Question about model identification and constraints in a 3-factor model

[Thanh Le]

Dear GenomicSEM team,

I am fitting the following SEM:

F1 =~ T1 + T2 + T3 

F2 =~ T4 + T5 + T3 

F3 =~ 1*F1 + 1*F2 

F3 ~~ a*F3 

a > .001 

F1 ~~ 0*F2

The traits loaded onto each factor were selected based on EFA loadings, using a threshold of ≥ 0.3. In the EFA results, the three-factor model did not appear to substantially increase the percentage of variance explained compared with the two-factor model.

Because I am interested in the shared genetic liability across all traits, I specified F3 as a higher-order factor on which GWAS can be performed. However, for the model to be identified, two fewer parameters need to be estimated, so I fixed the loadings of F1 and F2 onto F3 to 1.

Could you please advise whether this constraint is technically acceptable in GenomicSEM?

Thank you very much for your help.

Best regards,

Thanh