Between effects in Random Slopes Models
Message/Author
 Kate Barford posted on Tuesday, April 12, 2016 - 7:37 pm
Hi There,

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;

Thank you.
 Bengt O. Muthen posted on Wednesday, April 13, 2016 - 1:58 pm
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.
 Kate Barford posted on Thursday, April 21, 2016 - 10:35 pm
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.
 Bengt O. Muthen posted on Friday, April 22, 2016 - 8:54 am
xm can capture contextual effects - see the Raudenbush-Bryk multilevel book.
 Kate Barford posted on Thursday, April 28, 2016 - 9:54 pm
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?

Thank you very much for your help.
 Bengt O. Muthen posted on Friday, April 29, 2016 - 6:54 pm
You are right - this does give a latent between-part x on between (I had forgotten that we do that) and the "whole" observed x is used on within.

The WITH statement refers to the covariance between the residuals.
 Kate Barford posted on Sunday, May 01, 2016 - 5:37 pm
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.

Thank you for your help Dr. Muthen.