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I‘m wondering what is the best way to test measurement invariance on data with small N, since CbSEM requires at least N = 200, or 5 - 10 cases for each indicator. For example I want to test a reflective model (scale had been previously published and is well known in literature) with two latent variables and 32 indicators. I have two groups with n1 = 47 and n2 = 58. How to proceed best for testing model fit and measurement invariance here or is there any possibility?

Thanks!

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It doesn't require 5-10 cases per indicator to run, these are recommendations. It will run with fewer cases. However, the results might be less meaningful - and you won't be able to make strong statements about the absence of measurement invariance.

Therefore, the best way is to do whatever you would have done, but accept that you don't have power to detect measurement invariance.

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