I have 8 binary observed variables and I would like to compare several CFA models (1 to 3 factors; not all nested). It is a twin sample so I plan to use TYPE=COMPLEX and a CLUSTER variable to adjust for non-independence of observations.
First, I wanted to confirm that I cannot compare non-nested models using WLSMV. Further, when using MLR, BIC should be used to compare non-nested models, and the S-B x2 difference test (or logliklihood values and scaling factors) should be used to compare nested models?
Next, I gather that there is no way to evaluate overall model fit using MLR. I attempted to run the same models using WLSMV to evaluate model fit, but got an error (Theta is not positive definite; a correlation between factors greater than one; model may not be identified). Does this necessarily indicate a non identified model? Are DF calculated differently when using WLSMV vs MLR?
Finally, one of the models involves a factor with a single binary indicator. I intended to fix the residual variance to reflect the reliability of the scale; however, I have realized that this is not appropriate for binary indicators. What would you recommend? Is this appropriate? F1 BY b1* b2 b3; F2 BY b4* b5 b6 b7; F3 BY b8*; F1@1; F2@1; F3@1;
There is no way to compare non-nested models using WLSMV. With MLR, BIC can be used to compare non-nested models that have the same set of dependent variables and -2 etc. can be used to compare nested models.
There are no absolute fit statistics for MLR and categorical outcomes.
Currently degrees of freedom are calculated in the same way for WLSMV and MLR. Send the output and your license number to firstname.lastname@example.org regarding teh error message.
If you have a single-indicator, you should just use it in the analysis. Making a factor equivalent to it serves no purpose.