Measurement invariance with ordinal Likert items (WLSMV, marker method, cut-off criteria)

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Sara

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Sep 3, 2025, 11:22:30 AM (4 days ago) Sep 3

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Dear all,

I am testing longitudinal measurement invariance with ordinal indicators in lavaan. My procedure is:

Configural: freely estimated (no equality constraints on thresholds).
Metric: equal thresholds across time.
Scalar: equal thresholds and loadings across time.

I am using the WLSMV estimator with the ordered argument since I am dealing with Likert-type items. Now, I have been asked to use the marker method (fixing the first loading = 1 in all waves) for identification.

Previously, I had followed Rutkowski & Svetina (2017) and their cut-offs and found both metric and scalar invariance for my 1-factor model, so I proceeded to compare latent means.

My question:
When I use the marker method (fixing the first loading = 1) instead of std.lv, which cut-off criteria should I rely on for judging invariance?

Are Cheung & Rensvold (2002) (ΔCFI ≤ .01) and Chen (2007) still appropriate?
Or should I rely on Svetina criteria, even though they are usually discussed in the context of std.lv identification?

Any advice on how to justify the choice of cut-offs when using the marker method with ordinal data would be very welcome.