Testing of configural invariance
Message/Author
 Sung Kim posted on Monday, July 27, 2009 - 9:34 am
I am doing a configual invariance testing (MG-CFA) cross two groups. Could you let me know whether my syntax is correct? I have 10 factors measured by 50 indicators (ordered or continuous)?

After fitting the two models, I can do a chi-square difference test. Right?

Unconstrained model
GROUPING is gr (1=gr1 2=gr2);
Model:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];
[f1-f10]@0;

Constrained model
Model:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];

Model gr1:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];

Model gr2:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];
 Sung Kim posted on Monday, July 27, 2009 - 10:32 am
I've just looked at Mplus UG. In p.399, the most unrestrictive model, where intercepts, factor loadings, and residual variances free across groups but
factor means fixed at zero in all groups, represents the configural invariance? So the constrained model should be:

Constrained model
Model:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];

Model gr1:
[f1-f10]@0;

Model gr2:
[f1-f10]@0;

However, in the unconstrained model,
Model:
f1 by y1-y5;
...
f10 by y46-y50;
[y1-y5];
...
[y46-y50];

Is it correct? Thank you so much!
 Linda K. Muthen posted on Monday, July 27, 2009 - 11:03 am
The Topic 1 course handout contains the inputs for testing measurement invariance. You should check against those. The following specification is not correct:

[f1-f10]@0;

It should be:

[f1-f10@0];