Abstract: We presented two causal models that include either a mediated moderator or a moderated mediator. The “mediated moderator” model focuses on the moderating effect and the “moderated mediator” model focuses on the mediating effect. Both models can be analyzed using procedures similar to those for testing mediating effects. Each procedure, however, also consists of an extra step to test moderating effects. These procedures are summarized below:
The moderating effect of U on the relation between Y and X is mediated by W:
(1) Regress Y on , and . A significant coefficient associated with UX implies that U is the moderator of the relation between Y and X.
(2) Regress W on , and UX and look for a significant coefficient associated with UX.
(3) Regress on , , and W. A significant coefficient associated with W suggests the mediating effect of W on the moderated (by U) relation between X and Y. Moreover, the moderated effect of U on the relation between Y and X is completely mediated by W if the coefficient associated with is not significant.
The mediating effect of W on the relation between Y and X is moderated by U:
(1) Regress Y on , and look for a significant coefficient associated with X;
(2) Regress W on , and look for a significant coefficient associated with X;
(3) Regress on , and W, and look for a significant coefficient associated with W;
Steps 1-3 are used to test the mediating effect of W on the relation between Y and X .
(4) Regress on , , W and UW. A significant coefficients associated with UW suggests that the mediating effect of W on the relation between X and Y is moderated by U.
In addition to these two models, we also presented a mixed model including both a mediated moderator and a moderated mediator. Using an example to illustrate the mixed model, we showed that Teacher Liking as a mediator on the relation between students’ Antisocial Behavior and Peer Acceptance was moderated by Perceived Authoritative Teachering, and that Perceived Authoritative Teachering as a moderator on the relation between Antisocial Behavior and Peer Acceptance was mediated by Teacher Liking. The relative size of the mediating effect in the mixed model was also computed. It was further demonstrated that the moderator of the mediated relation represented a quadratic effect, whereas other relations examined in the mixed model were linear effects

Key words: moderating effect, mediating effect, mediated moderator, moderated mediator mixed model