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Re: st: xtmixed: BLUP=EB?


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtmixed: BLUP=EB?
Date   Wed, 27 Apr 2005 09:49:11 -0500

Michael Ingre <Michael.Ingre@ipm.ki.se> asks:

> It is confusing when the same concept may have different name in different
> literature.  Are the best linear unbiased predictors (BLUPs) obtained after
> -xtmixed- the same as the empirical Bayes estimates (EB) in other linear
> (e.g. HLM) and non-linear mixed models (e.g. -gllamm-). Also, what is the
> difference between BLUP and EBLUP?

Yes, BLUP and empirical Bayes are one and the same here.  As to the difference
between BLUP and EBLUP, the E stands for "estimated."  Technically speaking a
BLUP of a random effect is defined in terms of the theoretical
variance-covariance matrices for both the random effects and the overall
errors, but these matrices are taken as known.  The actual estimates you
obtain are EBLUPS, which are BLUPs with estimated variance components used in
place of their theoretical counterparts.

The BLUPs mentioned in -xtmixed- documentation are technically EPLUPs, but 
we just call them BLUPs since we have no need to distinguish between the 
two -- they are real predictions of random effects for your particular data.

--Bobby
rgutierrez@stata.com
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