Mediation (statistics)

In statistics, a mediation model is one that seeks to identify and explicate the mechanism that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third explanatory variable, known as a mediator variable. Rather than hypothesizing a direct causal relationship between the independent variable and the dependent variable, a mediational model hypothesizes that the independent variable causes the mediator variable, which in turn causes the dependent variable. The mediator variable, then, serves to clarify the nature of the relationship between the independent and dependent variables.

Direct vs. indirect effects
In the diagram shown above, path C depicts the direct effect of the independent variable on the dependent variable. The direct effect measures the relationship between the independent variable and the dependent variable in the absence of any mediation effects. Whether or not a mediation effect has occurred is determined by the extent to which the direct effect changes when the mediator variable is added to the model.

In contrast, the indirect effect (sometimes referred to as the mediated effect) refers to the extent to which the mediator variable intervenes in the relationship between the independent variable and the dependent variable. In the diagram shown above, the indirect effect is the product of paths A and B.

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 after controlling for 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.

Suppression
Suppression is defined as "a variable which increases the the predictive validity of another variable (or set of variables) by its inclusion in a regression equation . Basically this means that instead of the drop that you would see from the direct effect of the treatment 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 supressor

Significance of mediation
Bootstrapping  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 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)

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.