# Interpreting Random-effects Parameters results from a 3-level model

I am trying to interpret output from a 3 level HLM (city, school, individual). Would the following interpretation be accurate?

.0143922 is the variance explained between cities .006966 is the variance explained between schools .7206755 is the variance within schools/between subjects?

Output from Stata xtmixed:



------------------------------------------------------------------------------
Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
city_id: Identity            |
var(_cons) |   .0143922   .0088338      .0043218     .047928
-----------------------------+------------------------------------------------
school_id: Identity          |
var(_cons) |    .006966   .0026191      .0033338    .0145552
-----------------------------+------------------------------------------------
var(Residual) |   .7206755   .0074094      .7062988    .7353449
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 250.45                Prob > chi2 = 0.0000


The other thing to consider is whether these are conditional variances coming from a model in which you have included predictors or whether these are unconditional variances from a model without predictors. Often people calculate intraclass correlation coefficients from a model without predictors to get a sense of how much relative variation in the outcome is sitting at these different levels. In Stata, you can get ICCs using estat icc after your model.