Moderated Mediation Model

[Dom Weinberg]

Hi all,

I'm trying to run a Moderated Mediation Model as in Model 1 in Preacher et al., 2007 - i.e., M is both moderator and mediator. In this case Y, X and M are all continuous.

I tried extending my mediation model by adding the interaction term (b2*PJW:FAS) as below, but I realise I am now very unsure how to use b1, c1, a1 and especially b2 to understand the total and indirect effects. (Diving into the literature on conditional/controlled indirect effects, I'm wondering if the simple answer I'm hoping may not exist...)

(Simplified model for the forum - I think I may be able to do this using Process, but I have multiple Ys for other models, so would prefer to use SEM.)

Y ~  b1*M + c1*X + b2*X:M

M ~ a1*X

ind_Y_M_X := a1*b1

total_Y_X := c1 + (a1*b1)

I've been looking for answers on the group already, hope I haven't missed something, but it seems they deal with slightly different things (e.g., the thread on Model 2 in the Preacher paper), and I can't work out how to apply it to my own model.

Thanks,

Dom

[John Jamison]

Good timing since I'm wrestling with this at the same time. Like you, I also have multiple DVs, so am running it in lavaan (also I don't like spss).

Hayes does include this in his Process for SPSS (model 74 shown below), but Process doesn't produce conditional indirect effects (he makes special note of this in the book).

A challenge is that you can conceptualize your theoretical model like Preacher, Rucker, and Hayes (first diagram below), or as I'm doing for my model (second diagram). Mathematically, these are the same, but they have big implications for your indirect effects. In the first, the X is moderating the second stage effect in your mediated path. In the first, you've simply got a moderator that also happens to be the mediator. So for my model, I'm only computing unmoderated indirect effects since there's no theoretical reason to expect a moderated indirect effect. And I suspect that the reason that Hayes doesn't include them in Process is because it would be impossible to tell which pathway was which. This may also explain why the Preacher et al model doesn't include a path Through XM (third diagram below).

If you're really keen to calculate your moderated indirect effect, I think you're going to have to use a method involving X+1SD and X-1SD. See, your indirect effect is missing some of what Preacher et al discuss, which would be:

## ind_Y_M_X := a1*(b1+(b2*X))

But of course lavaan can't put a variable into the computed effects. Just for fun, I tried plugging my X variable into the equation and lavaan just laughed at me. But I've seen people calculate this by calculating your x upper and lower limits and creating two equations where the [] are calculated numbers entered by hand.
## ind_Y_M_X := a1*(b1+(b2*[X+1SD]))

## ind_Y_M_X := a1*(b1+(b2*[X-1SD]))

Then you do some tests of significance on the difference, but you may do better reading some dedicated blogs on that.

[Dom Weinberg]

Many thanks John, good to know I'm not the only one! Your images/diagrams didn't come up (perhaps just email me?), but I've seen model 74 and so think I've understood that you're saying - X moderating M-Y is mathematically the same as M moderating X-Y, but conceptually different.* My hypothesis regards the latter. My idea was simply: do the mediation (Y_M_X, which we expected, and found) and the moderation (M moderates YX, which we also expected, and found) both still exist when we take them both into account? (Hmm, but maybe I need to give this 'taking both into account' idea more thought - what would it actually mean if one/both of the effects disappeared...?)

And your method for the moderated indirect effect sounds like a good place to go next, I was thinking on much the same lines. I'm glad you were the one to try the "plugging X into the equation" trick - I have had enough of lavaan laughing at me over the past few days ;)

*I think this distinction is what vanderWeele, 2014 is all about, but not having an epi background, it's taking time to sink in...

[Mariia Samoilenko]

I often use medflex https://www.jstatsoft.org/article/view/v076i11 for causal mediation. It can handle exposure-mediator interaction / moderated mediation.