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Re: st: RE: Shrinkage factor


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Shrinkage factor
Date   Thu, 15 Oct 2009 08:59:47 -0400

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.
> >>>>>
> >>>>> *
> >>>>> *   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
> >>>> *
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> >>>>
> >>>>
> >>>>         
> >>> *
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> >>>       
> >> *
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> >>     
> > *
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> >   
> 
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