I'd like to ask you for some help in finding a (hopefully citable) way of analyzing panel data when looking for mediation and moderation effects.
Problem I have is that my measured variables don't really change across time waves (3 of them), so using longitudinal setups, as described by Selig and Preacher (2009) for example, don't really work here. My guess is, that's because of autoregressive paths that simply "kill" the variance in the outcome (I'm talking gut feelings only).
A typical model from Selig and Preacher article that's being often pointed by reviewers as a "standard" is this:
My situation here is that I have a mediation (indirect) effect within each time point (replicated in other studies, both correlational and experimental) that won't show up between time waves as in attached picture: X1 -> M2 -> Y3.
If I run a model only on X1 - M2 - Y3 the indirect effect is there. X1 - M1 - Y2 as well, X2-M2-Y3 as well and so on. But as soon as I add autoregressive paths it all falls apart.
I used to refer to my study as a longitudinal study, but when I realized that i'm not after showing or controlling for change in time, maybe I'm using a wrong approach.
I did not find any precedence in literature reporting mediation effects on measurements taken at different waves only (that is, ignoring all time specific paths).
But I also didn't found any article, discussing such models in a context of traits (measurements) that are stable / static and not dynamic as in most longitudinal models.
I can provide more details, answer any questions if only could help me out with a workable solution here. Workable in a sense, that would convince reviewers on it's validity, when writing about indirect effects that are present between time waves.