Correcting the Bias Correction for the Bootstrap Confidence Interval in Mediation Analysis

The bias-corrected bootstrap confidence interval (BCBCI) was once the method of choice for conducting inference on the indirect effect in mediation analysis due to its high power in small samples, but now it is criticized by methodologists for its inflated type I error rates. In its place, the percentile bootstrap confidence interval (PBCI), which does not adjust for bias, is currently the recommended inferential method for indirect effects. This study proposes two alternative bias-corrected bootstrap methods for creating confidence intervals around the indirect effect: one originally used by Stine (1989) with the correlation coefficient, and a novel method that implements a reduced version of the BCBCI's bias correction. Using a Monte Carlo simulation, these methods were compared to the BCBCI, PBCI, and Chen and Fritz (2021)'s 30% Winsorized BCBCI. The results showed that the methods perform on a continuum, where the BCBCI has the best balance (i.e., having closest to an equal proportion of CIs falling above and below the true effect), highest power, and highest type I error rate; the PBCI has the worst balance, lowest power, and lowest type I error rate; and the alternative bias-corrected methods fall between these two methods on all three performance criteria. An extension of the original simulation that compared the bias-corrected methods to the PBCI after controlling for type I error rate inflation suggests that the increased power of these methods might only be due to their higher type I error rates. Thus, if control over the type I error rate is desired, the PBCI is still the recommended method for use with the indirect effect. Future research should examine the performance of these methods in the presence of missing data, confounding variables, and other real-world complications to enhance the generalizability of these results.

Automated summary

This study proposes two alternative bias-correction methods for creating confidence intervals around the indirect effect. Comparisons with other methods using a Monte Carlo simulation show that these methods fall between the BCBCI and PBCI in terms of balance, power, and type I error rate. An extension of the simulation suggests that the increased power of these alternative methods might be due to their higher type I error rates. Therefore, the PBCI is still recommended if control over the type I error rate is desired for inference on the indirect effect.