The general question is: If Model 1 has a certain structure, and in Model 2 you free some of the parameters, and fix others, are the models nested?
Specifically in the case I'm dealing with:
One model is a bifactor model (see Reise, 2012), but with two 'general' factors, and the specific-level factors correlated. So: My indicators each load on two factors - 1 of 6 specific factors, and one of 2 'general' factors. The correlations within the specific factors are free.
The second model removes the correlations within the specific factors (i.e., fixes them to zero) and adds a truly general factor (so that all the indicators load on it; so the loadings are freed compared to the previous model).
Are these models nested?
Figures of the models: