Why residual between DV and slope in ...
Message/Author
 Danny Osborne posted on Wednesday, January 11, 2017 - 4:12 pm
Hi there,

I noticed that there is some variability in how cross-level interactions are estimated in the literature. Here's a basic model, as specified in the MPlus Users' Guide:

%WITHIN%
s | y ON x;
%BETWEEN%
y s ON w xm;
y WITH S;

Some people include the "y WITH s;" statement to estimate the residual correlation between the slope and DV, whereas others do not. What is the rationale for including the "y WITH s;" statement? Are there situations where it is sensible to leave that statement out? Thanks!
 Bengt O. Muthen posted on Wednesday, January 11, 2017 - 4:37 pm
If you don't get y WITH s by default you should include it. It is simply very likely that they are correlated.
 Tengiat Loi posted on Thursday, April 04, 2019 - 9:58 am
Dr. Muthen,

If there are two DVs.

%WITHIN%
s1 | y1 ON x;
s2 | y2 ON x;

%BETWEEN%
y1 y2 s1 s2 ON w xm;

y1 WITH s1;
y2 WITH s2;

Should we also correlate below?
s1 with s2 y2;
y1 with y2 s2;
 Bengt O. Muthen posted on Thursday, April 04, 2019 - 5:35 pm
I would add correlations between all the DVs.
 Tengiat Loi posted on Friday, April 05, 2019 - 10:01 am
Thanks Bengt.

If extending this concept to a simple mediation with two DVs.

%WITHIN%
c1 | y1 ON x;
c2 | y2 ON x;
a | m ON x;
b1 | y1 ON m;
b2 | y2 ON m;

1. Should we also correlate all below in between?

%BETWEEN%
y1 with y2 m b2 b1 a c2 c1;
y2 with m b2 b1 a c2 c1;
m with b2 b1 a c2 c1;
b2 with b1 a c2 c1;
b1 with a c2 c1;
a with c2 c1;
c2 with c1;

2. Can we remove them if they are not significant?
 Bengt O. Muthen posted on Saturday, April 06, 2019 - 12:49 pm
1. Yes.

2. Sure.
 Tengiat Loi posted on Saturday, April 06, 2019 - 3:48 pm
1. Why should we correlate residuals between mediator and DV? It seems we usually don't follow this practice at single level study.
 Bengt O. Muthen posted on Monday, April 08, 2019 - 9:25 am
But on Between you don't have Y ON M so that is different from the single-level case. You are just specifying a free covariance matrix for all your random effects.