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Evans' original question:
> 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
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