WLSMV for latent moderated SEM using product terms?

[ahmad]

Hi,

Is the WLSMV estimator suitable for latent moderated SEM using product terms (i.e., continuous indicators × binary/ordinal indicators)?

Best,

A  

[Terrence Jorgensen]

Is the WLSMV estimator suitable for latent moderated SEM using product terms (i.e., continuous indicators × binary/ordinal indicators)?

Generally, no.  Because you cannot calculate a product with a latent response underlying an ordinal indicator, the product indicator approach is only available if you are willing to treat the ordinal indicators as continuous (i.e., treating whatever arbitrary numerical weights you assign to each category as though they were real numbers). 

A somewhat arbitrary exception could be made for a single dichotomous variable, representing groups across which you want to test invariance.

https://doi.org/10.3758/s13428-018-1151-3

https://doi.org/10.1007/978-3-319-77249-3_20

But I don't think this is the situation you are thinking of.

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

[Alex Schoemann]

If you have the items to parcel (and several categories per item) then a parceling method, first parcel item, then compute product term, may be an option:

https://pmc.ncbi.nlm.nih.gov/articles/PMC7047260/

https://doi.org/10.1080/10705511.2025.2487678