st: Hierarchical model

[Evans Jadotte <evans.jadotte@uab.es>]

Dear statalisters,

I am estimating a linear three-level hierarchical model via "restricted 
maximum likelihood-REML" with the /xtmixed/ command, with households 
(level-1) nested into villages (level-2) nested into regions (level-3). 
Specification seems alright. However, the empirical Bayes random 
intercept at level-3, which according to theory should be inferior or 
equal to the corresponding calculated REML estimate, do not reflect the 
REML estimate that I calculated at that level. Specifically, I have an 
empirical Bayes (the BLUP r.e. computed by Stata) that  is more than 300 
times the REML estimate calculated at level-3. At level-2 it seems 
reasonable, empirical Bayes = 0.87 REML estimate.

Moreover, I expected the sum of the variances (that of raw residuals at 
level-1 + that of  residuals REML level-2 + that of residuals REML 
level-3). When I compute them however, the result gives an estimated 
total variance that is lower than that of the raw residuals at level-1.

I am pretty confident about the model specification and the computation 
but evidently things do not match as they should. Can anyone familiar 
with these models give me any feedback? I would so much appreciate and 
thanks in advance.

Evans
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