Fit indices for CFA with categorical ...
Message/Author
 Lena Catherine Quilty posted on Thursday, November 30, 2006 - 2:07 pm
I am aware that a CFA with categorcal indicators, using ULS estimation, only provides the chi-squared statistic as a measure of goodness of fit. Is there any way to calculate additional fit indices?
 Linda K. Muthen posted on Friday, December 01, 2006 - 9:48 am
I just ran a CFA with categorical indicators using ULS and I get all fit statistics. Perhaps you are using an older version of Mplus.
 Hyunzee Jung posted on Wednesday, March 12, 2014 - 6:28 pm
Hi!

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!!

Number of Free Parameters= 62

Loglikelihood

H0 Value -16281.545

Information Criteria

Akaike (AIC) 32687.090
Bayesian (BIC) 33009.470
Sample-Size Adjusted BIC 32812.523
(n* = (n + 2) / 24)
 Linda K. Muthen posted on Thursday, March 13, 2014 - 7:19 am
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.