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I am comparing different models in Confirmatory Factor Analysis (CFA) to decide what my optimal number of factors and factor structure should be. The main indices I have been using are chi square , Comparative Fit Index (CFI) , RMSEA and Incremental Fit index (IFI. I am aware that there is cut off values available for these indices. However, I am unsure if there is any way of saying statistically if one of the models is better than the other.

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