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 p-value is .00. In another case, S.D. is also actually larger than the variance coef., and again, the p-value 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. between-level factor (around .989 and .992). For the other 2 indicators with lower factor loading everything seems to be fine.
Note that the Bayesian p-value that is given is the part of the posterior distribution that is below/above zero for a positive/negative estimate. So your zero p-value 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.