I'm very new to MPLUs. I am running two-level model and testing a cross-level interaction (moderation). I've been advised that, using the approach below, my between effects are actually between minus within effects, so I should add back in the within variance using model constraint. My question is, does this also apply to my moderation effect? Should I also have a model constraint adding back in the within variance to my moderation effect?
BETWEEN are OI; !only varies between individuals CLUSTER are id; !level 2 is person ...... ANALYSIS: TYPE is TWOLEVEL RANDOM;
MODEL: %WITHIN% sMixlfb| likefb ON mixKN;
%BETWEEN% likefb ON mixKN (LC);!(between-within) [sMixlfb] (LW); !Within effect sMixlfb ON OI; !moderation effect
Model constraint: new(LB);! true between effect of likeFB on mixKN LB = LC+LW;
Not clear on the advise you got. First, note that with a random slope, the x variable (mixKN) needs to be declared as a Within variable - no latent variable decomposition into Within and Between takes place in this case. See UG ex 9.1 and 9.2.
This means that on Between you need to create a cluster-mean version of mixKN.
Note also that when you add the moderator variable OI, the mean of the random slope is no longer [sMixlfb} - that's just the intercept.
Thank you for your clear and very helpful response. I just have one question about example 9.2
VARIABLE: NAMES = y x w xm clus; WITHIN = x; BETWEEN = w xm; CLUSTER = clus; ! CENTERING = GRANDMEAN (x); DEFINE: CENTER x (GRANDMEAN); ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% s | y ON x; %BETWEEN% y s ON w xm; y WITH s;
Why would one want to control for xm in the regression equation (s ON w xm)? Are there any cases in which one might not want to do this? If it helps, in my study, our main focus is on whether w is a moderator of the y ON x relationship. I'm a bit unsure about how to interpret s ON w when also controlling for xm (where xm is the cluster mean centered version of x). What is the purpose of including this variable here? Thank you.
Thank you. Apologies, I have two further questions.
One is that in the users guide, it gives an alternate version of example 9.2
TITLE: this is an example of a two-level regression analysis for a continuous dependent variable with a random slope and a latent covariate DATA: FILE = ex9.2b.dat; VARIABLE: NAMES = y x w clus; BETWEEN = w; CLUSTER = clus; ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% s | y ON x; %BETWEEN% y s ON w x; y WITH s;
However, In your previous response on this thread, you stated that "no latent variable decomposition into Within and Between" occurs for the x variable in this case. So, what exactly is happening in this case then, and would you recommend against using this second version?
Finally, is the y WITH s statement output the correlation between the residuals of y and s?
For anyone else that might be interested in this thread, I just wanted to correct my mistake of referring to xm in the 9.2 example as the "cluster mean centered" version of x, when I believe it is actually meant to be the "cluster mean" version (i.e., the aggregate version) of x.