Mediation and Model Constraint
Message/Author
 Scott C. Roesch posted on Friday, January 11, 2013 - 6:52 am
I want to test a 2-1-1 mediated effect. What I want to know is if the code below is doing this accurately. Moreover, does this code use the Sobel method to calculate the standard error for the indirect effect?

MODEL: %WITHIN%
implsuc ee_ebp;
implsUc ON ee_ebp(b);

%BETWEEN%
implsuc ee_ebp TF;
ee_ebp ON TF(a);
implsuc ON ee_ebp(b);
implsuc ON TF;

MODEL CONSTRAINT:
NEW(med);
med=a*b;
 Linda K. Muthen posted on Friday, January 11, 2013 - 10:56 am
Yes, this is correct if tf is a between variable.
 Xu, Man posted on Friday, August 11, 2017 - 9:46 am
Dear Dr.s Muthen,

I used the MODEL CONSTRAINT (MLR estimator, multiple group analysis, with weight is) approach to calculate the indirect effect a*b. This was because I wanted to create averaged indirect effect from distinct subset of groups from the model (for example whether mediation effects are comparable from two cultural groups of different set of country groups).

I guess there are actually two things: the a*b in each group and the averaged a*bs from each set of groups. I would like to verify, does the indirect effect obtained this way correspond to the Sobel method then?

I noticed that for individual groups indeed this is the case (stat test of the self-calculated a*b is equal to the one from model indirect). I also read in other posts that in some cases the mplus MODEL INDIRECT sobel is same as delta. So I guess it is the case in my analysis, but would it also be the case for the group aggregated a*b (e.g. [a1*b1+a2*b2]/2)?

Also, an additional question would be, is there a way to use bootstrapping? I tried to use bootstrap but the system said I should have replication weight or something.

Thank you!
 Bengt O. Muthen posted on Friday, August 11, 2017 - 10:12 am
Our FAQ

Delta method and Sobel

explains the relationship between Delta and Sobel. Delta is the general approach and is the same as the simplifications of Sobel in some cases. I don't think Sobel applies to average indirect effects.

All you need is the general Delta method and that is what Mplus always gives.
 Xu, Man posted on Friday, August 11, 2017 - 3:17 pm
Thank you. I had a look at the FAQ. I guess the group specific self calculated a*b and model indirect approach gives same estimates because the covariannce of a and b is close to zero tolerance (even under MLR).

But how do I get correct estimate of indirect or total effects of group averages? I think the delta method you suggested only works with model indirect function and it gives output for each individual group instead of being constrained?

For example when I have six groups, I want to know the average mediation effect of the first three groups, the average of the last three groups, and the difference between these two groups. What would be the best way to go?
 Bengt O. Muthen posted on Saturday, August 12, 2017 - 10:48 am
The Delta method is general and always gives you the right answer.