1-1-1-1 two-step mediating effect
Message/Author
 Niki Su posted on Sunday, December 17, 2017 - 6:37 pm
There is a X-M1-M2-Y two-step mediating model, and all are level-1 variables.
The indirect effect should be a1a2a3+ca1ca2+ca2a3+ca1a3?

model:

%within%
sa1|M1 on X;
sa2|M2 on M1;
sa3|Y on M2;
sc|Y on X;

%between%
[sa1](a1);
[sa2](a2);
[sa3](a3);
sa1 with sa2(ca1a2);
sa3 with sa2(ca2a3);
sa1 with sa3(ca1a3);
 Bengt O. Muthen posted on Monday, December 18, 2017 - 12:16 pm
You need to derive the expectation of the product of the 3 random slopes to check.
 Niki Su posted on Tuesday, December 19, 2017 - 11:37 pm
Thank you very much. But maybe I didn't describe the question clearly. In a 1-1-1 model, the indirect effect should be the product of 2 random slopes plus their covariance. But when it is a 1-1-1-1 model, I don't know how to deal with the covariance. Back to the 1-1-1-1 model described initially, should the indirect effect be the product of the 3 random slopes plus covariances of each two of the 3 random slopes?
 Bengt O. Muthen posted on Wednesday, December 20, 2017 - 12:25 pm
Yes, that's what I understood you to say. I suggested that you derive this indirect effect (by starting with the expectation of the 3 random variables).
 Bengt O. Muthen posted on Wednesday, December 20, 2017 - 4:20 pm
Ok, I derived it for you. You may want to check it, but here is what I get - in your notation the indirect effect should be

a1*a2*a3+ca1a2*a3+ca2a3*a1+ca1a3*a3