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Re: st: RE: Shrinkage factor


From   Evans Jadotte <evans.jadotte@uab.es>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Shrinkage factor
Date   Thu, 15 Oct 2009 15:37:47 +0200

Robert A Yaffee wrote:
Evans,
      Sorry my salutation and message got left-
truncated. I suspect it is some inadvertently programmed
hot-key that snipped the beginning of my email. Nonetheless, I think you understand the idea.
       Because the notion applies to multiple levels, the notion
of pooling may avoid some ambiguity. Best, 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: Evans Jadotte <evans.jadotte@uab.es>
Date: Thursday, October 15, 2009 4:48 am
Subject: Re: st: RE: Shrinkage factor
To: statalist@hsphsun2.harvard.edu


Hi Bob,

In fact, this is the formula I have. My problem is the malleability of n_j. Since I have 496 clusters at level-2 with many unbalanced observations within each cluster, the manual calculation can make one go crazy! I think I will have to dedicate some gooood time to this! In any case many thanks for your output.

Evans
Robert A Yaffee wrote:
prefer the use of "a pooling factor" in multilevel models to indicate the the degree to which elements are pooled together.

They use the same formula for the residual intraclass coefficient that
is used for the shrinkage factor on population distribution a,
 but refer to 1-B  as the pooling factor
when B = 1 - [ sigma^2/(sigma^2 + sigma_y^2/n_j)]

for them,   a_j (multilevel) =  B mu_a +  (1-B) ybar_j
where
ybar_j = avg of the y's within each group j
mu_a = average of the population

B = 0 when there is no pooling a_j=ybar_j
   = 1 when there is complete pooling  a_j = mu_a

- Hope this helps. This comes from Gelman and Hill Data
Analysis using regression and multilevel/hierarchical models, Cambridge University Press, p. 477.
    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: Robert A Yaffee <bob.yaffee@nyu.edu>
Date: Wednesday, October 14, 2009 8:18 pm
Subject: Re: RE: st: RE: Shrinkage factor
To: statalist@hsphsun2.harvard.edu


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" <cohened@upmc.edu>
Date: Wednesday, October 14, 2009 1:40 pm
Subject: RE: st: RE: Shrinkage factor
To: "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>


Just based on the index, the following book may be helpful:

http://www.stata.com/bookstore/mlmus2.html

- Elan
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Evans Jadotte
Sent: Wednesday, October 14, 2009 1:07 PM
To: statalist@hsphsun2.harvard.edu
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 n.j.cox@durham.ac.uk
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.

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I tried under both findit shrinkage and findit reliability (this
last
one took me to xtmepoisson but no further help), with no luck.

Evans
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Hello Bob,

Certainly I gathered the idea from your email!

Thanks again for your input,

Evans
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