Comparative Robustness of Recent Methods for Analyzing Multivariate Repeated Measures Designs

Abstract

This study evaluated the robustness of two recent methods for analyzing multivariate repeated measures when the assumptions of covariance homogeneity and multivariate normality are violated. Specifically, the authors' work compares the performance of the modified Brown-Forsythe (MBF) procedure and the mixed-model procedure adjusted by the Kenward-Roger solution available in SAS PROC MIXED. The authors found that, overall, the MBF procedure appeared to be the least sensitive to the factors examined in the present study; however, this is not necessarily the case for all data sets. As the results show, for tests of the between-subjects main effect, the MBF approach outperformed the mixed-model method when fitting either a patterned or nonpatterned covariance structure. But for tests of within-subjects effects, its Type I error control advantages decrease.

Robust tests for multivariate factorial designs under heteroscedasticity

“…In the specific context of univariate factorial designs, previous studies had revealed that the two procedures were generally robust to violations of underlying assumptions (Keselman, Carriere, & Lix, 1995;Vallejo et al, 2010a, b). On the other hand, MBF and MLM have also been proven to be robust when they have been used to analyze longitudinal data with unequal dispersion matrices (Vallejo & Ato, 2006;Vallejo et al, 2007). Our results are consistent with those obtained in the aforementioned studies; furthermore, they provide new findings that help researchers in the selection of feasible alternatives for testing main and interaction effects.…”

“…Although a number of estimation strategies are available, the present article uses REML estimation as implemented through the SAS Institute's (2008) PROC MIXED program. Following Vallejo et al (2007), the multivariate linear model (hereafter referred to as MLM) described in Eq. 1 can be fitted using PROC MIXED by stacking the p nvectors y i into a single np × 1 vector e y; the p q-vectors β i into a pq × 1 vector e β; and the p n-vectors e i into a np × 1 vector e e: The resultant vector form can be written as…”

“…Among them, Johansen (1980) generalized Welch's univariate approximate df solution to analyze multivariate data collected in one-way and multiway layouts. Coombs and Algina (1996) extended the univariate Brown-Forsythe (BF) approach to analyze multivariate data collected in a one-way layout, and Vallejo and Ato (2006) and Vallejo, Arnau, and Ato (2007) extended the approximate df BF procedure to the univariate and multivariate repeated measures context. Algina (1994) had previously presented its applications in the context of a split-plot design.…”

Sphericity estimation bias for repeated measures designs in simulation studies

“…Data were generated using SAS/IML (version 9.4), since this software is one of the most suitable for simulating data (Kashyap, Butt, & Bhattacharjee, 2009) and is also one of the most popular for implementing the Vale and Maurelli method (Keselman & Lix, 1997;Lix et al, 2003;Vallejo, Arnau, & Ato, 2007;Vallejo & Livacic-Rojas, 2005).…”

“…In several simulation studies of repeated measures designs, the distributions were classified as either normal or slightly, moderately, or strongly biased distributions (Berkovits, Hancock, & Nevitt, 2000;Vallejo et al, 2007). Among the strongly biased distributions, a number of simulation studies have analyzed the log-normal distribution Keselman, Kowalchuk, & Boik, 2000;and Kowalchuk et al, 2004, among others).…”