006; Chung and Romano, 2013) .”

“, 2006; Chung and Romano, 2013) . Most of these procedures, however, rely on specific distributional assumptions (such as multivariate normality) and/or specific covariance or correlation structures (e.g., homogeneity between groups or, for RM, compound symmetry; possibly implying equal correlation between measurement…”

“In case of a = 2 this includes the famous multivariate Behrens-Fisher problem as, e.g., analyzed in Yao (1965); Nel and Van der Merwe (1986); Christensen and Rencher (1997); Krishnamoorthy and Yu (2004) or Yanagihara and Yuan (2005).”

“The validity of this procedure (also named parametric bootstrap WTS) is proven in Konietschke et al. (2015).”

“In case of a = 2 this includes the famous multivariate Behrens-Fisher problem as, e.g., analyzed in Yao (1965); Nel and Van der Merwe (1986); Christensen and Rencher (1997); Krishnamoorthy and Yu (2004) or Yanagihara and Yuan (2005).”

“…the packages flip (Finos et al., 2018) and ffmanova (Øyvind Langsrud and Mevik, 2019) contain interesting permutation and rotation tests, which, however, require certain invariances resulting in model restrictions (see, e.g., the discussion in Huang et al., 2006; Chung and Romano, 2013) .”

“This test statistic tends to rather conservative decisions in case of small sample sizes and is even asymptotically only an approximation, thus not providing an asymptotic level α test, see Brunner (2001); Friedrich et al. (2017a).”

“…Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et al. (2016); Friedrich et al. (2017a); Livacic-Rojas et al. (2017); Friedrich and Pauly (2018) and the references cited therein.”

“…Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et al. (2016); Friedrich et al. (2017a); Livacic-Rojas et al. (2017); Friedrich and Pauly (2018) and the references cited therein.”

“…Department of Neurology, University Clinic of Salzburg, 160 patients were diagnosed with either Alzheimer’s Disease (AD), mild cognitive impairment (MCI), or subjective cognitive complaints without clinically significant deficits (SCC), based on neuropsychological diagnostics (Bathke et al., 2018).”

“This test statistic tends to rather conservative decisions in case of small sample sizes and is even asymptotically only an approximation, thus not providing an asymptotic level α test, see Brunner (2001); Friedrich et al. (2017a).”

“, analyzed in Yao (1965); Nel and Van der Merwe (1986); Christensen and Rencher (1997); Krishnamoorthy and Yu (2004) or Yanagihara and Yuan (2005). • Crossed Two-Way (A× B): Splitting the index into two and writing μij = ν + αi + βj + γij we obtain the model X ijk = ν + αi + βj + γij + eijk, 1 ≤ i ≤ a, 1 ≤ j ≤ b, 1 ≤…”

“ive procedures have been developed that tackle the above problems and have been compared in extensive simulation studies, see amongst others Brunner (2001); Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2016); McFarqu…”

“ustifiable in real data. In particular, with decreasing sample sizes and increasing dimensions, such presumptions are almost impossible to verify in practice and may lead to inflated type-I-errors, cf. Vallejo et al. (2001); Lix and Keselman (2004); Vallejo Seco et al. (2007); LivacicRojas et al. (2010). To this end, se…”

“…and have been compared in extensive simulation studies, see amongst others Brunner (2001); Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et al. (2016); Friedrich et al. (2017a);…”

“In particular, with decreasing sample sizes and increasing dimensions, such presumptions are almost impossible to verify in practice and may lead to inflated type-I-errors, cf. Vallejo et al. (2001); Lix and Keselman (2004); Vallejo Seco et al. (2007); Livacic-Rojas et al. (2010).”

“In particular, with decreasing sample sizes and increasing dimensions, such presumptions are almost impossible to verify in practice and may lead to inflated type-I-errors, cf. Vallejo et al. (2001); Lix and Keselman (2004); Vallejo Seco et al. (2007); Livacic-Rojas et al. (2010).”

“…that tackle the above problems and have been compared in extensive simulation studies, see amongst others Brunner (2001); Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et…”

“…Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et al. (2016); Friedrich et al. (2017a); Livacic-Rojas et al. (2017); Friedrich and Pauly (2018) and the references cited therein.”

“t al. (2010). To this end, several alternative procedures have been developed that tackle the above problems and have been compared in extensive simulation studies, see amongst others Brunner (2001); Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and…”

“…see amongst others Brunner (2001); Lix and Lloyd (2007); Gupta et al. (2008); Zhang (2011); Harrar and Bathke (2012); Konietschke et al. (2015); Xiao and Zhang (2016); Bathke et al. (2018); McFarquhar et al. (2016); Friedrich et al. (2017a); Livacic-Rojas et al. (2017); Friedrich and Pauly…”

“Since in most cases at least one assumption for parametrical testing was violated, we decided to compute more conservative semiparametrical analyses with the MANOVA.RM package (Friedrich et al., 2019).”