Local Influence and Robust Procedures for Mediation Analysis

Abstract

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis can be misleading. In this article, we propose 2 approaches to alleviate these problems. One is to identify cases that strongly affect testing of mediation using local influence methods or robust methods. The other is to use robust methods for parameter estimation and subsequently test the mediated effect based on the robust estimates. The application of these 2 approaches is illustrated using 1 simulated and 2 real data examples. The interest in 1 real data set is the relationship among marital conflict, children's emotional insecurity, and children's internalizing problems. The other example is concerned with whether ethnic identity mediates the effect of family cohesion on Korean language fluency. Results show that local influence and robust methods rank the influence of cases similarly, but robust methods are more objective. Moreover, when the normality assumption is violated, robust methods give estimates with smaller standard errors and more reliable tests of the mediated effect compared with normal-theory ML. An R program that implements the local influence and robust procedures for mediation analysis is also provided.

Notes

¹The robust SE estimator is just the sandwich-type SE estimator that will be introduced in the next section. It is different from the robust estimator that we propose to use. Robust estimators are for model estimator, whereas sandwich-type SEs are for the variability of model parameter estimates.

*Significant at level .05.

^a Δ of the lower and upper limits of confidence intervals divide the _BS using ML under D ₀.

*Significant at level .05.

^a Δ of the lower and upper limits of confidence intervals divide the _BS using ML under D ₀ ⁽⁰⁾.

*Significant at level .05.

^a Δ of the lower and upper limits of confidence intervals divide the _BS using ML under data set ALL.

*Significant at level .05.

^a Δ of the lower and upper limits of confidence intervals divide the _BS using ML under data set ALL.