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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 programmedhot-key that snipped the beginning of my email. Nonetheless,I think you understand the idea.Because the notion applies to multiple levels, the notionof pooling may avoid some ambiguity.Best,BobRobert 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.eduHi Bob,In fact, this is the formula I have. My problem is the malleability ofn_j. Since I have 496 clusters at level-2 with many unbalancedobservations within each cluster, the manual calculation can make onegocrazy! I think I will have to dedicate some gooood time to this! Inanycase many thanks for your output.Evans Robert A Yaffee wrote:prefer the use of "a pooling factor" in multilevel models toindicate 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 DataAnalysis 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.eduElan, Evans,Carlin and Lewis in their 3rd edition of Bayesian Methods forDataAnalysis describe the Bayesian Shrinkage factor B = sigma^2/(sigma^2 + tau^2)where tau^2 would be the variance of the prior distribution whilesigma^2would be the normal density of the sample (or likelihood), p.17.B is also used to compute the posterior mean = B (mu) + (1-B)ya 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 OfEvans JadotteSent: 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 findit.-findit shrinkage- yields no hits. Did you try a Stata orGoogle search?Nickn.j.cox@durham.ac.ukEvans JadotteI am estimating a three-level hierachical model usingxtmixed and wantto get the 'shrinkage factor' (Rj) to help me with thecalculation ofthe variance for an empirical Bayes estimate. My model has manycovariates and clusters and this makes a manual calculationof the Rjnot 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 (thislastone 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/* * 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/

Hello Bob, Certainly I gathered the idea from your email! Thanks again for your input, 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/

**References**:**st: Shrinkage factor***From:*Evans Jadotte <evans.jadotte@uab.es>

**Re: st: RE: Shrinkage factor***From:*Evans Jadotte <evans.jadotte@uab.es>

**Re: RE: st: RE: Shrinkage factor***From:*Robert A Yaffee <bob.yaffee@nyu.edu>

**Re: st: RE: Shrinkage factor***From:*Evans Jadotte <evans.jadotte@uab.es>

**Re: st: RE: Shrinkage factor***From:*Robert A Yaffee <bob.yaffee@nyu.edu>

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