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I understand that scalar invariance, in the context of Structural Equations Modeling (SEM), is having the intercepts for observed variables loading on the same latent variable be invariant across multiple groups. However - what does scalar invariance mean substantially? What are its implications?

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It means that for the same score on the latent variable, people in the two groups do not have different intercepts on the observed variables.

Say you're comparing two racial/ethnic groups on a measure of ability that's used in job selection. You find that you don't have scalar invariance for one item. That means that one group finds one question easier than the other group. That means that if you take the total score, you're going to get a biased score. There's an example of that here: https://www.talentqgroup.com/media/84831/policy_assessment_and_the_law-march-2013-.pdf (look at the British Rail example).

Second example: You want to measure depression, so you ask about crying. Women cry more than men, whether they're depressed or not. Women are therefore going to get higher scores on the measure of depression, even if they're equally depressed.

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  • $\begingroup$ Related to the question, I was wondering the following. I am doing a CFA on 4 time points and the Latent Variable I try to measure is expected to change over time. Say if it does. Do you then expect to find a certain level in measurement invariance, or none at all? I am especially unsure of how to 'guarantee' (I realise you never really can) that I am still measuring the same construct over time, when the score of ppl on the latent variable might actually change over time. $\endgroup$
    – Amonet
    Mar 18 '18 at 12:20
  • $\begingroup$ You're right. I asked it as a question here: stats.stackexchange.com/questions/335284/… In case someone answers it might be useful to have the link here for other people interested in it. $\endgroup$
    – Amonet
    Mar 18 '18 at 20:17

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