Many SEM-based studies examine mediation between variables. To mediate is to go in the middle, like a negotiation mediator comes between the labor union and management.
In statistical analysis, we often start out with a relationship between two variables. Using an example from one of my grad-school mentors, Patricia Gurin, cigarette smoking and lung cancer are positively associated.
Cigarette Smoking ==> Lung Cancer
Why does this relationship exist? A more fine-grained understanding would be that smoking leads to lung tissue damage, and tissue damage leads to cancer. Tissue damage would thus be considered the mediator or mechanism.
Cigarette Smoking ==> Tissue Damage ==> Lung Cancer
Reuben Baron and David Kenny published an article in 1986 on mediation that has been cited over 126,000 times (as of April 2024)! Kenny summarizes the process in a nutshell here. In the following figure, I apply Baron and Kenny's "old school" method to Gurin's example. Note that one would run the model twice.
(Illustration of Baron and Kenny's [1986] logic. Example from Patricia Gurin, University of Michigan, circa 2002-2003, link)
This worksheet from Jason Newsom contains a nice four-step chart for implementing Baron and Kenny's framework for mediation.
The above diagram presents the scenario of full mediation (i.e., the initially significant direct path from antecedent to outcome becomes nonsignificant). One can then say that the mediator accounts fully for the antecedent-outcome relationship. If the initial direct path from antecedent to outcome remains significant after addition of the two mediational paths, but the initial direct path is reduced in magnitude, one can claim partial mediation (see Huselid and Cooper, 1994, "Gender roles as mediators of sex differences in expressions of pathology").
(As noted above, my perspective is that the antecedent and outcome should first be shown to relate significantly, before one pursues the further steps to test mediation. For an opposing view, that a significant antecedent-outcome path should not be a "gatekeeper" for mediation analyses, see here.)
As Kenny writes on his website, "More contemporary analyses focus on the indirect effect." The leading names associated with contemporary mediational analysis are Andrew Hayes and Kristopher Preacher, who indeed emphasize indirect effects. The indirect effect can be calculated by multiplying the standardized paths from antecedent to mediator, and from mediator to outcome (think back to our unit on path-analysis tracing rules).
The indirect effect is .15 in the above example. If each of the two segments of the indirect effect (A to M, and M to O) is each statisically significant (i.e., different from zero), we would be confident that the indirect effect also is significant. As Hayes (2009, "Beyond Baron and Kenny: Statistical mediation analysis in the new millennium") notes, however, "it is possible for an indirect effect to be detectably different from zero even though one of its constituent paths is not." What is called for is a significance test of the indirect effect of .15 (or whatever value one has).
The problem is that there is no existing theoretical distribution such as the z, t, F, or chi-square distribution to judge the statistical significance of an indirect effect (i.e., whether or not one's obtained indirect effect falls in the upper or lower 2.5% of the distribution for a two-tailed p < .05 significance level). Therefore, researchers use a "synthetic" statistical distribution for testing the significance of indirect effects, known as a "bootstrap" distribution. Kenny discusses this on his website and it is also illustrated in slide 6 of this slideshow. In 2022, my colleague Sylvia Niehuis and I published an encyclopedia entry on bootstrapping, which can be obtained via ResearchGate.
Yzerbyt, V., Muller, D., Batailler, C., & Judd, C. M. (2018). New recommendations for testing indirect effects in mediational models: The need to report and test component paths. Journal of Personality and Social Psychology, 115, 929–943.
The above diagram presents the scenario of full mediation (i.e., the initially significant direct path from antecedent to outcome becomes nonsignificant). One can then say that the mediator accounts fully for the antecedent-outcome relationship. If the initial direct path from antecedent to outcome remains significant after addition of the two mediational paths, but the initial direct path is reduced in magnitude, one can claim partial mediation (see Huselid and Cooper, 1994, "Gender roles as mediators of sex differences in expressions of pathology").
(As noted above, my perspective is that the antecedent and outcome should first be shown to relate significantly, before one pursues the further steps to test mediation. For an opposing view, that a significant antecedent-outcome path should not be a "gatekeeper" for mediation analyses, see here.)
As Kenny writes on his website, "More contemporary analyses focus on the indirect effect." The leading names associated with contemporary mediational analysis are Andrew Hayes and Kristopher Preacher, who indeed emphasize indirect effects. The indirect effect can be calculated by multiplying the standardized paths from antecedent to mediator, and from mediator to outcome (think back to our unit on path-analysis tracing rules).
The indirect effect is .15 in the above example. If each of the two segments of the indirect effect (A to M, and M to O) is each statisically significant (i.e., different from zero), we would be confident that the indirect effect also is significant. As Hayes (2009, "Beyond Baron and Kenny: Statistical mediation analysis in the new millennium") notes, however, "it is possible for an indirect effect to be detectably different from zero even though one of its constituent paths is not." What is called for is a significance test of the indirect effect of .15 (or whatever value one has).
The problem is that there is no existing theoretical distribution such as the z, t, F, or chi-square distribution to judge the statistical significance of an indirect effect (i.e., whether or not one's obtained indirect effect falls in the upper or lower 2.5% of the distribution for a two-tailed p < .05 significance level). Therefore, researchers use a "synthetic" statistical distribution for testing the significance of indirect effects, known as a "bootstrap" distribution. Kenny discusses this on his website and it is also illustrated in slide 6 of this slideshow. In 2022, my colleague Sylvia Niehuis and I published an encyclopedia entry on bootstrapping, which can be obtained via ResearchGate.
So where do things stand in the field regarding the "classic" Baron and Kenny approach (with its emphasis on the significance of different paths) vs. the "modern" Hayes and Preacher approach (with its focus on the significance of the indirect pathway from antecedent to mediator to outcome)? As the above quote from Kenny suggests, the Hayes/Preacher method predominates in the field, with some commentators seemingly thinking the Baron/Kenny framework is as outmoded as viewing movies through VHS tapes or using a rotary phone.
The Hayes/Preacher method is not without its skeptics, however. Vincent Yzerbyt and colleagues point out that, under certain circumstances, the overall indirect effect can be significant even when only one of the components (antecedent-to-mediator or mediator-to-outcome) is large. Further, they recommend that, "Claims of mediation should properly be guided by
the component approach and be based on joint-significance tests [i.e., showing that the antecedent-to-mediator and mediator-to-outcome paths are both significant] to
avoid spurious mediation claims" (p. 941).
For an earlier illustration of how one might draw on both the classic and modern approaches to mediation, please see the following:
Niehuis, S., Reifman, A., Fischer, J. L., & Lee, K.-H. (2016). Do episodic self- and partner-uncertainty mediate the association between attachment orientations and emotional responses to relationship-threatening events in dating couples? Cognition and Emotion, 30, 1232–1245.
One sometimes posits multiple mediators in a model. For an illustration of what are known as parallel mediation (i.e., the mediators have no causal relations amongst themselves) and serial mediation (i.e., one mediator causes another mediator and so on, in a sequence), see:
Guthrie Yarwood, M. F. (2013).The relationship between love styles and digital dating outcomes: A multiple mediation test of the Perceived Importance of Dating Features Scale. Dissertation, Texas Tech University (LINK). See especially pp. 56-62.
An additional source for studying mediation in SEM is:
Li, S. (2011). Testing mediation using multiple regression and structural modeling analyses in secondary data. Evaluation Review, 35, 240-268.
Guthrie Yarwood, M. F. (2013).The relationship between love styles and digital dating outcomes: A multiple mediation test of the Perceived Importance of Dating Features Scale. Dissertation, Texas Tech University (LINK). See especially pp. 56-62.
