Comparison of Approaches to Constructing Confidence Intervals for Mediating Effects Using Structural Equation Models

Abstract

Mediators are variables that explain the association between an independent variable and a dependent variable. Structural equation modeling (SEM) is widely used to test models with mediating effects. This article illustrates how to construct confidence intervals (CIs) of the mediating effects for a variety of models in SEM. Specifically, mediating models with 1 mediator, 2 intermediate mediators, 2 specific mediators, and 1 mediator in 2 independent groups are illustrated. By using phantom variables (Rindskopf, 1984), a Wald CI, percentile bootstrap CI, bias-corrected bootstrap CI, and a likelihood-based CI on the mediating effect are easily constructed with some existing SEM packages, such as LISREL, M plus, and Mx. Monte Carlo simulation studies are used to compare the coverage probabilities of these CIs. The results show that the coverage probabilities of these CIs are comparable when the mediating effect is large or when the sample size is large. However, when the mediating effect and the sample size are both small, the bootstrap CI and likelihood-based CI are preferred over the Wald CI. Extensions of this SEM approach for future research are discussed.

ACKNOWLEDGMENT

Preparation of this work was supported by an Academic Research Fund from the National University of Singapore.

Notes

¹The generic terms mediating effect and indirect effect are used interchangeably here.

²It is frequently suggested that CIs are better alternatives than null hypothesis significance testing (American Psychological Association, 2001; Wilkinson & Task Force on Statistical Inference, 1999). This article focuses onmethods of constructing CIs rather than on testing the significance of the mediating effect (e.g., MacKinnon et al., 2004). Although this article uses CIs, the results can be easily applied to null hypothesis significance testing.

³Likelihood-based CI does not assume that the parameters are normally distributed. However, it does assume that the data are multivariate normally distributed.

⁴Mplus (Muthén & Muthén, 2006) provides a MODEL INDIRECT command to calculate the total and specific indirect effects. However, the use of phantom variables is more general because it enables the testing of nearly any model involving mediators. Mx provides functions to create new matrices to simplify the model specification involving phantom variables. Users can create a new matrix that contains the mediating effect and request the CI on that matrix directly. LISREL also provides a function to create additional parameters (AP; Jöreskog & Sörbom, 1996). This may simplify the model specification. The LISREL, Mplus, and Mx codes to fit the mediating models discussed in this article are available at http://courses.nus.edu.sg/course/psycwlm/internet/ or they can be obtained from the author.