when you were testing the multilevel models, you have to take care about the fixed effects and the random effects, I mean, usually the level variable is the random variable. To identify the random variable first you have to test the dependent variable vs the level variable. in stata the command is mixed , so the written will be:
mixed depended variable fixed variables || random variable :
if your random variable is categorical you have to create the categories.
I also would suggest multilevel models. When you build community or district-level variables starting from household-level variables someone uses "non-self means", that is the mean of a given household variable at district level excluding household's own observation.