The Analysis of Repeated Measurements with Mixed-Model Adjusted F Tests

Abstract

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of their data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach, available through SAS PROC MIXED, was compared to a Welch-James type statistic. The Welch-James approach is known to provide generally robust tests of treatment effects in a repeated measures between-by within-subjects design under assumption violations given certain sample size requirements. The mixed-model F tests were based on Kenward-Roger’s adjusted degrees of freedom solution, an approach specifically proposed for small sample settings. The authors investigated Type I error control for repeated measures main and interaction effects in unbalanced designs when normality and covariance homogeneity assumptions did not hold. The mixed-model Kenward-Roger’s adjusted F tests showed superior Type I error control in small sample size conditions in which the Welch-James type statistic was nonrobust; power rates, however, did not favor one approach over the other.