I ran a CFA model with four factors and categorical (ordered) indicators. The fit statistics that I got are shown below (copied from the output). It says that THE CHI-SQUARE TEST IS NOT COMPUTED BECAUSE THE FREQUENCY TABLE FOR THE LATENT CLASS INDICATOR MODEL PART IS TOO LARGE.
I wonder about how I can determine the fit of my model to the data (just like I do with CFI, RMSEA, or Chi-square) since I do not compare this model to any other models here. Thank you!!
It sounds like you are are using maximum likelihood estimation. In this case, chi-square and related fit statistics like RMSEA, CFI, etc. are not available. Two chi-squares comparing observed versus estimated frequencies are computed when the frequency table is not too large. Generally these values should not be interpreted for more than 8 categorical indicators and should not be interpreted if the two do not agree. There are no absolute fit statistics in this situation. Nested models can be compared by using -2 times the loglikelihood difference which is distributed as chi-square.