Abstract: Because few sampling distributions of mediating effect are normally distributed, in recent years, some asymmetric interval methods such as parametric residual bootstrap, Monte Carlo methods, and Bayesian methods have been developed and proposed for analyzing multilevel mediation. These approaches do not impose the assumption of normality of the sampling distribution of mediating effects. However, little is known about how these methods perform relative to each other. This study conducts a simulation using R software. This simulation examines several approaches for testing 2-1-1 multilevel mediation with fixed slope. Four factors were considered in the simulation design: (a) sample size of level two ( =10, 20, 30, 50, 100); (b) sample size of level one ( =10, 20); (c) parameter combinations (a=b=0, a=.39 and b=0, a=0 and b=.59, a=b=.14, .39, .59); (d) method for testing multilevel mediation (Monte Carlo method, parametric percentile residual Bootstrap method, bias-corrected parametric percentile residual Bootstrap method, Bayesian method with informative prior and Bayesian method with non-informative prior). A total of 60 treatment conditions were designed in the 4-factor simulation. 500 replications were generated for each treatment condition. For the Bootstrap method, 1,000 bootstrap samples were drawn in each replication. For the Monte Carlo method, 5,000 samples were drawn in each parameter with normal distribution. For the Bayesian methods, 11,000 Gibbs iteration were implemented in each replication, 10,000 posterior samples of the model parameters were recorded after 1,000 burn-in iterations. The methods were compared in terms of (a) Relative mean square error, (b) TypeⅠerror rate, (c) Power, (d) Interval width, (e) Interval imbalance. The simulation study found the following results: 1) the performance of Bayesian method with informative prior were superior to that of the other methods in terms of Relative mean square error. 2) The Power of the Bayesian method with informative prior was the highest among all the methods. However, extra power comes at the cost of underestimation of Type I error. Power of bias-corrected parametric percentile residual Bootstrap method was the second greatest, with elevated Type I error in some conditions. 3) The performance of Monte Carlo method was superior to that of the other methods for Type I error. 4) Interval width of Bayesian method with informative prior is the smallest among different methods. Interval width of Monte Carlo method was the second smallest. 5) Interval imbalance of Bayesian method with informative prior is smallest among different methods. The simulation results indicated that 1) when informative prior was available, Bayesian method was recommended to analyze mediation. 2) If informative prior was not available, Monte Carlo method should be adopted to analyze mediation.

Key words: multilevel mediation, Bayesian method, Monte Carlo method, parametric bootstrap method, prior information

摘要： 比较了贝叶斯法、Monte Carlo法和参数Bootstrap法在2-1-1多层中介分析中的表现。结果发现：1)有先验信息的贝叶斯法的中介效应点估计和区间估计都最准确；2)无先验信息的贝叶斯法、Monte Carlo法、偏差校正和未校正的参数Bootstrap法的中介效应点估计和区间估计表现相当，但Monte Carlo法在第Ⅰ类错误率和区间宽度指标上表现略优于其他三种方法，偏差校正的Bootstrap法在统计检验力上表现略优于其他三种方法，但在第Ⅰ类错误率上表现最差；结果表明，当有先验信息时，推荐使用贝叶斯法；当先验信息不可得时，推荐使用Monte Carlo法。

关键词: 多层中介效应, 贝叶斯法, Monte Carlo法, 参数Bootstrap法, 先验信息