Mediational Models

(Updated November 19, 2018)

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 nearly 80,000 times (as of November 2018)! 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)

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.

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.

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.