Power of Product Tests of Mediation as a Function of Mediator Collinearity

Abstract

In a mediation model, the a coefficient represents the relationship of the independent variable (X) to the mediator (Z) and the b coefficient represents the partial relationship of the mediator (Z) to the outcome (Y). The amount of mediation can be estimated as the product of the two sample coefficients (ab). Although it would seem that an increase in a would increase statistical power for product tests, it also increases the standard error of the product tests due to the necessary increase in the collinearity between X and Z. Thus, power can actually be decline with increases in a.