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 Melanie Wall posted on Wednesday, September 14, 2016 - 2:00 pm
Is it possible within the mixture EFA environment to do either of the following:
1. fit different numbers of factors within different classes, e.g. 1 factor in class 1 and 3 factors in class 2.
2. add constraints to some of the factor loadings or factor variances within any of the specific classes
 Tihomir Asparouhov posted on Wednesday, September 14, 2016 - 3:00 pm

We don't have these capabilities yet but here are some thoughts

A. Mixture with 3 factors in both classes is a more general model then the one with 1 factor in class 1 and 3 factors in class 2. If you have only one factor the loadings will simply be estimated to 0

B. You can setup unrotated EFA models within each class of any size you want - kind of like this
f1-f3 by y1-y10*1; f1-f3@1;
f1 by y1@0 y2@0;
f2 by y2@0 y3@0;
f3 by y1@0 y3@0;

You can rotate later using the estimated correlation like this (class by class)

DATA: FILE IS estimatedCR.dat; type=correlation;
ANALYSIS: TYPE = EFA 3 3; estimator=ml;

C. Target rotation can be used for some loading approx constraints

D. If you can extract the latent class variable move to multiple group framework and we have more opportunities there, although still not the one with different number of factors.
 Melanie Wall posted on Wednesday, September 14, 2016 - 4:04 pm
We had figured out that we could do the EFA within Mixture CFA model using the errors in variables formulation you specify, i.e. with constraining 6 loadings to zero, but it is *very helpful* to see how we could use Mplus to do the rotation automatically by exporting the estimated correlation matrix into the EFA procedure (nice trick). We will try and if run into problems be back to you.
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