Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

Abstract

One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.

Keywords:

• confidence interval
• mediation analysis
• Monte Carlo

Notes

¹ Monte Carlo is also referred to as parametric resampling (Efron & Tibshirani, 1993).

² In general, g(b) should be a “well-behaved’’ (smooth) function of indirect and direct effects in the model.

³ The simulation study was conducted on high-performance computing (HPC) clusters.

Additional information

Funding

This research was supported in part by National Institute on Drug Abuse DA09757.