I have constrained two models to be equal, and based on the $\chi^2$ test there is no difference between the models, they are invariant. These two models contain exactly the same path coefficients. However, the first model uses the data obtained at the 2nd month, and the second model uses the data obtained at the 4th month from the same participants.
I obtained the path coefficients in the
Mplus results for each model separately, and they are slightly different across the models. However, I get only one set of model fit indices.
How can I obtain two sets of results?
Also, when I run only one model instead of multi-group modeling, the path coefficients are different from what I have obtained for that specific model when doing multi-group model analysis.
Can anyone explain the differences between these models to me? Why do I get different results when they are constrained to be invariant in multi-group modeling? Should I report path coefficients values for two models?
If the $\chi^2$ difference test shows no significant difference across the models, does it make sense to combine all data and run a single model?