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Direct vs. indirect effects
In the diagram shown above, assuming linear relationships, the indirect effect is the product of paths coefficients A and B. In general, including nonlinear models, the total effect is equal to the difference between the direct effect and the indirect effect of a unit decrease in the independent variable[3]. In contrast, the indirect effect (sometimes referred to as mediated effect) refers to the extent to which the dependent variable changes when the independent variable is held fixed and the mediator variable changes to the level it would have attained had the independent variable increased by one unit[3].
Complete vs. partial mediation
When the direct effect between the independent variable and the dependent variable (path C in the diagram above) is no longer statistically different from zero fixing the mediator variable, the mediation effect is said to be complete.
If, however, the absolute size of the direct effect between the independent variable and the dependent variable is reduced after controlling for the mediator variable, but the direct effect is still significantly different from zero, the mediation effect is said to be partial. In all cases, the operation of "fixing a variable" must be distinguished from that of "controlling for a variable", which has been inappropriately used in the literature [1][2][4].
Suppression
Suppression is defined as "a variable which increases the predictive validity of another variable (or set of variables) by its inclusion in a regression equation.[5] Basically this means that instead of the drop that you would see from the direct effect of the treatment on the outcome when the mediator is introduced, the opposite happens. The inclusion of the mediating variable into the equation increases the relation between the treatment and outcome rather accounts for (decreases in terms of the size of the statistical relation).
Suppression is a contentious issue and continues to be debated in the literature. However recent discussions have suggested that suppression rather than been seen as a confound or problem, as adding something interesting to the results. It has been also suggested though that testing for suppression should be based on a priori assumptions about the theoretical relation between the variables and the role of the mediating variable as a suppressor[5][6].
Pearl (2000, page 139)[4] has argued that "suppression" is an illusionary effect emanating from confusing causal and associational relationships, as in Simpson's Paradox.
Significance of mediation
Bootstrapping [1] [2] is becoming the most popular method of testing mediation because it does not require the normality assumption to be met, and because it can be effectively utilized with smaller sample sizes (N<25). However, mediation continues to be (perhaps inappropriately) most frequently determined using the (1) the logic of Baron and Kenny [3] or (2) the Sobel test.
Moderated Mediation
Moderated mediation is when the effect of the treatment effect "A" on the mediator "B", and/or when the partial effect of "B" on "C", depends on levels of another variable (D). This has been outlined recently by Muller, Judd, and Yzerbyt (2005) and Preacher, Rucker, and Hayes (2006)[7][8]
Mediated Moderation
Mediated moderation is a variant of both moderation and mediation. This is where there is initially overall moderation and the direct effect of the moderator variable on the outcome, is mediated either at the A -> B path or at the B ->C. The main difference between mediated moderation and moderated mediation is that for the former there is initial moderation and this effect is mediated and for the later there is no moderation but the effect of either the treatment (A) on the mediator (B) is moderated or the effect of the mediator (B) on the outcome (C) is moderated.[7]
External links
- Free Sobel test calculator for the significance of mediation
- Free indirect effect calculator for mediation models
- Free interactive statistics tests for mediation and interactions
- summary of mediation methods at PsychWiki
- SPSS and SAS macros for bootstrapping indirect effects
References
Preacher, Kristopher J. & Hayes, Andrew F. (2004), "SPSS and SAS procedures for estimating indirect effects in simple mediation models.", Behavior Research Methods, Instruments, and Computers 36: 717--731, <http://www.comm.ohio-state.edu/ahayes/sobel.htm>
Preacher, Kristopher J. & Hayes, Andrew F. (in press), "Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models", Behavior Research Methods, <http://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm>
- ^ a b Kaufman, J. S., MacLehose R. F., Kaufman S (2004). A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation. Epidemiology Innovations and Perspectives, 1:4.
- ^ a b Robins, J. M., Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3(2):143-55.
- ^ a b c Pearl, J. (2001) Direct and indirect effects. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, 411-420.
- ^ a b Pearl, J. (2000) Causality: Models, Reasoning and Inference, Cambridge University Press.
- ^ a b MacKinnon, D. P., Krull, J. L., Lockwood, C. M. (2000). Equivalence of the Mediation, Confounding and Suppression Effect. Prevention Science, 1(4), 173-181.
- ^ Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: new procedures and recommendations. Psychological Methods, 7(4), 422-445.
- ^ a b Muller, D., Judd, C. M., Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. Journal of Personality and Social Psychology, 89(6), 852-863.
- ^ Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2006). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227.
