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For RMSEA there seems to be a regular value and two robust values. Are there any recommendations on which of the three values to report? Would you report 1, 2 or 3 from lavaan?

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Mar 26, 2022 at 23:34

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I think this is not a question for CrossValidated because it is about norms for reporting, not the statistics. But I also don't think the choice between these versions of RMSEA has anything to do with scale development. For more information about differences among the 3, you can read this article:

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

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  • $\begingroup$ Actually there is a reporting tag here so at least from my perspective it is still on topic given it still relates to statistics. $\endgroup$
    – Shawn Hemelstrand
    Commented Mar 2 at 10:44
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I agree with @Terrance that the choice between the three versions of RMSEA does not have anything to do with scale development. That being said, I do believe I can clarify a couple of things.

First, in order to give a recommendation on which version of the RMSEA to use, I would need to know more. For example, is your data categorical? I assume yes, because most scales contain categorical data (e.g., responses to items that are dichotomously scored as correct or incorrect, or a Likert scale). If your data is categorical, then certain robust RMSEA variants may not be appropriate, as some were developed specifically for models fit using ML. For more information on this, see Savalei (2018)¹.

Second, while goodness-of-fit (GOF) indices such as the RMSEA are commonly used for scale development, many disagree. For example, Thissen (2013) touches on this, and while the article pertains to item response theory (IRT), his insights are equally applicable to confirmatory factor analysis (CFA) models used for scale development.

$^1$ The reference @Terrence provides, Brosseau-Liard, Savalei, and Li (2012), is also a good resource.

References

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.

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.

Thissen, D. (2013). The meaning of goodness-of-fit tests: Commentary on “Goodness-of-fit assessment of item response theory models”. Measurement: Interdisciplinary Research and Perspectives, 11(3), 123-126.

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To add to the pile here, there have been a number of recent simulation studies which have studied the properties of the typical fit indices in CFA which you may find useful to look at in addition to what has already been said. As noted by Preston, there are certain characteristics of your data which may shape what normal or robust estimators say. In short, even the normal indices change a lot depending on the context.

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