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I am running a confirmatory factor analysis with lavaan. I don't have any experiences with CFA, so I have one question regarding the output. My chi-square value is non-significant and all of the fit-indices are acceptable. All factor loadings are significant. However, I discovered that the variance of one of my latent variables is non-significant. I am not sure what this means for my model. Do I have to discard my model based on the non-significant variance of the latent variable, even though the overall model-fit is good? Or is it common to ignore a non-significant factor variance in such a case? I would be very grateful if somebody could help me, since I am not quite sure how to proceed.

Thank you very much in advance!

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It means that your latent variable isn't doing very much. You can (probably) remove that latent variable without the model fit getting much worse.

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  • $\begingroup$ Thanks for your response! As I'm still a beginner and it’s for my bachelor’s thesis, I have a follow-up question and I would really appreciate your input to that. I'm still confused about how it’s possible to get good fit indices and a non-significant variance of a latent variable at the same time. I understand from your response that the latent variable might exist, but it doesn’t explain very much – did I get that right? Is it still possible to keep the latent variable in the model? It is based on an established test, so I’d rather not discard the whole factor. Thank you for your time! $\endgroup$
    – guest0206
    Jul 2, 2021 at 8:36
  • $\begingroup$ Yeah, you can keep it. $\endgroup$ Jul 2, 2021 at 15:57
  • $\begingroup$ It suggests that it's not doing much though. If the theory says it should be there, it might be better to keep it. Imagine a dataset where all variables were correlated 0.05 - almost any model would give a good fit (by some fit measures). $\endgroup$ Jul 2, 2021 at 15:58

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