WLSMV output, standard/scaled/robust estimates and chatGPT

Stephen

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Jun 14, 2025, 7:18:52 AM6/14/25

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Dear all,

Apologies if this topic has been discussed before, I've searched the forum and read the threads about this and I still don't quite understand.

I'm a PhD-student and a novice regarding R and CFA. I've been reading alot of articles and asked chatGPT in order to try and understand the output of my CFA using WLSMV since my data is ordinal. From what I understand the WLSMV estimator is using scaled test statistics and therefore should give me a "robust" estimate. But I don't understand what value I am supposed to use in the output (see below). And why are they different? Specifcally I am becoming increasingly confused since I don't feel like a can confirm what chatGPT is saying. I can't find what methods are used in the lavaan package, or I don't understand when reading the articles. Below I will share the output, and what chatGPT says about these estiamtes. Is chatGPT correct?

R output:

ChatGPT answers

Apologies if this question isn't appropriate for this forum, I'm new here.

Thank you!

Combasco

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Jun 15, 2025, 5:52:46 AM6/15/25

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Dear Stephen,

Let me begin by saying I'm also a complete beginner in the field of CFA and R.

I have however scoured this forum before because I've had a similar issue to yours (the same problem but with multiple imputed data (CFA.mi) instead of a normal CFA).

You're right that quite a few forum posts already exist about this topic. They might help you further:
https://groups.google.com/g/lavaan/c/M-dXvCVrH34

https://groups.google.com/g/lavaan/c/rhxtAgeg0uk

https://groups.google.com/g/lavaan/c/JJTVgrDAXmA

https://groups.google.com/g/lavaan/c/DlVaoP41MyI

https://groups.google.com/g/lavaan/c/GcCIQ5Bgcwc

From what I've gathered, the following happens.

Chisq is used as the basis for the formulas for CFI, TLI and RMSEA.

SRMR is always the same. This is robust as-is so everywhere you see it, it should be the same value.

Standard CFI, TLI and RMSEA use the standard chisq and their standard formula's.

This is not the correct way to go about it when dealing with WLSMV data because the calculations assume normality (among other things) and ordinal data isn't normal.

The scaled variants use a robust version of chisq (a 'mean and variance adjusted chisq to account for non-normality'), this version is called the scaled chisq.

However, this scaled chisq is used in the 'normal' formula's for CFI, TLI and RMSEA. i.e. a robust variable is used in a non-robust formula.

This estimation is better, which is why you should rapport this instead of the standard variable if you only have these two, but it still isn't completely legit so you should instead report the robust variable if it's available.

Now with these robust indices I myself am still quite confused.

As most of the forum posts will tell you, they never existed as: "The correct calculation of robust fit measures proposed by Brosseau-Liard & Savalei has only been proposed for mean-adjusted chi-squared statistics (estimators MLM, MLR, WLSM, ULSM), not mean- and variance-adjusted (or "scaled & shifted") statistics (estimators MLMV, WLSMV)." (by Dr. T. Jorgensen)

However, recently I've also found robust fit statistics in my estimations. I'm guessing some new update incorporated true robust calculations. How these work I have no idea.

When asked about this though, Dr. T. Jorgensen did give me these links.

http://dx.doi.org/10.1080/00273171.2012.715252

http://dx.doi.org/10.1080/00273171.2014.933697

In any case: you should always report the robust statistic, if that's unavailable the scaled statistic, and if that's unavailable the standard statistic, but this one needs big asterisks on them as ordinal data violates the normality assumption.

Hopefully this clears it up somewhat!

Best of luck to you,

Tim

Op zaterdag 14 juni 2025 om 13:18:52 UTC+2 schreef Stephen:

Stephen

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Jun 15, 2025, 11:36:47 AM6/15/25

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Thank you, Tim!

Your input aligns with what I've come to understand as well. My problem right now is that I don't actually know what logic the robust adjustments are using. I spoke to a statistician about this who told me that I could view the output different levels of robustness. The standard values aren't adjusted for non-normality at all, the scaled values adjusts for moderate departures from normality and the robust values should be used when data severely violates normality. I am currently trying to book a new meeting with our statistician to unpack this further, because obviiously I don't feel confident in what values to present.