I am wondering which is the best estimator to use for my data in a CFA. Some of my indicators for the latent factor are categorical and some are continuous. I was hoping to use ML to best account for missing data but when I run this with categorical variables it does not give me the CFI/TLI or RMSEA. What is the best way of assessing model fit in this situation? Or would you recommend I use WLSMV as the estimator instead?
If you want fit statistics like chi-square and related measures, you should use WLSMV. If you have a lot of missing data, you should use maximum likelihood. For each factor with categorical indicators and maximum likelhood, one dimension of integration is required. This is also true for residual covariances among categorical indicators. If you have more than four, you should consider weighted least squares.
There are no absolute fit statistics when means, variances, and covariances are not sufficient statistics for model estimation. You can compare nested models using -2 times the loglikelihood difference which is distributed as chi-square or you can compare models with the same set of dependent variables using BIC.
My question is - what is the best estimator to use for the CFA? I have read a lot on line and it seems that MLR is suggested but does not give the fit statistics I usually use (RMSEA, CFI, TLI). Is WLSML inappropriate? Or is there some other estimator you would recommend? Please advise.