[R] Question about measurment invariance in a multigroup SEM

[Paul Miller]

Hello All,

I have a question about measurement invariance in a multigroup SEM. I am of the impression that one cannot test the equality of structural paths across groups without demonstrating measurement invariance of latent factors first. At a minimum, this would involve demonstrating that corresponding factor loadings do not differ across groups using, say, a difference in chi-square test. 

Am I right about this? 

Is there any published work that argues it is possible to compare the structural paths without demonstrating measurement invariance first?

Thanks,

Paul