I am trying to run a third-order factor CFA with TWO second-order factors both of which have TWO first-order factors each. I understand that this model is not directly identified but I have substantive reasons to suggest such a model. Moreover, I have come across articles where similar models were run. Could you please advice on the appropriate syntax to use that would return an output without errors?
For the second-order model, this is the syntax I feel is most reasonable:
Model: f1 by sglse41 sglse42 sglse67 sglse76 sglse100 sglse30 sglse40 sglse55 sglse83 sglse92 sglse97 sglse102; f2 by sglse3 sglse17 sglse25 sglse68 sglse35 sglse58 sglse78 sglse84 sglse94 sglse96 sglse98;
f3 by f1* f2; f3@1; Output: Sampstat standardized mod;
For the third-order model, this is the syntax I feel is most reasonable:
Model: f1 by sglse3 sglse17 sglse25 sglse68; f2 by sglse41 sglse42 sglse67 sglse76 sglse100; f3 by sglse35 sglse58 sglse78 sglse84 sglse94 sglse96 sglse98; f4 by sglse30 sglse40 sglse55 sglse83 sglse92 sglse97 sglse102;
A second-order factor must have a minimum of three first-order factors to be identified unless you place a restriction on the model such as having both factor loadings equal to one. The model with three second-order factors may be identified by borrowing from other parts of the model.