Elan, Evans,
Carlin and Lewis in their 3rd edition of Bayesian Methods for Data Analysis
describe the Bayesian Shrinkage factor B = sigma^2/(sigma^2 + tau^2)
where tau^2 would be the variance of the prior distribution while sigma^2
would be the normal density of the sample (or likelihood), p. 17.
B is also used to compute the posterior mean = B (mu) + (1-B)y
a weighted average of the prior mean and that of the sample.
Regards,
Bob
Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University
Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf
CV: http://homepages.nyu.edu/~ray1/vita.pdf
----- Original Message -----
From: "Cohen, Elan" <[email protected]>
Date: Wednesday, October 14, 2009 1:40 pm
Subject: RE: st: RE: Shrinkage factor
To: "'[email protected]'" <[email protected]>
> Just based on the index, the following book may be helpful:
>
> http://www.stata.com/bookstore/mlmus2.html
>
> - Elan
>
>
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of
> > Evans Jadotte
> > Sent: Wednesday, October 14, 2009 1:07 PM
> > To: [email protected]
> > Subject: Re: st: RE: Shrinkage factor
> >
> > Nick Cox wrote:
> > > If there were, then a simple search would almost certainly find it.
> > > -findit shrinkage- yields no hits. Did you try a Stata or
> > Google search?
> > >
> > >
> > > Nick
> > > [email protected]
> > >
> > > Evans Jadotte
> > >
> > > I am estimating a three-level hierachical model using
> > xtmixed and want
> > > to get the 'shrinkage factor' (Rj) to help me with the
> > calculation of
> > > the variance for an empirical Bayes estimate. My model has many
> > > covariates and clusters and this makes a manual calculation
> > of the Rj
> > > not malleable. Is there any user-written command to get the Rj?
> > >
> > > Hope my request is not too confusing and can receive some help.
> > >
> > > *
> > > * For searches and help try:
> > > * http://www.stata.com/help.cgi?search
> > > * http://www.stata.com/support/statalist/faq
> > > * http://www.ats.ucla.edu/stat/stata/
> > >
> > I tried under both findit shrinkage and findit reliability (this
> last
> > one took me to xtmepoisson but no further help), with no luck.
> >
> > Evans
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
> >
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
