1-1-1 unconflated MLM with dichotomou...
Message/Author
 DL posted on Tuesday, September 22, 2020 - 5:13 pm
Hello, I have modified Preacher et al.'s syntax (example H) to run an unconflated MLM (not MSEM) with fixed slopes. However, my predictor is dichotomous (0 = did not use intervention, 1 = used intervention) and is uncentered.

Current syntax is below, but am wondering if I would need to use a 'xmean' variable to get an accurate assessment of the between-person indirect and total effects despite the fact that this variable is meant to be uncentered...? (My concern with the below is that the indirect and total between effects are not interpretable since an uncentered level 1 variable, x, would be predicting mmean at level 2).

USEVARIABLES ARE ID x m y mmean;
CLUSTER IS ID;
BETWEEN IS mmean;
WITHIN IS m;
DEFINE: CENTER m(GROUPMEAN);
ANALYSIS: TYPE = TWOLEVEL; ESTIMATOR = MLR;
MODEL: %WITHIN%
y ON x (cpw);
m ON x (aw);
y ON m (bw);
[m@0];
%BETWEEN%
mmean y;
mmean ON x (ab);
y ON mmean (bb);
y ON x (cpb);
MODEL CONSTRAINT: NEW (indb indw totalb totalw total);
indb = ab*bb;
indw = aw*bw;
totalb = ab*bb + cpb;
totalw = aw*bw + cpw;
total = ab*bb + aw*bw + cpw + cpb;
(where total is meant to measure the overall, conflated effect).
 Bengt O. Muthen posted on Tuesday, September 22, 2020 - 5:32 pm
The way you have it now, you get a latent variable decomposition of x. You could declare x as within (not centered) and use the more transparent "xmean" on between, that is, the proportion. But does the intervention proportion really have an effect on Between or should between be involving only m and y?
 DL posted on Wednesday, September 23, 2020 - 9:35 am
Thanks for your clarification. It hadn't occurred to me that the above was a variant of SEM, and given my using mmean on between, I reckon I should be consistent.

If I went the route of using the xmean on between, wouldn't that simply be interpreted as, for example: the greater the proportion people use this intervention, the more they were generally satisfied (Y) because of a greater degree of using M?

Finally, is it feasible/interpretable to only involve M and Y on the between level? I suspect one would then not be able to interpret the indirect and total between effects.

Thanks very much, and pardon any ignorance- I am new to this area!
 Bengt O. Muthen posted on Wednesday, September 23, 2020 - 5:41 pm
Q1: Right

Q2: Perhaps you are thinking of a so called 1-2-2 model. See the Preacher pdfs on our Mediation page:

http://www.statmodel.com/Mediation.shtml