Hayes (2018) p. 540 writes

I will not take a firm position on whether construing $M$ as a simultaneous mediator and moderator of a variable’s effect could ever make substantive or theoretical sense. I am uncomfortable categorically ruling out the possibility that $M$ could be a moderator just because it is correlated with $X$. My guess is that there are many real-life processes in which things caused by $X$ also influence the size of the effect of $X$ on $Y$ measured well after $X$. But $M$ would have to be causally prior to $Y$ in order for this to be possible, implying that $M$ could also be construed as a mediator if $M$ is caused in part by $X$ but also influences $Y$ in some fashion.

Hayes is referring to a situation like the one depicted on p. 539, i.e. a conditional process model in which $X$ moderates its own indirect effect. The top diagram he describes as conceptual and the bottom one as statistical.

Conceptual and Statistical diagram of conditional process model

The model would translate into the following equations

$M = i_M = a_X + e_M$

$Y = i_Y + c'_1X + bM + c'_2XM + e_Y$

It follows that the direct effect of $X$ in this model would not be $c'_1$ but rather $c'_1 + c'_2M$. So long as $c'_2M \neq 0$, $M$ moderates $X$'s direct effect on $Y$.

Unlike this question, I am not asking whether it can be done mathematically - I am aware that it can. Instead, I am asking: under what circumstances it will be sensible theoretically/substantively interpretable? Also, why has this question proved a controversial one in the mediation literature?

Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford publications.



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