I am trying to better understand the output for a multi-level mixed effects model. Specifically, I am confused on how to interpret the random-effects parameters, and the random effects variance. Is there something I should look for here to confirm the model is working as it should? And should I report this value in an output table, or is it more of an embellishment to include?
Parameters for _cons being a random effect means that the model assumes it to be a Gaussian random variable with a mean equal to zero and variance equal to var(_cons). The parameters for each of the levels of _cons are assumed to be realizations of this random variable. So this is what the model estimates. Check the What is the difference between fixed effect, random effect and mixed effect models? thread or one of many books for more details. The variance would be "wrong" if it would be zero, infinite, or not a number, but otherwise, the values would depend on your model and the data.
