how to proceed after finding partial metric invariance

[Laura]

Hello all, 

I conduct measurement invariance testing for a 5-item-scale. I now found partial metric invariance. If I loose constrains on one of my five items (its a one-factor model) the partial metric model is fine. My question now is: do I keep this argument , the loose constraint for the one item when I test for scalar invariance? and can i therefore inherently only find partial scalar invariance too, since the models are nested? 

my code for the metric partial invariance is: 

cfa.metric.par <- cfa(modelB, data = mi, estimator = "DWLS", group = "SD01", group.equal = c("loadings"), group.partial = "f1=~item2")

so is my model for scalar invariance testing now option one or two?

1. cfa.scalar.par <- cfa(modelB, data = mi, estimator = "DWLS", group = "SD01", group.equal = c("loadings","intercepts"))

2. cfa.scalar <- cfa(modelB, data = mi, estimator = "DWLS", group = "SD01", group.equal = c("loadings","intercepts"), group.partial = "f1=~item2")

Same goes for strict invariance of course. Do I stop analysing once partial invariance is found in one step? Or can I theoretically report partial metric invariance because of the 1 item, but (full?) measurement invariance in total (with regard of the factor loads of item 2)? 

Thanks so much!

Laura 

[Edward Rigdon]

Laura--

Scalar invariance implies metric invariance, so if full metric invariance fails then full scalar invariance has already failed.

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[Laura]

Dear Edward,

Ok understood, so can I still test for partial scalar invariance when I release the constrains of the one item again? same goes for strict then i guess? Thanks already! 

Laura 

[Edward Rigdon]

There is also the alignment method for assessing measurement invariance:

https://journals.sagepub.com/doi/pdf/10.1177/0049124117701488?casa_token=lw5D5BpZU-UAAAAA:UsuZnlH2waGoMCpDKmPhhkHkWk3B9kX3zxEpdGQoxNGYkyZpYJUxuVgkJC6Kh3oFCwClP89RzMqX

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/027b7fc5-34d3-40ba-9f42-8d1095e2b4den%40googlegroups.com.

[Maria]

Hi Laura,

you could look for modification indices to get an idea which constraints should be released to test for partical scalr invariance and look if the model fit improves.

Maybe this helps : "Improving Multiple-Group confirmatory factor analysis in R – A tutoria" by Gerrit Hirschfeld and Ruth von Brachel (umass.edu)

Best

Maria

[Terrence Jorgensen]

so can I still test for partial scalar invariance when I release the constrains of the one item again?

Yes, but you would already allow intercepts to differ for any items without equal loadings.  So you would only test for additional uniform DIF of items whose loadings are equal.

same goes for strict then i guess?

Not necessarily.  You can still validly test equality of residual variances.  But if that equality holds, it wouldn't really be "strict invariance" if equality of loadings doesn't hold.

 

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen