Robust CFI

[Shu Fai Cheung (張樹輝)]

I understand that how the row "Robust CFI" is computed depends on several factors. I am trying to summarize my understanding, based on version history and posts I located here. I am not sure if I overlooked or misunderstood anything. Please correct me if I am wrong, and feel free to copy and update the summary.

First, if any of these is in `test` (see lavOptions), robust CFI will be printed

- "satorra.bentler", "yuan.bentler.mplus", "yuan.bentler", "scaled.shifted".

How robust CFI is computed will then be determined by these steps:

1) If all variables are categorical, the formula proposed by Savalei (2021) will be used.

2) If not all variables are categorical but FIML is used for missing data, then Zhang and Savalei (2022) will be used.

3) If not all variables are categorical and FIML is not used for missing data, then

 3a) If "scaled.shifted" is in test, then Savalei (2018) will be used.

 3b) If "scaled.shifted" is not in test, then Brosseau-Liard and Savalei (2014) is used.

I am not 100% certain about my understanding. Please correct any mistakes I made.

I did not use MLM, MLMV, etc. because they are shorthand to set settings. It is more precise, to me, to use the factors above.

I believe the steps are similar to TLI. I would like to have a similar summary for RMSEA but I would like to start with CFI first.

-- Shu Fai

Brosseau-Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indices for monnormality. Multivariate Behavioral Research, 49(5), 460–470. https://doi.org/10.1080/00273171.2014.933697

Savalei, V. (2018). On the computation of the RMSEA and CFI from the mean-and-variance corrected test statistic with nonnormal data in SEM. Multivariate Behavioral Research, 53(3), 419–429. https://doi.org/10.1080/00273171.2018.1455142

Savalei, V. (2021). Improving fit indices in structural equation modeling with categorical data. Multivariate Behavioral Research, 56(3), 390–407. https://doi.org/10.1080/00273171.2020.1717922

Zhang, X., & Savalei, V. (2022). New computations for RMSEA and CFI following FIML and TS estimation with missing data. Psychological Methods. https://doi.org/10.1037/met0000445

[Shu Fai Cheung (張樹輝)]

Hi All,

Some recent posts reminded me of this old post of mine. It's good that lavaan adopted some new ways to compute the robust measures. However, it is sometimes not clear how a robust measure is computed or the source of the method used, such as a reference to the method.

It would be nice to have the information available in the output or the help page. However, it seems that, for now, the information is officially only available in the version history (please correct me if I am wrong). Yes, they can be found in this group, too, but the original source is usually the version history.

The information would be useful for users who would like to know how things are computed, and for users who may wonder why the values are different from those in other SEM programs.

I would be happy to contribute to this topic, a post or an update to the help page of lavaan, as my memory is bad, and it will be useful to me too. However, as demonstrated in the previous post of mine, it is not easy. Therefore, I would like to make sure that I understand correctly how lavaan decides what measure to compute before doing anything. (And that post is old, and there may be updates I missed.)

-- Shu Fai

[Yves Rosseel]

I have now added a 'Details' and 'References' section to the man page of
fitMeasures(). If you have further suggestions on how we can improve the
manual page, let me know (or send me a pull request).

Yves.

--
Yves Rosseel
Department of Data Analysis, Ghent University

[Shu Fai Cheung (張樹輝)]

The updated manual page makes it easier for me to explain why the robust indices should be used whenever reported, and also makes it easier for students to find the references if they want to learn more about those indices. I was asked many times what those numbers are, and it is understandable because they don't see these numbers in other SEM programs. I can now refer them to the manual page.

Thanks a lot!

-- Shu Fai

[Michael Filsecker]

Thank you for that too Prof. Rosseel, I read the information and helps a lot to understand lavaan procedures.

Michael.

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