CFI vs TLI with categorical & contino... PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Joseph A. Olsen posted on Friday, October 01, 2010 - 11:35 am
I have a model with one dichotomous outcome, one dichotomous predictor (treated as a dummy variable), and 46 continuous indicators of 10 first-order and 2 second-order factors which serve as mediators. When the model is (incorrectly) estimated without declaring the outcome as categorical, I get the following results:

ML: CFI = .963, TLI = .959, RMSEA = .030, 188 free parameters.

However, when the outcome is properly specified as categorical, I get the following:

WLSMV: CFI =.005, TLI = .964, RMSEA = .050, 187 free parameters.

The difference in the number of free parameters is due to the fact that the residual variance and threshold of the dichotomous outcome are not separately identified with WLSMV.

It appears that the CFI and TLI use different baseline models when both categorical and continuous variables are analyzed. My guess is that CFI uses a baseline model which fits only the means and thresholds, while TLI uses a baseline which also fits the variances of the continuous variables. If this is true, one would recommend using the CFI under WLSMV only where all of the variables are categorical.
 Linda K. Muthen posted on Saturday, October 02, 2010 - 10:47 am
The baseline model is means and variances for continuous outcomes, thresholds for categorical outcomes, and means, variances, and covariances among observed exogenous variables. CFI and TLI use the same baseline model.
 Joseph A. Olsen posted on Saturday, October 02, 2010 - 10:28 pm
Thanks for the gentle correction. My speculation about the possible source of an observed extreme discrepancy between CFI and TLI was clearly misguided and I should have checked better before posting. A more direct comparison would have been between the WLSM (CFI = .967, TLI = .964, RMSEA = .050) and WLSMV (CFI = .005, TLI = .964, RMSEA = .050) results for the same model. The WLSM and WLSMV TLI, RMSEA, parameters, and standard errors were identical, so it is hard to see why there should there be such large CFI differences.
 Linda K. Muthen posted on Sunday, October 03, 2010 - 6:52 am
I would have to see the outputs to understand why the CFI values are so different. You can send them and your license number to I assumed the CFI value of .005 was a typo.
 Tracy Zhao posted on Thursday, March 10, 2011 - 5:32 pm
Hi Dr. Muthen,

I'd like to know if the CFIs produced by WLSM and WLSMV are always the same for CFA models. If not, why? Could you please also provide some reference on that?

 Bengt O. Muthen posted on Thursday, March 10, 2011 - 6:19 pm
No, because they are chi-2-based they vary as a function of the chi-2 value. Here is how we do chi-2 in the current version:
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