Adjusting for a Mediator in Models With Two Crossed Treatment Variables

In a simple mediation model, the effect of a manipulated variable X on a dependent variable Y over and above the effect of the mediator Me can be estimated by regressing Y on X and Me. The impact of X on Y in such a model is adjusted for the relationship both between X and Me and between Me and Y . The authors examine the adjustment function in the context of a 2× 2 design with two manipulated variables. In such a situation, the mediator could be affected by either one of the main effects and/or the interaction between two manipulated variables. To adjust for the impact of the mediator, a standard procedure has been to rely on an ANCOVA that includes only the mediator. The authors show, both analytically and with simulations, that this leads to improper control of the mediator and to biased estimates of the model parameters.