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Dear Linda and Bengt, I am fitting a multilevel model with moderation effects on the 2nd level. Because of a small number of clusters (17) and complexity of the model I use Bayesian estimator. The model seems to fit fine (based on traceplots), but there's one question that bothers me. Some of the residual variances are significant, although I can't see why this is the case. For instance, for the observed (2nd level) indicator X, I get the fully standardized variance estimate = .021, S.D. = .026, 95% C.I. = [0.001  0.096], yet the pvalue is .00. In another case, S.D. is also actually larger than the variance coef., and again, the pvalue is significant. This is only the case with the observed dependent variables on the 2nd level which seem to have very high loading into the. betweenlevel factor (around .989 and .992). For the other 2 indicators with lower factor loading everything seems to be fine. Please advice if I am missing something here. Thanks in advance for your feedback, Dmiriy 


Note that the Bayesian pvalue that is given is the part of the posterior distribution that is below/above zero for a positive/negative estimate. So your zero pvalue for the variance means that there is no part of the posterior that is below zero. I would simply report the 95% CI as you mention. 


Dr. Muthen, Thank you for your prompt reply. This makes perfect sense now. 

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