参数和非参数Bootstrap方法的简单中介效应分析比较

A Comparison of the Analysis of Simple Mediating Effect of the Parametric and Nonparametric Bootstrap Methods

采用数据模拟技术比较了(偏差校正和未校正的)参数和非参数Bootstrap方法在简单中介效应分析中的表现。结果表明,1)偏差校正的Bootstrap方法的总体表现优于未校正的Bootstrap方法,但在某些条件下会高估第Ⅰ类错误率,导致在ab=0时的置信区间偏差较大。2)参数Bootstrap方法优于非参数Bootstrap方法,偏差校正的参数百分位残差Bootstrap法的综合表现最优,且具有适用范围广,对原始样本依赖性小的优点,最具实用性。

It is well known that there are two Bootstrap methods, nonparametric Bootstrap and parametric Bootstrap. The nonparamet- ric Bootstrap method has been widely applied in simple mediation analysis. But the parametric Bootstrap method has not yet been used in simple mediation analysis. In this paper, parametric Bootstrap method was introduced in simple mediation for the first time. After in-troducing each of the Bootstrap methods in detail, the performance of the two Bootstrap methods in simple mediation was compared. A simulation study was conducted for comparison by means of 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 = .39, b = 0, a= 0, b = .59, a = b = . 14, a = b = . 39, a = b = 0. 59）. 30 treatment conditions in total were generated in terms of the above 2-factor simulation design . One thousand replications were run for each condition. For each replication in each condition, four Bootstrap methods （ bias-corrected and un-correeted parametric percentile residual Bootstrap methods, bias-corrected and un-corrected nonparametric percentile Bootstrap methods） 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 terms of （a） type I error, （b） power, （c） the coverage of their confidence intervals, and （d） the confidence interval bias. The simulation study found the following results ： （ 1 ） the behaviors of the bias-corrected Bootstrap method were better than the behaviors of the un-corrected Bootstrap method in type I error, the confidence interval coverage, power and the confidence interval bias under the condition of nonzero mediation. However, the bias-corrected Bootstrap method had slightly inflated confidence interval bias under the condition of zero mediation because this method overestimated type I error in some conditions; （2） compared with the non- parametric Bootstrap method, the performances of the parametric Bootstrap method was preferred ; the bias-corrected parametric percen- tile residual Bootstrap method was superior to the bias-corrected nonparametric percentile Bootstrap method in confidence interval bias and Type I error. There are three reasons why bias-corrected parametric percentile residual Bootstrap is recommended for testing simple mediating effects. First, the simulation results showed that the overall performance of the bias-corrected parametric percentile residual Bootstrap method was best in different Bootstrap methods. Second, the parametric Bootstrap method can be applicable to all types of mediations. It has a wider applicability than the nonparametric percentile Bootstrap method. Third, the parametric Bootstrap method generates new bootstrap samples using the Monte Carlo method ,which further reduces the dependence on the original samples.