A Simulation Study on the Correlated Mediators in Multiple Mediation Models

Introduction: Intervention researchers often test multiple mediation models with more than one mediator; that is, models in which independent variables affect dependent variables indirectly through those mediator variables (Williams & MacKinnon, 2008). In such models, the mediator variables are very likely to be correlated due to being affected by the common independent variables. As such correlation, called multicollinearity, likely affects the estimation and significance tests in multiple regression models, it needs to be considered when testing multiple mediation models (Iacobucci, 2008). Under such circumstance, the effects of the mediators on dependent variables are often attenuated to the degree to which the mediators are correlated, that is, the multicollinearity can compromise the significance of particular specific indirect effect (Preacher & Hayes, 2008). This study investigates that how these correlations influence the bias, standard error, and coverage of the confidence interval for indirect effects.

 Methods: Williams and MacKinnon (2008) conducted extensive simulations to evaluate resampling methods in complex mediation models. However, in this simulation study, a relatively simpler model with two mediators is considered at the different levels of correlations between two mediators (high and low) in order to focus on the possible impacts of highly correlated mediators. Two popular estimation methods for assessing indirect effects of the mediation models, Standard Z (Sobel, 1982) and Nonparametric Bootstrap Resampling (NBR) methods (Efron & Tibshirani, 1993), are used and compared in their performance. Three analytic criteria such as bias, standard error, and coverage of the confidence interval are investigated for estimating and testing the indirect effects (both individual and total indirect effects).

 Results: The biases from both methods are pretty minimal and very comparable. In terms of standard errors, Sobel’s Standard Z Test (SSZT) provides smaller standard errors than NBR method. However, NBR method has better precision to include the true value of the parameter via its confidence interval than SSZT has. Also, the simulation results show that the mediation models with higher correlations between two mediators (i.e., possible multicollinearity problems) have lower probabilities for its confidence interval to include the true value of the parameter.

Conclusions: This study indicates that extra attention is needed for the researchers to estimate and test the indirect effects of the mediation models with more than one mediator.