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Likelihood Ratio Type Statistics for Repeated Measures Designs with Heterogeneous Covariance Matrices

Because of their simplicity, Wald statistics are typically used in complex experimental designs. Likelihood ratio statistics in factorial designs are more flexible than Wald statistics in the sense of adapting to non-saturated designs by fitting only as many parameters as the model calls for. This leads to a significant gain in power. Here we propose likelihood ratio type statistics for testing hypotheses in repeated measures designs with heterogeneous covariance matrices, and derive their asymptotic distribution in one general theorem that does not require normality or even continuity of the responses. Simulation studies demonstrate their advantages over the Wald statistics.