Repeated measures multiple comparison procedures with a mixed model analysis
Kowalchuk, Rhonda K. D.
One approach to the analysis of repeated measures designs allows researchers to model the variance-covariance structure of their data rather than presume a certain structure as is the case with conventional univariate and multivariate test statistics (Littell, Milliken, Stroup, & Wolfinger, 1996). This mixed-model approach was evaluated for testing all possible pairwise differences among repeated measures marginal means in a between- by within-subjects design. Specifically, Type I error control and power were examined for simultaneous and stepwise multiple comparison procedures using SAS' (1996) PROC MIXED in an unbalanced repeated measures design when normality and variance covariance homogeneity assumptions did not hold. The potential advantage of the MIXED procedure with its ability to specify various variance-covariance structures was compared to known robust multiple comparison procedures based on a between-subjects heterogeneous unstructured form of the variance-covariance matrix with Satterthwaite (1941, 1946) degrees of freedom (Keselman, 1994; Keselman, Keselman, & Shaffer, 1991; Keselman & Lix, 1995). Specifically, the testing strategies of always fitting an unstructured variance-covariance matrix, fitting the true population structure, or allowing two model selection criteria available through PROC MIXED to select the best structure were investigated. Rates of Type I error control were similar across the testing strategies for each of the multiple comparison procedures. The recommendation of always fitting an unstructured variance-covariance matrix to the data was based on the fact that a researcher does not need prior knowledge about the true population structure and does not need to rely on a model selection criterion to provide good Type I error control. Furthermore, results showed two stepwise multiple comparison procedures as particularly notable. Shaffer's (1986) sequentially rejective Bonferroni and Hochberg's (1988) sequentially acceptive Bonferroni procedures had superior performance with regards to Type I error control and power to detect true pairwise differences across the investigated conditions.