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

[Sara]

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.

Thank you in advance!

[Terrence Jorgensen]

 

• Metric: equal thresholds across time.

This is threshold invariance.

 

• Scalar: equal thresholds and loadings across time.

This is metric invariance.  Scalar invariance additionally equates intercepts. 

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?

Different methods of scaling common factors yield identical fit. 

https://doi.org/10.5964/meth.10177

 

• Are Cheung & Rensvold (2002) (ΔCFI ≤ .01) and Chen (2007)  still appropriate?

They never were.  This is not what fit indices were designed to inform us about.

 

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

There are numerous posts on this forum about identifying DIF and quantifying its impact.  For example:

https://doi.org/10.1093/pan/mpt014

https://doi.org/10.1093/pan/mpv020

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen