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

I wonder whether it is justifiable to compare fit indices (such as CFI, RMSEA, SRMR, 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?

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?