Cross-Level Interaction in DSEM (inte...
Message/Author
 L.Greiner posted on Sunday, June 28, 2020 - 12:41 pm
I calculate the following model (s.below) and have the following questions on how to define a cross-level interaction and how to interpret the results.

a) Is this the correct way to specify a cross-level interaction for the time-consistent/between-cluster variable M on the within-level relationship of the time-variable x and y?

b) assuming that the random intercept xx has a negative sign (e.g. -0.10) and the effect of M on xx is positive (e.g. 0.50) - does this mean that with each increase in the unit M the xx relationship increases by 0.50 (resulting in a positive xx relationship for above-average values in M?)

c) Is there a way to visualize the cross-level interaction in Mplus?

Here's the model:

DEFINE:
Center M (grandmean); !grandmean variable M

ANALYSIS:
TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROC = 2; !
BITER = (1000);
THIN = 10; !

MODEL:
%WITHIN%
xx | x ON x&1;
yy | y on y&1;
xy | x on y&1;

%BETWEEN%
xx WITH yy xy x y;
yy WITH xy x y;
xy WITH x y;

xy ON M; !cross-level interaction

OUTPUT:
TECH 1 TECH8 STDYX;

PLOT:
TYPE = PLOT3;
FACTORS = ALL;
 Bengt O. Muthen posted on Sunday, June 28, 2020 - 4:29 pm
When you say x on y, note that this is saying that you regress x on y, that is, y influences x. It does not mean that x has an influence on y. With this caveat, a) is ok.

You say xy on M in the input but you imply xx on M in the text. With this caveat, b) is correct.

Regarding c), see cross-level plotting at

http://www.statmodel.com/Mediation.shtml
 L. Greiner posted on Sunday, June 28, 2020 - 11:00 pm
Thanks for your quick help, this was really helpful. And yes you were right assuming that I was talking about xy and not xx - sorry for the confusion.