关键词: 简单中介效应, Bootstrap方法, 置信区间, Monte Carlo模拟

Abstract: It is well known that there are two Bootstrap methods called Nonparametric Bootstrap and parametric Bootstrap. Nonparametric Bootstrap method has been widely applied in simple mediation analysis, but parametric Bootstrap method has not yet used in simple mediation analysis. In this paper, parametric Bootstrap method was introduced in simple mediation firstly, after introduced each of Bootstrap methods in detail, the performances of two Bootstrap methods in simple mediation was compared. A simulation study was conducted to the comparison by R software. Two 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); Totally, 30 treatment conditions were generated in terms of the above 2-factor simulation design (i.e., ). One thousand replications were run for each condition. For each replication in each condition, four Bootstrap methods (bias-corrected and un-corrected parametric percentile residual Bootstrap method, bias-corrected and un-corrected nonparametric percentile Bootstrap method) were used to test for simple mediation. For the Bootstrap methods, 1,000 bootstrap samples were drawn in each replication. Those methods were compared in term of (a) TypeⅠerror, (b) Power, (c) the coverage of their confidence interval, (d) confidence interval bias. The simulation study found the following results: 1) the behaviors of the bias-corrected Bootstrap method was better than un-corrected Bootstrap method in TypeⅠerror, Power and confidence interval bias under the condition of nonzero mediation. However, the bias-corrected Bootstrap method have slightly inflated confidence interval bias under the condition of zero mediation because this method overestimate TypeⅠerror in some conditions. 2) Compared with the nonparametric Bootstrap method, the performances of parametric Bootstrap method was preferred, in particular, bias-corrected parametric percentile residual Bootstrap method was superior to bias-corrected nonparametric percentile Bootstrap method in confidence interval bias and TypeⅠerror. There are three reasons why bias-corrected parametric percentile residual Bootstrap is recommended for testing simple mediating effect. Firstly, the simulation result shows that the overall performance of bias-corrected parametric percentile residual Bootstrap method was best in the different Bootstrap methods. Secondly, parametric Bootstrap method can apply in all types of mediations, parametric Bootstrap method has a wider applicability than nonparametric percentile Bootstrap method. Thirdly, parametric Bootstrap method generate new bootstrap sample using Monte Carlo method, which further reduce the dependence on the original samples.

Key words: simple mediation, Bootstrap method, confidence interval, Monte Carlo simulation