中介效应的点估计和区间估计:乘积分布法、非参数Bootstrap和MCMC法

Assessing Point and Interval Estimation for the Mediating Effect:Distribution of the Product,Nonparametric Bootstrap and Markov Chain Monte Carlo Methods

针对中介效应ab的抽样分布往往不是正态分布的问题,学者近年提出了三类无需对ab的抽样分布进行任何限制且适用于中、小样本的方法,包括乘积分布法、非参数Bootstrap和马尔科夫链蒙特卡罗(MCMC)方法。采用模拟技术比较了三类方法在中介效应分析中的表现。结果发现:1)有先验信息的MCMC方法的ab点估计最准确;2)有先验信息的MCMC方法的统计功效最高,但付出了低估第Ⅰ类错误率的代价,偏差校正的非参数百分位Bootstrap方法的统计功效其次,但付出了高估第Ⅰ类错误率的代价;3)有先验信息的MCMC方法的中介效应区间估计最准确。结果表明,当有先验信息时,推荐使用有先验信息的MCMC方法;当先验信息不可得时,推荐使用偏差校正的非参数百分位Bootstrap方法。

Because few sampling distributions of mediating effect are normally distributed, in recent years, Classic approaches to assessing mediation （Baron ＆ Kenny, 1986; Sobel, 1982） have been supplemented by computationally intensive methods such as nonparametric bootstrap, the distribution of the product methods, and Markov chain Monte Carlo （MCMC） methods. These approaches are suitable for medium or small sample size and 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 extends Mackinnon and colleagues＇ （Mackinnon, Lockwood ＆ Williams, 2004; Yuan ＆ Mackinnon, 2009） works by conducting a simulation using R software. This simulation examines several approaches for assessing mediation. Three factors were considered in the simulation design： （a） sample size （N=25, 50, 100, 200, 1000）; （b） parameter combinations （a=b=0, a=0.39 b=0, a=0 b=0.59, a=b=0.14, a=b=0.39, a=b=0.59）; （c） method for assessing mediation （distribute of the product method, nonparametric percentile Bootstrap method, bias-corrected nonparametric percentile Bootstrap method, MCMC method with informative prior and MCMC method with non-informative prior）. A total of 30 treatment conditions were designed in the 3-factor simulation. 1,000 replications were run for each treatment condition. For the Bootstrap method, 1,000 bootstrap samples were drawn in each replication. For the MCMC methods, 11,000 Gibbs iterate 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） Bias （absolute of bias）, （b） Relative mean square error, （c） Type I error, （d） Power, （e） Interval width. The simulation study found the following results： 1） the performance of MCMC method with informative prior were superior to that of the other methods for Relative mean square error and Bias. 2） The Power of the MCMC method with informative prior was greatest among all the methods. However, extra power comes at the cost of underestimation of Type I error. Power of bias-corrected nonparametric percentile Bootstrap method was the second greatest, with elevated Type I error in some conditions. 3） Interval width of MCMC method with informative prior is smallest among different methods. The simulation results indicated that 1） when informative prior was available, MCMC method with informative prior was recommended to analyze mediation. 2） If informative prior was not available, bias-corrected nonparametric percentile Bootstrap method should be adopted to analyze mediation. We also provide Mplus6 syntax to facilitate the implementation of the recommended bootstrapping and MCMC methods.