I'm suspicious about "perfect fit" in my SEM path analysis, with fit indices of CFI = 1 and RMSEA = 0 which I would expect from an just-identified model. However, since I have 3 degrees of freedom, the model is over-identified. What might this indicate?
Hello Björn,
these happen usually when you have a non-significant chisquare test. Perhaps you can tell a bit more about your model in order to better evaluate it.
Best,
--Holger
Hello Holger and thanks for your response!
I've attached a screenshot outlining the model and this would be the lavaan-summary:
Model estimates show substantial effects and R^2 for Y == .812, so maybe it's not entirely inconceivable that RMSEA and CFI approximations are trustworthy?
Thank you and best wishes
Björn
EDIT NOTE: Something went wrong when I made the screenshot. The exogenous variables are labeled A, B & C
Björn,
as it seems, the 3 df come from the 3 predictors being uncorrelated (as the structural model is saturated). Hence, the only thing your are testing is whether these restrictions hold. It seems that this is the case. But the bad side of the story is that the good fit does not really provide a good basis for evaluating the correctness of the specified effects as there will be hundreds (literally) of alternative models with different arrow directions which would lead to the same fit.
Best,
--Holger
One thing as you asked bout whether the CFI and RMSEA are trustworthy. Yes, of course but the main questions in every model testing/evaluation situations are
a) what exactly is being tested (i.e. what the tested data implications of the model)
b) which equivalent models (models with other directions of effects) would have the same data implications
If a model fits well but you have ton of other models that would lead to the same fit, then this is no real support for the model.
HTH
Holger
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