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 Timo Mandler posted on Wednesday, February 28, 2018 - 5:40 am
Dear Dr. Muthen,

we specified a multi-group ESEM model with 35 binary indicators that load on 6 factors which, in turn, are related to three DVs.

Because we would like to allow for some overlap between factors (theoretically expected), we use an oblique rotation. The model converges, not much to complain about, BUT: There are few correlations among specific factors (from .50 up to .80) that raise the question of multicollinearity.

I haven't come across a discussion of this issue in the context of ESEM and don't know how to address such concerns, since (a) the exclusion of indicators/factors would affect the overall solution and (b) running simple regressions with saved factor scores (to test the robustness of the coefficients when excluding relevant factors) also seems problematic to me.

How to best address such (multicollinearity) concerns? Your help would be much appreciated!
 Tihomir Asparouhov posted on Wednesday, February 28, 2018 - 5:05 pm
If the sample size is sufficiently large and the correlations are significantly different from 1, it shouldn't be much of a problem. Alternatively you can try bi-factor efa with rotation=bi-geomin; that may reduce the correlations. See user's guide example 4.7.
 Timo Mandler posted on Thursday, March 01, 2018 - 2:56 am
Dear Dr. Asparouhov,

thank you for your quick reply.

Sample size is pretty large. The overall N is about 700,000, split into 10 groups with Ns ranging from 40,000 to 120,000. With this sample size, virtually every correlation is significantly different from 1, even .95.
I am worried that reviewers would not be easily convinced by this type of evidence. Are there any references that could be used to support this argument?

Also, thank you for suggesting an alternative approach. I will have a look into it!
 Tihomir Asparouhov posted on Thursday, March 01, 2018 - 9:01 am
You might find something useful here

Both studies conclude that ESEM correlations are smaller than CFA.

I would also consider modification indices. Including some residual correlations among the indicators in the ESEM model may reduce the correlations.
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