MMP.19:5.4 - State which mediated contrast is being calculated

Take the supplied mechanisms M=A+U and Y=3A+2M+AM, with U=0 or 1. Compare actions 0 and 1 for the same u. The total change is 6+u.

First retain the mediator at M_0=u while changing A: Y_(1,M_0)-Y_(0,M_0)=3+u. Then change the mediator to M_1=1+u while retaining A=1: Y_(1,M_1)-Y_(1,M_0)=3. The components sum to 6+u.

Reversing that decomposition gives mediator change 2 at A=0, followed by direct change 4+u at M_1. These components also sum to 6+u. The interaction AM makes the two decompositions different. A request for “the part caused through M” must select its intended contrast. Knowing the total effect alone supplies neither decomposition; observing data that identify it is a further question.