When models are nested you may compare the fit and df?s of these models to determine which model is preferred. A nested model which has more degrees of freedoms will always have equal or higher value of ?2ll than the more saturated model. If the difference in ?2ll?s is not statistically significant for the difference in df, the model with the most degrees of freedom is preferred.
The difference in ?2ll?s between two models follows a chi-square distribution and p-values can be found in regular statistical tables. You can also ask Mx to compare models with ?option multiple issat?.
For example:
the ACE model has a ?2ll of 10.60 and 250 df
the CE model has a ?2ll of 11.50 and has 251 df
The difference between the ACE and CE model is 0.90 chi-squared, with 1 df. This is not a significant worsening of the fit (p= 0.34) and the CE model is preferred over the ACE model.