Hello
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
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Let me see if I understand what you are asking.
It appears that your RMSEA is poor for models with restrictions, but isn't poor for the saturated model.
There is a significant difference between AIC of the saturated model and the restricted model.
The saturated model, by definition, fits the best of any possible model.
Thus your restricted models fit worse (not better) than the saturated model. This is the significant difference in AIC. So both RMSEA and AIC are reporting the same thing: Your restricted models fit more poorly than one would expect for a given number of degrees of freedom.