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 Christopher Cambron posted on Friday, January 05, 2018 - 12:26 pm
Hi,
We are attempting to test 2-1-1 mediation using DSEM and could use some guidance on code construction. We are using time-varying EMA data on mood and smoking for m and y. X is a time-invariant measure of SES for 375 participants.

My primary question is what it means for interpreting the ab path to also have y on m estimated at the Between level in DSEM. Preacherís 2-1-1 models have this path whereby the within b path is added to the between b path before multiplying ab. Thanks so much.

%WITHIN%
s_my | y on m; ! L1 b path
phi | y on y&1; ! L1 control for autoreg
y m; ! L1 residual variances

%BETWEEN%
x m y; ! L2 residual variances
s_my WITH phi y m; ! covariances
phi WITH y m;
y WITH m;

[phi]; ! L2 autoreg mean
[s_my] (bw); ! L2 b path mean
y on x (c);
m on x (a);

y on m (bb); ! What would this path mean in DSEM?

MODEL CONSTRAINT:
NEW (ab); ab=a*bw;
 Bengt O. Muthen posted on Saturday, January 06, 2018 - 12:09 pm
The answer to this is a bit involved - we'll get back to you shortly.
 Tihomir Asparouhov posted on Saturday, January 06, 2018 - 8:31 pm
I would refer you to Appendix F in https://www.statmodel.com/download/Preacher.pdf for understanding and interpreting the model. The bb parameter is the most straight forward to interpret, it is the bw parameter that requires insight.

If you are using DSEM then you need to understand the sentence containing equation (61) in http://statmodel.com/download/DSEM.pdf From there using plausible values you need to compute bw=E(s_my/(1-phi)). That is the only way unfortunately such an expectation is generally undefined for two normal random effects.

In the next Mplus version we will have some of these steps simplified.
 Tihomir Asparouhov posted on Monday, January 08, 2018 - 11:17 am
A great first step would be to simplify the model by replacing

phi | y on y&1;

with

y on y&1 (phi);

In many case Var(phi) is too small anyway so it would not be detrimental to assume the same autocorrelation across subjects. In that case the indirect effect is simplified substantially and you can simply use

MODEL CONSTRAINT:
NEW (ab); ab=a*(bb+bw/(1-ph));
 Christopher Cambron posted on Monday, January 08, 2018 - 2:54 pm
Great. Thank you for the help!
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