Resampling and Distribution of the Product Methods for Testing Indirect Effects in Complex Models

Abstract

Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional z test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a simulation was conducted to evaluate these alternative methods in a more complex path model with multiple mediators and indirect paths with 2 and 3 paths. Methods for testing contrasts of 2 effects were evaluated also. The simulation included 1 exogenous independent variable, 3 mediators and 2 outcomes and varied sample size, number of paths in the mediated effects, test used to evaluate effects, effect sizes for each path, and the value of the contrast. Confidence intervals were used to evaluate the power and Type I error rate of each method, and were examined for coverage and bias. The bias-corrected bootstrap had the least biased confidence intervals, greatest power to detect nonzero effects and contrasts, and the most accurate overall Type I error. All tests had less power to detect 3-path effects and more inaccurate Type I error compared to 2-path effects. Confidence intervals were biased for mediated effects, as found in previous studies. Results for contrasts did not vary greatly by test, although resampling approaches had somewhat greater power and might be preferable because of ease of use and flexibility.

ACKNOWLEDGMENTS

This research was supported by National Institute on Drug Abust grant R01DA09757 (David P. MacKinnon, Principal Investigator) and the Health, Social and Economics Research Unit, RTI International (Al Miedema, Vice President). We gratefully acknowledge the contributions of Sanford Braver, Siek-Toon Khoo, Alex Zautra, and Roger Millsap to this work, which was based on the first author's doctoral dissertation.

Notes

^aProportion outside Bradley (1978) robustness interval.

^aValue outside Bradley (1978) robustness interval.