# Re: st: RE: Shrinkage factor

 From Evans Jadotte 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 -----
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
*
*   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/
```
```*
*   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!