Thread by @hardsci

And now a thread of things that must be true in order to validly interpret a standard mediation analysis.

These are assumptions you must defend with outside knowledge. They are not tested as part of the analysis, and often they are not testable even in principle.

Here goes...

1. The effect of M on X is exactly zero

2. The effect of Y on M is exactly zero

3. The effect of Y on X is exactly zero

4. Either there exists no variable correlated with X that affects M, or there are multiple such variables working in different directions that happen to exactly cancel each other out

5. Either there exists no variable correlated with M that affects Y, or there are multiple such variables working in different directions that happen to exactly cancel each other out

(5b. A special case of a variable correlated with M that affects Y would be another mediator. So that means you are assuming that the M you are studying is the only mediator between X and Y. Or else some kind of complicated canceling-out thing)

6. Either there exists no variable correlated with X that affects Y, or there are multiple such variables working in different directions that happen to exactly cancel each other out

7. Either the effects of X on M and M on Y do not vary (for every person, X affects that person's M to the exact same degree and likewise for M affecting Y) OR...

... the people for whom X affects M are the same people for whom M affects Y (fudged this a little to assume that "how much X affects M" is binary, it's a little more complicated if - more realistically - it's continuous)

There's lots more. This is just from a causal modeling perspective, doesn't get into the standard assumptions if you're doing OLS regression etc. Also people who know causal inference better than me will probably correct/complicate my list so check back for replies

And in the meantime read this johnbullock.org/papers/mediati…