Measurement invariance of 2nd-order f... PreviousNext
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 Joseph E. Glass posted on Sunday, August 19, 2012 - 11:41 pm
Hello,

I have identified a second-order CFA model with ordinal indicators and WLSMV (see below). I would like to test the second order measurement parameters for loading and intercept invariance. Can you point me to reference materials on this topic or instruct me on how to do this? Thank you.

f1 by
var1 var2 var3 var4;
f2 by
var5 var6 var7 var8;
f3 by
var9 var10 var11 var2;
f4 by f1 f2 f3;

model g1:
[f1@0 f2@0 f3@0];
model g2:
[f1@0 f2@0 f3@0];
 Linda K. Muthen posted on Monday, August 20, 2012 - 3:02 pm
The model you show above would be your constrained model. In the second model, you would free the factor loadings and thresholds, fix the mean of f4 to zero, and fix all scale factors at one. See multiple group analysis in the Topic 2 course handout for example inputs for how to do this.
 Mi-young Webb posted on Friday, May 08, 2015 - 2:28 pm
What is the best way to test measurement invariance of a second-order factor model with binary data?

For continuous data, measurement invariance tests goes in a sequence:
1. Configural invariance
2. First-order factor loadings invariance
3. Second-order factor loadings invariance
4. Intercepts of first-order factor indicators (observed variables) invariance
5. Intercepts of second-order factor indicators invariance
6. Disturbances of first-order factors invariance
7. Residual variance of first-order factor indicators or observed variables invariance

For measurement invariance with binary data, I have been advised to test loadings and intercepts invariance together. If so, should I test first-order factor loadings and indicator intercepts invariance test and proceeds to second-order factor loadings and intercepts?

Thank you for your help!!!
 Bengt O. Muthen posted on Friday, May 08, 2015 - 2:48 pm
Regarding 5. for continuous items, don't you always have those fixed at zero?

Regarding binary items, yes, I would recommend doing loadings and thresholds together. See my answer to Eiko Freid today.
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