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Anonymous posted on Wednesday, May 12, 2010  3:55 pm



I am testing a CFA model for measurement invariance. If the loadings for a particular measure cannot be constrained, is it appropriate to try to constrain the error variances for that measure? 


I think you are asking whether you should test for invariance of residual variances when you don't have factor loading invariance. I don't think so. 

Jon Heron posted on Friday, May 14, 2010  5:21 am



In Timothy Brown's book on CFA he discusses partial measurement invariance and what is possible if not all loadings can be constrained. I assume you're talking about invariance over two groups. He references Byrne et al (1989) so this might be worth a look if you're not lucky enough to have access to Tim's book. Byrne et al (1989) Psychological Bulletin, 105, pp 456466. Hmm, that last author sounds familiar. 

Anonymous posted on Friday, May 14, 2010  10:51 am



Thank you both for the info! I will check out the Byrne article and hopefully gain some insight on how to proceed. 


I am testing measurement invariance with a bifactor model where every item loads on the main factor and one of two item group factors (binary indicators). Along the lines of the section on partial measurement invariance in chapter 13 of the User’s Guide, if I find that the loading for an item on one of the two factors is not invariant, would you recommend that I relax the equality constraint on the other factor in addition to relaxing the equality constraint for the threshold to test for partial invariance? Thank you very much for your assistance. 


I can see going either way, but I would probably do what you mention. 


Hello, in a multigroup configural invariant model with categorical indicators, latent means are zero in all groups. In a multigroup measurement invariant model with categorical indicators, latent means are freely estimated in the nonreference groups. What about the scenario of partial measurement invariance (where some loadings and thresholds are constrained across groups and others not)? Should the latent means be set at zero or freely estimated in the second and third groups (the nonreference groups)? It seems that setting the means to be zero in the nonreference groups creates a linear dependency (possibly through the thresholds)? Thank you. 


With partial measurement invariance, the means are zero in one group and free in the others. See Slide 170 of the Topic 2 course handout. 


Thanks, Linda. Yes, the slides were helpful, along with trial and error in Mplus to see what the program is doing by default. Thanks again. 


The multiple group defaults are described in Chapter 14 of the Mplus User's Guide under Multiple Group Analysis. 

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