Date:         Thu, 23 Oct 2008 00:23:28 -0700
Reply-To:     Oliver.Kuss@MEDIZIN.UNI-HALLE.DE
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Oliver.Kuss@MEDIZIN.UNI-HALLE.DE
Organization: http://groups.google.com
Subject:      Re: GLIMMIX 9.2 documentation question
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=windows-1252

On 23 Okt., 04:45, Ryan <Ryan.Andrew.Bl...@gmail.com> wrote:
> Hello,
>
> I've been spending quite some time in GLIMMIX documentation, and came
> across a statement that has confused me. The statement below comes
> from the article, "Growing Up Fast: SAS 9.2 Enhancements in the
> GLIMMIX procedure."
>
> • The quadrature rule in the GLIMMIX procedure is adaptive in the
> following sense:
> ...
>
> – The GLIMMIX procedure centers and scales the quadrature points by
> using the empirical Bayes
> estimates (EBEs) of the random effects and the Hessian (second
> derivative) matrix from the EBE
> suboptimization to improve the likelihood approximation.
>
> -----------------------
>
> I'm a bit confused by the use of the term "empirical Bayes estimates
> (EBE)." I didn't think Bayesian estimation was used in this procedure.
> Could anyone shed some light on this? What would be the benefits of
> using EBE?
>
> Thanks,
>
> Ryan

Hello Ryan,
you are right, PROC GLIMMIX does not use "real" Bayesian Estimation in
the sense of MCMC or something like that.
My understanding is that the implemented algorithm for numerical
quadrature in GLIMMIX (it is the same with PROC NLMIXED) is an
iterative one which needs updated estimates for the random effects in
each step. These random effects estimates are estimated by the
empirical Bayes method. Estimation is not very complicated here,
estimates result from a simple computational step. As such, empirical
Bayes is just an estimation principle which is used and has proven
sensible.

Hope that helps,
Oliver