Multi-level mediated moderation
Message/Author
 Elizabeth Ferguson posted on Tuesday, October 11, 2016 - 3:25 pm
I am seeking input regarding a case of mediated moderation, a topic that doesn't seem to come up very often in articles or message boards.

I have run a multi-level regression analysis and have found that the effect of my L1 predictor (x) on the L1 outcome variable (y) is moderated by a L2 variable (w). I would now like to test whether this effect is mediated by another L1 variable (m).

I believe this is a (1,2)-1-1 mediation. Unfortunately, this model is not covered in any publications which I could find. For example, Preachers (2010/2011) articles cover 2-1-1 and (1,1)-1-1, but not the case I've run into.

Are there any examples of this (1,2)-1-1 mediation code for Mplus?
 Bengt O. Muthen posted on Tuesday, October 11, 2016 - 5:38 pm

%Within%
s | y ON x;

%Between%
y s ON w;

This means that w moderates the effect of x on y by means of a cross-level effect using the random slope s.

2. Now you say that you want to see "whether this effect is moderated by another L1 variable (m)". The question is where to put this m, that is, what you mean by "this effect". One way would be to use the latent between-level part of m on Between in a model with m as a mediator:

%Between%
m on w;
y s ON m w;

This certainly has m mediating the moderating effect of w on y. The Within-level model can include the latent within part of m in some suitable way.

Or, is the effect of x on y that is mediated by m? If so, in which path does the moderation take place?
 Elizabeth Ferguson posted on Wednesday, October 12, 2016 - 10:15 am
Dr. Muthen, Thank you so much your reply. I am still very new to Mplus. My model is similar to Model 8 described in Stride et al(2015). In this model, the paths x -> y and x -> m are moderated by w. The m -> y path is straightforward. I'm also trying to follow the guidelines put forward by Preacher (2010;2011) for estimation of indirect effects in mlm. But this is another article that doesn't address moderation of the x -> y and x -> m paths.

I had initially run the following syntax adapted from Preacher's 2-1-1 mediation model:

BETWEEN IS w;
CLUSTER IS id;
DEFINE:
xw=w*x;
ANALYSIS: TYPE IS TWOLEVEL RANDOM;
MODEL:
%WITHIN%
x m y;
y ON m;
%BETWEEN%
xw x w m y;
m ON xw(a);
y ON m(b);
y ON xw;
MODEL CONSTRAINT:
NEW(indb);
indb=a*b;
OUTPUT: TECH1 TECH8 CINTERVAL;

Although the results are as I expected, I have come to think that this calculation is flawed because I used an interaction variables instead of specifying random slopes from x-y and x-m. Do you see any way to integrate the two approaches?
 Bengt O. Muthen posted on Wednesday, October 12, 2016 - 4:39 pm
It sounds like you simply want

Within:

sc | y ON x;
sa | m ON x;
y ON m (b);

Between:
y WITH m;
sc ON w;
sa ON w (g);
[sa] (a);

MOdel Constraint:

ind = (a+ g*mod)*b;

where mod gives values of the w moderator that you are interested in.