Facial feedback manipulation does not identify its mediator (source code)

= Facial feedback manipulation does not identify its mediator

Let $X$ be randomized assignment, $F$ facial activity, $M$ sensory feedback and $Y$ a report. One possible model is $F=X$, $M=F$, $Y=M$. A second is $F=X$, $M=F$, $D=X$, $Y=D$, where $D$ is an expectancy route. Both models predict the same observed $X,F,Y$ even though intervening on $M$ changes $Y$ only in the first. Therefore randomizing $X$ and measuring $F,Y$ does not distinguish these mechanisms. Identifying <causal mediation> requires further assumptions or interventions. The binary models are a logical counterexample, not participant data.