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:
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.
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.
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.