ISSN 0439-755X
CN 11-1911/B

Acta Psychologica Sinica ›› 2012, Vol. 44 ›› Issue (10): 1408-1420.doi: 10.3724/SP.J.1041.2012.01408

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

FANG Jie;ZHANG Min-Qiang   

  1. (1 College of Humanities and Communication, Guangdong University of Business Studies, Guangzhou 510320, China) (2 Research Center of Psychological Application, South China Normal University, Guangzhou 510631, China)
  • Received:2011-05-11 Published:2012-10-25 Online:2012-10-23
  • Contact: ZHANG Min-Qiang2 (1 College of Humanities and Communication, Guangdong University of Busin

Abstract: 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) TypeⅠerror, (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.

Key words: mediation, Distribute of the product method, Nonparametric Bootstrap method, Markov chain Monte Carlo (MCMC) methods, prior information