Survey for multilevel models
Stata 14 now provides survey-adjusted point estimates, standard errors, and tests for multilevel models. That includes adjustments for stratification, clustering, sampling weights, and finite-population corrections.
You can now use Stata's svy: prefix to fit multilevel mixed-effects models for continuous, binary, ordinal, count-data, and survival models.
Sometimes, researchers analyze multistage survey data using single-level models. Stata 13 could do that. To properly adjust a multilevel model, however, we need to exploit the weights available at each stage of the survey. Stata now allows you to enter those weights.
You just svyset your data.
After setting your data, you can fit single-level or multilevel models. If you fit a single-level model, Stata automatically produces the single-level weights it needs from the multistage weights.