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.
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?
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.
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;
Dave posted on Thursday, February 23, 2012 - 6:32 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.
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.