Second-order and bifactor model
Message/Author
 Marike Deutz posted on Wednesday, July 31, 2013 - 5:06 am
Hello,

Could you tell me whether the following syntaxis are correct (simplified for this question)?

For both models: WLSMV as estimator with all categorical (dichotomous) variables

Second-order model:
F1 by item1 item2 item3 item4;
F2 by item5 item6 item7 item8;
F3 by item9 item10 item11 item12;
GF by F1 F2 F3;

Bifactor model:

F1 by item1 item2 item3 item4;
F2 by item5 item6 item7 item8;
F3 by item9 item10 item11 item12
GF by item1 item2 item3 item4 item5 item6 item7 item8 item9 item10 item11 item12;

F1 with F2@0;
F1 with F3@0;
F3 with F2@0;

GF with F1@0;
GF with F2@0;
GF with F3@0;

Questions:
1) Would it be correct to estimate a bifactor model in which the factors (F1-F3) correlate with each other (and the variance of GF is fixed to 1 for convergence). This would make the most sense theoretically for me.
2) Would it be possible to estimate a model in which the specific factors (F1-3) correlate with GF? (seen this in a paper, but I don't understand why one would do this)
2) I've seen examples for bifactor models in which the variances of the factors are fixed to 1, why would one do this?

Thank you very much!
 Linda K. Muthen posted on Wednesday, July 31, 2013 - 9:26 am
It looks like your inputs are correct.

1. This is possible although not the traditional bifactor model. If you fix the variance of gf to one, you must free the first factor loading.

2. I don't think so and it does not make sense in my opinion.

3. There are two ways to set the metric of a factor -- fix a factor loading to one or fix the factor variance to one.
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