Mediation FAQ:

Q.  What articles would you suggest for someone just learning about mediation?

A.  Some good background references include:

Baron, R.M. & Kenny, D.A. (1986). The moderator-mediator distinction in social psychological research: Conceptual, Strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.

Judd, C. M., & Kenny, D. A. (1981a). Estimating the effects of social interventions. New York: Cambridge University Press.

Judd, C.M. & Kenny, D.A. (1981b). Process Analysis: Estimating mediation in treatment evaluations. Evaluation Review, 5, 602-619.

MacKinnon, D.P. (1994). Analysis of mediating variables in prevention and intervention research. In A. Cazares and L. A. Beatty, Scientific methods in prevention research. NIDA Research Monograph 139. DHHS Pub. No. 94-3631. Washington, DC: U.S. Govt. Print. Office, pp. 127-153.

MacKinnon, D.P. & Dwyer, J.H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158.

Q.  How do I conduct a mediation analysis?

A.  Mediation analysis uses the estimates and standard errors from the following regression equations (MacKinnon, 1994):

 Y = c X + e1  M = a X + e2  Y = c' X + bM + e3 The independent variable (X) causes the outcome variable (Y) The independent variable (X) causes the mediator variable (M) The mediator (M) causes the outcome variable (Y) when controlling for the independent variable (X). This must be true.

If the effect of X on Y is zero when the mediator is included (c' = 0), there is evidence for mediation (Judd & Kenny, 1981a, 1981b). This would be full mediation.

If the effect of X on Y is reduced when the mediator is included (c' < c), then the direct effect is said to be partially mediated.

Q.  How do you test for the significance of mediated effects?

A.  To calculate the significance of the mediated effect, divide the mediated effect by its' standard error (MacKinnon & Dwyer, 1993). The regression coefficients (a, b, c, and c' from above) and the standard errors for each of those regression coefficients (sec, sea, seb, and sec' ) come from the output from running the regressions above

Divide the mediated effect (a*b) by its' standard error. The result is a z-score. The formula for this standard error (seab) of the mediated effect (a*b) is below (Sobel 1982, 1986).
seab = Details may be found in:

Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.), Sociological Methodology 1982 (pp. 290-312). Washington, DC: American Sociological Association.

Sobel, M. E. (1986). Some new results on indirect effects and their standard errors in covariance structure models. In N. Tuma (Ed.), Sociological Methodology 1986 (pp. 159-186). Washington, DC: American Sociological Association.

Note that there is evidence that zab  is not normally distributed. There are also alternative methods to test the significane of the mediated effect.

Q. What are the different components of mediation models? I've heard mediated effect, direct effect, etc.

A. Using the regression coefficients from the models above, the components of a mediation model are

Total effect = a*b + c'     The total effect is the sum of direct and indirect effects of the X on the outcome (Y).

Direct effect = c'   The direct effect of X on Y when taking the mediator into account.

Mediated effect = a*b   The mediated effect is also called the indirect effect. This is because it is the part of the model that indirectly affects the outcome through the mediator.

Q.  What is the difference between an interaction effect and a mediation effect?

A.  Mediation implies a causal sequence among three variables X to M to Y (independent variable causes the mediator and the mediator causes the dependent variable).  For example, an intervention may change social norms and this change in social norms prevented smoking. An interaction means that the effect of X on Y depends on the level of a third variable. No causal sequence is implied by interaction.  For example, an intervention may be successful for males but not for females--an interaction effect.

Q.  What is the difference between a moderator effect and a mediation effect?

A.  A moderator effect is another term for an interaction effect. See above for the distinction between interaction effects and mediation effects.

Q.  Can you test for mediation in latent variable models?

A.  To test mediation in latent variable models, follow the same steps described above, substituting structural coefficients for regression coefficients.

Q.  What are good references for causal interpretation in mediation analysis?

A.  Some good references for issues of causality and mediation are:

Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models. Sociological Methodology, 18, 449-493.

Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945-970.

MacCallum, R. (1986). Specification searchers in covariance structure modeling. Psychological Bulletin, 100, 107-120.

MacKinnon, D. P. (2002). Mediating variable. In N. J. Smelser & P. B. Baltes (Eds.), International encyclopedia of the social and behavioral sciences (pp. 9503-9507). New York: Elsevier.

Robins, J. M., & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143-155.

Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688-701.

Spirtes, P., Glymour, P., & Scheines, R. (1993). Causation, prediction, and search. New York: Springer-Verlag.

Q.  Why doesn't c-c' equal a*b?

A.  See correspondence with Julie Maloy.

Q.  How do I calculate proportion in a multiple mediator model?

A.  See correspondence with Julie Maloy.

Q.  The regression coefficients of my direct and indirect effect are of opposite sign. What does that mean?

A.  See correspondence with Julie Maloy.