Two robust fit measures with MLR

[nika....@gmail.com]

Hello,

I have a question regarding the output of confirmatory factor analysis conducted with MLR estimator. I get two robust results for RMSEA, CFI and TLI - one in the column "Robust" and one in the same column, but called "Robust ...". Here is an example for CFI and TLI:

Estimator                                                    ML      Robust

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.913        0.962

  Tucker-Lewis Index (TLI)                        0.860        0.940

  Robust Comparative Fit Index (CFI)                         0.960

  Robust Tucker-Lewis Index (TLI)                             0.936

Since these two are different (and they are both different from the ML non-robust version), I'm wondering which one to report and what's the difference between them?

Thanks!

[Yves Rosseel]

On 11/23/2016 04:30 PM, nika....@gmail.com wrote:
> Since these two are different (and they are both different from the ML
> non-robust version), I'm wondering which one to report and what's the
> difference between them?

The 'robust' seems to be the better one. See:

Brosseau-Liard, P. E., Savalei, V., and Li, L. (2012). An investigation
of the sample performance of two nonnormality corrections for RMSEA.
Multivariate behavioral research, 47(6), 904-930.

Yves.

[nika....@gmail.com]

Thank you for the reply and the article.

[nika....@gmail.com]

Just one more quick check: you meant that "Robust Comparative Fit Index (CFI) = 0.960" is better (since both are "robust")?

[Terrence Jorgensen]

Just one more quick check: you meant that "Robust Comparative Fit Index (CFI) = 0.960" is better (since both are "robust")?

Yes, that is the better one.  The one on the regular CFI line in the "Robust" column (0.962) is the naïve calculation, which is not population-consistent.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Nikola Ćirović]

Hello! A follow-up question on reporting practices. Is it then that an author has to report that he/she used "robust CFI" rather than just writing  "CFI" (I am talking only about those using MLR). Because I somewhat rarely come across authors (talking about assessment/measurement journals) that specify to have used "robust CFI/RMSEA/TLI", does that mean that others use naive ones or that people generally take the robust one only rarely be specific about stating it? 

[Terrence Jorgensen]

Is it then that an author has to report that he/she used "robust CFI" rather than just writing  "CFI"

I would cite the Brousseau-Laird et al. paper(s) that clearly describe(s) which CFI(/RMSEA) formula you are using.

https://doi.org/10.1080/00273171.2012.715252

https://doi.org/10.1080/00273171.2014.933697

https://doi.org/10.1080/00273171.2018.1455142

(I am talking only about those using MLR)

It is the same formula used with MLM and MLR (which are asymptotically equivalent, only the latter is available with incomplete data).  

does that mean that others use naive ones or that people generally take the robust one only rarely be specific about stating it? 

Without a citation or sufficient description, who can tell?

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Nikola Ćirović]

Dear professor Jorgensen, thank you for a quick reply and the literature. 

Reading these papers you gave, I too would expect a citation for robust incremental fit indices ("robust CFI") or specific statement to avoid confusion, whereas I would expect to find scaled ones if an author reported only "CFI" or "RMSEA" obtained under some robust ML estimation without a citation or without specifying that they are robust ones - the majority of papers I see.  But I had to check whether I am unaware of research practice that goes on (i.e. switching scaled for robust without saying so).  Especially since I do not know what other programs give in their outputs while lavaan provides all (so I thought you were the guys to ask).

Thank you once again.

среда, 23. новембар 2016. 16.30.40 UTC+1, Nika је написао/ла: