A Generalized Likelihood Ratio Approach to Mixed Repeated Measures: Robustness, Power and an Application to Educational Data

Abstract

Disadvantages of the usual repeated measures analyses, repeated measures ANOVA and MANOVA, are the assumptions of sphericity and homogeneity of covariance matrices, respectively. In this study a Generalized Likelihood Ratio (GLR) approach to repeated measures is proposed and investigated; a method that is not based on these assumptions. A simulation study was performed to compare the robustness and power of the GLR approach, the repeated measures ANOVA, and MANOVA under various violations of aforementioned assumptions and for different sample sizes. In addition, we applied the GLR to an existing educational dataset on teacher-student relationships. The GLR was robust with equal or higher power in all investigated scenarios with sample sizes larger than 50, where the ANOVA and MANOVA were not robust under violation of homogeneity. Therefore, we recommend the use of the GLR with sample sizes larger than 50 and with any sample size when assumptions are violated.