Abstract: The analysis of mediation effects is important in education, psychology, and other social sciences research. The approaches used in regression and path analysis for investigating such effects are widely known. These methods, however, are inappropriate if the data are clustered in nature, due to the violation of the assumption of independence of observations and biased standard errors. Therefore, a method for analyzing the mediation effects within multilevel models has been developed and proposed. Several procedures have been recommended and implemented in existing commercial software for testing of mediation effects in multilevel models. But most of these methods assumed that the effects are fixed, even for random indirect model. As a result, it is highly needed to examine the indirect effects under different conditions. There are few studies on this topic in Mainland till now.
Following Bauer, Preacher, and Gil’s (2006) study, the purpose of the present article focused on the multilevel random mediation effect model (1-1-1) and examined various analytical procedures for random multilevel meditation analysis. The performances of these procedures under different conditions were compared using Monte Carlo simulations method. First, in order to address why multilevel random mediation model is necessary, the improvement in using the random multilevel mediation model compared to two compact models, the multilevel fixed mediation model and the single-level traditional mediation model is examined. Second, three different estimation methods, restricted maximum likelihood estimate (REML), maximum likelihood estimate (MLE), and minimum variance quadratic unbiased estimate (MIVQUE) are compared in different conditions. The results indicate that we can obtain unbiased estimation of the mediation effect, correct standard error, and proper result of hypothesis test through using the multilevel random mediation model, comparing with using the other two compact models. Moreover, the differences of multilevel fixed mediation model and single-level traditional mediation model are trivial. For the estimation random mediation effects in multilevel random mediation model, it is better to use restricted maximum likelihood estimate (REML) and maximum likelihood estimate (MLE), comparing with minimum variance quadratic unbiased estimate (MIVQUE). Only when the model has problem on converging, can one use MIVQUE instead, but researches should pay attention to the reliability of MIVQUE under different conditions.
This paper consider the use of multilevel modeling to estimate mediation models in which there is lower level mediation, and all terms are random. It could be concluded that tests of random multilevel mediation can be problematic when more fixed effects models are used. For testing random indirect effects, different estimation methods might reach similar results. The REML method of SAS MIXED procedure is better than that of the MIVQUE method in the studied conditions. Recommendations are provided for testing multilevel mediation.

Key words: mediation model, multilevel, random effect, simulation of Monte Carlo