Understand CFA index output

General
1

Hi everyone,
I'm using the Satorra Bentler test while doing the CFA for my model like this:
fit <- cfa(model = model, data = data, estimator= "MLM", test="satorra.bentler"
but I'm a little confused about the output I'm getting:

		                                             Standard    Robust
Comparative Fit Index (CFI)                           0.717       0.894
Tucker-Lewis Index (TLI)                              0.799       0.879
                                                                  
 Robust Comparative Fit Index (CFI)                               0.872
 Robust Tucker-Lewis Index (TLI)                                  0.864

What is the difference between CFI under the robust 0.894 value and the one next to Robust Comparative Fit Index (CFI) which is 0.872?
Which one should I use and why?
Thank you and I apologize for my english.

2

Don't. English is a language used worldwide by first-tongue and learned speakers and writers. The purpose of every language is to communicate, and that requires effort on both the initiating and receiving end. The post doesn't present any obstacles to understanding except only the implicit assumption that the cfa function is from the lavaan package.

The four index results apply different algorithms. The robust versions take into account departures in the data of the multi-variate normality assumption required for validity of the non-robust varieties and the whether variables or ordinal categories.

Whether to select one over the other depends on the reasonableness of the normality assumption and the degree of bias inherent in the robust methods as the number of variables becomes small. See the wiki

3

Thank you so much for your reply!
I'm dealing with dichotomous variable so I think I should go for the Robust Comparative Fit Index (CFI) .872 indices, did I understand it correctly?
Since my variable is dichotomous I've also tried using Robust Weighted Least Squares (WLSMV) and I've got this output:

Standard      Robust
Comparative Fit Index (CFI)                    0.987       0.815
Tucker-Lewis Index (TLI)                       0.968       0.801
                                                              
Robust Comparative Fit Index (CFI)                           NA
Robust Tucker-Lewis Index (TLI)                              NA

I don't quite understand why this time I've got an NA answer. Also the standard (CFI) 0.987 (TLI) 0.968 should be the results of DWLS estimator while the (CFI) 0.815 (TLI) 0.801 indicate Robust Weighted Least Squares, is it right?
I do feel a lot confused so I'm really grateful for all your help.
Thanks again!

4

This tutorial may help in the absence of a reprex that allows the model to be examined.

5

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