Comparison and robustness of the REML, ML, MIVQUE estimators for multi-level random mediation model

This article concentrates on the multi-level random mediation effects model (1-1-1) and reviews the maximum likelihood (ML), restricted maximum likelihood (REML), and minimum variance quadratic unbiased estimation (MIVQUE) estimation methods provided by the SAS MIXED process. This paper uses Monte Carlo simulation to make a comparison of the performance of these estimators under a wide variety of different conditions. First, REML and ML produced equivalent results and both of them outperformed MIVQUE, no matter whether the normality assumption was satisfied. Second, the results indicated that the distribution of the $ {\boldsymbol{e}_{\boldsymbol{Yij}}} $ eYij does not influence the mediation effect. The deviation of the normal distribution of $ {\boldsymbol{b}_{\boldsymbol{j}}} $ bj or ‘ $ {\boldsymbol{a}_{\boldsymbol{j}}} $ aj and $ \boldsymbol{b}_{\boldsymbol{j}} $ bj’ affected the mediation effect, particularly in condition that not only the magnitude of the deviation but also the covariance between these two effects were large. This thesis ends with the implications, suggestions and recommendations for the application.