"Robust RMSEA"

[Shu Fai Cheung (張樹輝)]

This post is on robust RMSEA, a follow-up to a previous post on robust CFI:

https://groups.google.com/g/lavaan/c/72fAZ1_NU5s/m/i6hS6qAqCgAJ

To my understanding, how the robust RMSEA, if printed, is computed depends on several factors, just like robust CFI. There are not one, but several, versions of robust RMSEA in the printout of lavaan output.

In teaching, I would like to provide the reference for a measure whenever possible. Therefore, I am trying to summarize my understanding, based on the version history and posts I located here, and the source code, to find the correct reference for each version of robust RMSEA.

This is what I recovered so far. (I used a format similar to the one I used in the previous post.)

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

- "satorra.bentler", "yuan.bentler.mplus", "yuan.bentler", "scaled.shifted". (This part is not important because this is usually determined by the estimator users used. Users rarely set this option directly.)

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

1) If all variables are categorical, the formula proposed by Savalei (2021) will be used. (Equation 6a).

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

2a) If scaled test statistics are requested for nonnormal data, V3 (version 3) is used

2b) If scaled test statistics are not requested, V6 (Version 6) is used.

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

3a) If "scaled.shifted" is in test, then Savalei (2018) will be used. (Eq 7?)

3b) If "scaled.shifted" is not in test, then Brosseau-Liard and Savalei (2012) is used. (Eq. 9?)

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

I am not 100% certain about my understanding and so I share the summary here. Please correct any mistakes I made. Please also feel free to suggest any better ways to present how robust RMSEA is computed in lavaan.

Thanks.

-- Shu Fai

Brosseau-Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate Behavioral Research, 47(6), 904–930. https://doi.org/10.1080/00273171.2012.715252

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

[joh4nd]

I am also curious about this and would perhaps consider looking at the source code on github.

Yet, regarding 2) and 3), I don't think FIML is used for categorial data, since that would imply polychoric correlations that allowed only listwise and pairwise deletion.

[Shu Fai Cheung]

Thanks a lot! You are right. The first condition should be

1) If at least one variable is categorical, the formula proposed by Savalei (2021) will be used. (Equation 6a).

In the source code, @categorical is checked to see whether it will do Case 1. It is TRUE as long as at least one endogenous variable is categorical, as far as I understand.

I believe I used "all" (the draft was done a while ago) because I were not sure whether the method by Savalei (2021) can be used when only some of the elements are polyphonic or tetrachoric correlations. I don't have the paper at hand. I will check later.

Thanks again.

-- Shu Fai

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[Shu Fai Cheung (張樹輝)]

This is another post, on robust RMSEA:

https://groups.google.com/g/lavaan/c/XUCs8mOo8vU/m/hYNm7zw7AAAJ

Please see my post below on "reviving" this old post:

https://groups.google.com/g/lavaan/c/72fAZ1_NU5s/m/5A22le11BQAJ

There are some mistakes in the conditions. I will try to fix them soon. But all are welcome to copy and correct them and then share them in this group.

-- Shu Fai