When the Three-Path Mediation Model Has More Power Than the Single Mediator Model

Introduction:Mediation models are often used to explain the mechanisms through which effects are achieved. In the context of prevention research, mediation can also be used to assess a program’s efficacy and to determine which components of an intervention program are successful. Recently it has been discussed that including a mediator in a model (when there is theoretical support for inclusion) can also increase power to detect effects (MacKinnon et al., 2002; O’Rourke & MacKinnon, 2013). This study calculates and compares analytical power of a single and a sequential two mediator model in order to determine whether the multiple mediator model results in a gain in power over and above the single mediator model.

 Methods:A SAS program was written to calculate analytical power for a sequential (three path) two mediator model using the joint significance test of mediation (Taylor, MacKinnon, & Tein, 2008). Path coefficients corresponding to small, medium, and large effect sizes were used (.14, .29, and .59, respectively), and sample sizes of 50, 100, 200, 500, and 1000 were used to reflect sample sizes commonly used in studies in the social sciences. Analytical power of the sequential two mediator model was then compared power to both a bivariate significance test and a single mediator model significance test.

 Results: The test of the total effect had more power than the test of the three-path mediated effect only at N = 50 when two of the three coefficients were small, at N = 100 when all three of the coefficients were small, and at N =5000 when all three of the coefficients were large (in this case, power for both tests was equal to one). For all other combinations of parameters and sample sizes, the test of the three-path mediated effect had more power than the test of the total effect. Comparing across the three models showed that the test of the total effect has the least power of the three models and the test of the sequential two mediator model has the most power of the three models for all conditions. The single mediator model had power values that fall between the test of the total effect and the test of the sequential two mediator model.

 Conclusion: These results indicate that not only does the test of the single mediator model have more power to detect effects than the test of the total effect, the test of the sequential two mediator model has more power to detect effects than either the test of the single mediator model or the test of the total effect. The finding that the sequential two mediator model has power over and above the single mediator and bivariate models supports the literature for making theories more complex. Fit with earlier literature and future directions in this line of research are then discussed.