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 Herb Marsh posted on Thursday, November 08, 2012 - 6:36 pm
In BFLPE multi-countgry studies (eg PISA2007 studies) used two-level model (students & schools) w country as a multiple-groups.

contextual effect is difference in the effects of achievement (Ach) on Academic Self-concept (ASC) for L2 (school ) and L1 (student ), defined with model constraints. along w complete/partial invariance of factor loadings .

I want to treat country as L3 (random effects) rather than a multiple group (fixed effect). At least initially, all I want is the L3 variance components -- the extent to which the contextual effects at L2 vary for different countries. This is easy to do in a MLwiN/HLM framework w manifest vars, but I want latent vars. I cannot see how to get simple estimates of country-to-country variation in L2 estimates in an Mplus framework (further complicated as contextual effect estimate derived in model constraint)

Eventually, I will want estimates (& CIs) for each countries and some country L3 covariates.

I tried
%within%
...
s | mscW on MAchP1W;
%between TIDCLASX7%
...
SS | mscB1 on MAchP1B1;!
%between IDCNTRX3%
s;
ss;


but got:
** ERROR in MODEL command
The following random slope is not allowed for TYPE=THREELEVEL.
Problem with: SS | MSCB1 ON MACHP1B1
 Linda K. Muthen posted on Friday, November 09, 2012 - 11:20 am
Please send your output, data, and license number to support@statmodel.com.
 Herb Marsh posted on Monday, November 12, 2012 - 11:54 pm
MODEL:
%within%
MSCW by MSCp1@.659 MSCn2 MSCn3 MSCp4 (1-4);
s | mscW on MACH;

%between TIDCLASX7%
s;
MSCB1 by MSCp1@.659 MSCn2 MSCn3 MSCp4 (1-4);
SS | mscB1 on MACHl2;

%between IDCNTRX3%
s;
ss;
OUTPUT:

In this model there is significant variation in SS (i.e., the mscB1 on MACHl2 regression) across the Level3 groups. How do I save or plot the values of this regression for each group (e.g., construct a caterpillar plot)

What are the implications of treating the L3 grouping variable (country) as an additional level vs. a grouping variable in a multigroup analysis
 Bengt O. Muthen posted on Tuesday, November 13, 2012 - 8:03 am
You can request saving factor scores for s and ss.

You bring up the classic random versus fixed mode modeling question, where the issue is mainly if the inference is to a population or this particular set of groups. Mplus Version 7 has both of these approaches to analysis of many groups as discussed in our Version 7 videos from the August Utrecht workshops. You are adding an interesting wrinkle to this by considering the choice on level 3, so the multiple-group (fixed mode) approach is already a two-level analysis.
 Bengt O. Muthen posted on Tuesday, November 13, 2012 - 11:31 am
I should add that the random mode approach to the analysis of many groups follows a Bayesian idea of measurement parameters being random variables that come from a common population. Providing references to work by de Jong and Fox, this is discussed in the paper

Asparouhov & Muthen (2012). General random effect latent variable modeling: Random subjects, items, contexts, and parameters.

which is posted under Technical Appendices for Mplus Version 7.
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