# Can I compare a just-identified model and an overidentified model?

As far as I understand, a just-identified model has zero degrees of freedom and its model fit indices do not make much sense. On the contrary, overidentified models have a meaningful chi-square, CFI, etc. Some researchers compare just-identified models to overidentified ones using these fit indices.

Is it justifiable to compare fit indices (such as CFI, root mean square error of approximation (RMSEA), standardised root mean square residual (SRMR), and chi-square) between just-identified and overidentified models given these models are nested?

I know I can do it using AIC and BIC. But what about CFI and other ones?

• Could you give an example of "Some researchers compare just-identified models to overidentified ones using these fit indices."
– Kuku
Jun 5, 2021 at 17:28

Most model fit indices for just-identified SEMs are not useful, such as CFI and TLI of 1.0 or $$\chi^2$$ and RMSEA of 0.0, so obviously for those measures it makes no sense at all to use them for comparing a just-identitied model to an over-identified model.
• You're welcome. Any book on SEM should go into this. Apart from books a good resource is the Stata documentation for sem/gsem which is availble for free. Also, David Kenny's website has lots of good info, such as this Jun 4, 2021 at 21:08