Testing Level-1 moderator on Level-2 ...
Message/Author
 Mo Wang posted on Wednesday, July 01, 2009 - 2:38 am
Hi all, I have a question regarding how to test cross-level moderation when the hypothesized moderator is at Level-1 instead of Level-2.

Assuming at Level-2 (e.g., group-level) I have a variable C and Level-1 (e.g., individual level) two variables X and Y. I have a theory-based hypothesis that C will have a cross-level main effect on Y and this effect will be moderated by X. How to test this moderation effect? Shall I just estimate how C influence the random slope between X and Y at Level-1 as if I hypothesize that C moderates the main effect of X on Y?

My concern is that when we are testing cross-level moderation in this way, we are really only testing how the level-2 predictor influence the random slope at level-1. It is not like in OLS where the testing of interaction is symmetric (i.e., for an interaction term XY, you can interpret either as X moderating Y or Y moderating X). I am wondering whether this symmetric interpretation exists in cross-level moderation test as well. If so, can anyone provide me some references?

Thanks!

-Mo
 Bengt O. Muthen posted on Wednesday, July 01, 2009 - 12:53 pm
Yes, a random slope for y on x where c predicts this random slope seems to be a standard cross-level interaction. See our course handout for Topic 7, slide 42, on our web site.

I guess it would only be symmetric if there is no level 2 residual variance for the random slope regressed on c - otherwise it is x that multiplies that level 2 residual, not c. I don't know about references - does anyone else?
 Mo Wang posted on Thursday, July 02, 2009 - 2:02 am
Thank you for your response, Bengt. So, for my scenario (i.e., level-1 variable moderating level-2 effect), shall I just form a level-2 X and use the product of it and C to test the moderation effect?

-Mo
 Bengt O. Muthen posted on Thursday, July 02, 2009 - 8:58 am
No, you don't form a product of variables. Instead, see UG ex9.2 for how to handle this.
 Lois Downey posted on Friday, April 29, 2011 - 4:36 pm
So, just to confirm that I correctly understand Bengt's reply to Mo on July 2, 2009:

It makes NO DIFFERENCE whether you're testing ...
a) the moderating effect of C on the association between X and Y, or
b) the moderating effect of X on the association between C and Y.

You use the SAME TEST to answer both questions. Namely, you model the slope of Y on X as random, and then regress that slope on C.

Correct?

Thanks,
Lois Downey
 Bengt O. Muthen posted on Friday, April 29, 2011 - 5:44 pm
Yes.