It's not an expectation that invariance var/covar will hold, just that some indicators are better than others for making direct comparisons. If yr making direct comparisons at latent level, at least quantifying the bias introduced by nonvar. is an inescapable requirement.
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“Some items are better than others for making direct comparisons... at the latent level”. You’re saying the diagnosis of this isn’t based at all on x-group item variance or covariance? In any case, direct comparisons of what? Delta? I also have probs w/ IRT voodoo assumptions.
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A great set of thoughts on the new requirement of “measurement invariance” in x-cultural research
I would go further: if u expect the same pattern of variance or covariance across populations, u haven’t thought about how the mind works
Down with our psychometric overlords