Moderator and Mediator Variables

Mediator Variables

Graphically, mediation may be represented by the simple model x → m → y. In this model, m mediates the relationship between x and y. As this model illustrates, a mediator variable transmits variance between two other variables. Thus, a mediator serves as an explanatory mechanism in the model. That is, the mediator provides an explanation of how and, to some extent, why two variables are related. For example, consider a model in which a researcher believes that student learning is negatively related to class size (i.e., students in smaller classes learn more than students in larger classes). To explain this effect, the researcher includes a mediator variable (e.g., the amount of student–teacher interaction) in the model. That is, in smaller classes, teachers are expected to spend more time with each student, and that, in turn, is related to student learning. The amount of student–teacher interaction provides a mechanism through which the bivariate relationship between class size and learning can be explained.

The extent to which a variable serves as a mediator can be easily tested using a three-step process of ordinary least squares regression. In the first analysis, y is regressed on x. This step is necessary insofar as there must be a relationship for m to mediate. If x and y are unrelated, m cannot mediate a relationship that does not exist. In a second analysis, m is regressed on x. If x and m are unrelated, m cannot serve as a mediating mechanism. Finally, y is regressed on both x and m together, and the regression coefficient associated with x is compared with the regression weight computed in the first step. The extent to which m mediates the x–y relationship is defined in terms of the difference between these coefficients. If the regression weight associated with x is reduced to zero, m is said to fully mediate the relationship between x and y. In short, the effect of x on y is fully explained when m is included in the model. Evidence for partial mediation is provided to the extent that the regression weight associated with x drops but is not reduced to zero. In this case, m explains some of the variance in the x–y relationship, but there is still a direct effect of x on y. The Sobel test is often used to test for the presence of this indirect (i.e., mediated) effect.

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