Non-significant variance of latent variable when model fit is acceptable 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!

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.
