I have come across something peculiar. Baltagi and other sources suggest
that when estimating a random effects model the best linear unbiased
prediction (BLUP) of the random effect for the ith cross-sectional unit is
BLUP_i = [sigma_u^2/(sigma_u^2 + sigma_e^2/T)]*w_bar_i
where
sigma_u^2 is the variance of the random effect
sigma_e^2 is the residual variance
T is the length of the panel
w_bar_i is the mean of the combined residuals for the ith cross-sectional
unit
Stata appears to use this formula to derive the BLUPs when GLS is used to
estimate the random effects model (as does SAS' PROC MIXED). However, when
maximum likelihood is used to estimate the random effects model, Stata
computes the BLUP for the ith unit as w_bar_i. That is, predicting "u"
following the estimation of a MLE random effects model gives the
subject-specific mean of the combined residuals. On the other hand, SAS
computes the BLUPs using the formula given above.
Is there a reason for the difference between the two software packages?
Which prediction should be preferred?
Thank you for your help.
--
Jim Shaw
Graduate Research Associate
College of Pharmacy
The University of Arizona
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