I am trying to fit multigroup models with 15 groups. When I want to assess the fit of my models, I encounter problems :
(1) on one hand, the fit measures like Chi or RMSEA are never good for any model different from the saturated model
(2) on the other hand, if I compare the AICs of nested models I can see that the saturated model can be improved by removing or setting equal among groups many paths. As far as I understand, the saturated model is just the more parametrized model that can be wrotten, so I can compare its AIC with that of nested models, with some path removed or setting equal among groups, is that wright ?
I suppose my problem comes from the fact that with 15 groups, every restriction on the model result in many ddf : If for instance, I specify that the covariance between A and B is either the same among groups, or nul, I 'save' 14 or 15 ddf. As a result, the difference in ddf between the saturated model and the model of interest is high (464). Can it explains why the difference in AIC is very significant (DelatAIC = 68.29, whereas the RMSEA is quite bad = 0.13 ? Or is there anything that I didn't catch in how I must assess the model fit ?
Thank you in advance