Effects from within to between level
Message/Author
 Christoph Weber posted on Thursday, August 11, 2011 - 12:37 am
Dear. Dr. Muthen,

is it possible to estimate effects from a within level variable to a between level variable (random slope) with Mplus.

My case is the following:

2 level panel data (between N = 31), 2 waves.

I am using a latent difference score approach to model the change of a dep. variable Y.

My hypothesis is, that the change at the between level is affected by an interaction of Y at time 1 (within) and an indep. var X (within).

Best regards
Christoph Weber
 Linda K. Muthen posted on Thursday, August 11, 2011 - 6:19 am
Example 9.2 shows a random slope model.
 Christoph Weber posted on Thursday, August 11, 2011 - 11:49 am
Thanks, but is it possible to specify:

%within%

s | y ON x w;
xw | x xwith w;

%BETWEEN%
y s ON w x xw;
 Linda K. Muthen posted on Friday, August 12, 2011 - 8:49 am
Your specification is not allowed and is not the way to obtain a cross-level interaction between x and w. Example 9.2 is the way to do that. To see how the formulas work, see Slide 45 of the Topic 7 course handout on the website.
 Christoph Weber posted on Friday, August 12, 2011 - 11:21 am
Thanks, I know that this is not a common multilevel model.

But actually my hypothesis is, that individual factors (and their interaction) have an effect on the development on cluster level. Do you have any ideas how to model this?

Thanks

Christoph Weber
 Bengt O. Muthen posted on Friday, August 12, 2011 - 11:51 am
Typically you want the between part of the subjects' scores to influence a cluster-level (between-level) DV, but it sounds like that's not what you are after. It sounds like you somehow want the within-cluster part of a subject's score to influence a cluster-level DV - is that right? Could this be an example: If a student misbehaves much more than the classroom average, this influences the teacher's well-being? If so, I have not seen this attempted in multilevel modeling - someone else?
 Christoph Weber posted on Friday, August 12, 2011 - 1:45 pm
I have the following design.
31 classes, 2 measures and an intervention between T1 and T2 that should change the environmental consciousness (EC). The EC are measured at T1 and T2. Further I have a measure of social capital at T1.

The hypothesis is, that in those classes, where students with high social capital have a low EC, there should be a worsening of EC on class level.

Thus I thought it would be necessary to model an interaction effect of social capital and EC on the change of EC on class level.
 Bengt O. Muthen posted on Saturday, August 13, 2011 - 1:59 pm
I think you can use regular multilevel modeling to accomplish this. You need a between-level interaction for the latent between-level parts (random intercepts) of ec and sc (social capital). In Mplus terms you say:

.
.
.
cluster = classrm;
! ec and sc are allowed to vary on both !within and between, so not on Within= or !Between= lists

Analysis:
Type = twolevel;

Model:
%between%
int | ec1 xwith sc;
ec2 on ec1 sc int;

%within%
ec2 on ec1 sc;
ec1 with sc;
 Christoph Weber posted on Monday, August 15, 2011 - 6:33 am
Many thanks for your help!
Christoph Weber
 Dave posted on Thursday, February 23, 2012 - 12:32 pm
Building on this series of postings, I am interested in cross-level interactions between within and between level variables. I am interested in testing a model similar to example 9.5 (below) in the version 6, April 2010 user guide. I have dropped x1 from the model to simplify the example.

VARIABLE: NAMES ARE y1 y2 x2 w clus;
WITHIN = x2;
BETWEEN = w;
CLUSTER IS clus;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
MODEL:
%WITHIN%
s2 | y2 ON y1;
y2 ON x2;
s1 | y1 ON x2;
%BETWEEN%
y1 y2 s1 s2 ON w;

As I understand this example, it is testing cross-level interactions between x2 and w predicting the mediating variable y1 and between y1 and w predicting y2. x2, y1 and y2 are at the within level.

I am wondering if it is possible to adapt this model to accomodate y1 at the between level rather than at the within level. The moderating variable w would remain at the between level and the cross-level interaction would be between x2 and w predicting between-level y1 and y1 and w predicting y2. If this is possible, how would I adapt the code? Thanks in advance for your assitance.
 Bengt O. Muthen posted on Thursday, February 23, 2012 - 3:45 pm
A cross-level interaction is due to a random slope. If y1 is between only, it cannot have a random slope. You can have an interaction between x2 and w influencing the between-level y1 if x2 has between-level variation. If that between-level variation is latent, you use XWITH.