Hi dear all,
I have a question about shinkage. I read an article about shinkage (Radojka
M. Savic and Mats O. Karlsson Importance of Shrinkage in Empirical Bayes
Estimates for Diagnostics: Problems and Solutions 2009) and try to use
shinkage to diagnose my model. An ETA-shinkage is negative in my result.
According to the article, negative shinkage may occur in the situation where
a parameter variance is fixed to a lower value than the true value or in
rich data from a small number of subjects. I wonder that if the parameter
variance is fixed, shinkage is 100% in my result. And if it is the data
problem, why is the shinkage of this kind of data negative? Besides, I
wonder that whether the negative shinkage indicate the model
misspecification? How important is shinkage to diagnose a model? Is it more
used to evaluate the relationship between the covariate and parameters or to
choose a model?
Thanks!
Li Mengyao
question about shinkage
Hi Li
I’m not aware of specific interpretations for negative shrinkage other than the
evaluation of the SD of the ETAs is greater than the estimate of the sqrt of
OMEGA for the same parameter. Since OMEGA itself is an estimate then ETA
shrinkage may occur due to either the EBEs being underdispersed, the estimate
of OMEGA being inflated or both and vice versa for negative ETA shrinkage.
You might imagine a situation in which you had intensive sampling per
individual and few individuals. In this setting you might expect the EBEs to
be well estimated and the ETA distribution to reflect an accurate empirical
value. It is also likely that your estimate of OMEGA may be biased and hence
positive or negative ETA shrinkage may occur as a function of the influence of
the design on your estimate of OMEGA.
I wouldn’t interpret the value as having overt qualities but rather consider it
as a guide.
Regards
Steve
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Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of ???
Sent: Wednesday, 1 June 2011 2:34 a.m.
To: [email protected]
Subject: [NMusers] question about shinkage
Hi dear all,
I have a question about shinkage. I read an article about shinkage (Radojka M.
Savic and Mats O. Karlsson Importance of Shrinkage in Empirical Bayes Estimates
for Diagnostics: Problems and Solutions 2009) and try to use shinkage to
diagnose my model. An ETA-shinkage is negative in my result. According to the
article, negative shinkage may occur in the situation where a parameter
variance is fixed to a lower value than the true value or in rich data from a
small number of subjects. I wonder that if the parameter variance is fixed,
shinkage is 100% in my result. And if it is the data problem, why is the
shinkage of this kind of data negative? Besides, I wonder that whether the
negative shinkage indicate the model misspecification? How important is
shinkage to diagnose a model? Is it more used to evaluate the relationship
between the covariate and parameters or to choose a model?
Thanks!
Li Mengyao
Hi Li,
Well, do you have rich data and a small number of subjects?
How much shrinkage exactly? A very small negative number might just be due to
(hopefully) non-important numerical issues. It could also be due to early
termination of the estimation, not doing enough iterations, problems with
rounding errors, etc.
The use of shrinkage to diagnose model problems isnt powerful enough to try to
solve a problem without knowing anything about the model or the data. So, it
depends on your problem. What you usually encounter is that high shrinkage
means that a dataset is not informative enough to estimate a paramater in the
individuals. I would interpret negative shrinkage as meaning that something
went wrong with the estimation. In that case you cant trust the resulting
estimations (or shrinkage for that matter) to be meaningful anyway.
You might want to look a constructing likelihood profiles for you model
estimations as well. I find they work nicely in conjuction with considering
shrinkage.
Douglas Eleveld
Quoted reply history
-----Original Message-----
From: [email protected] on behalf of ???
Sent: Tue 5/31/2011 4:33 PM
To: [email protected]
Subject: [NMusers] question about shinkage
Hi dear all,
I have a question about shinkage. I read an article about shinkage (Radojka
M. Savic and Mats O. Karlsson Importance of Shrinkage in Empirical Bayes
Estimates for Diagnostics: Problems and Solutions 2009) and try to use
shinkage to diagnose my model. An ETA-shinkage is negative in my result.
According to the article, negative shinkage may occur in the situation where
a parameter variance is fixed to a lower value than the true value or in
rich data from a small number of subjects. I wonder that if the parameter
variance is fixed, shinkage is 100% in my result. And if it is the data
problem, why is the shinkage of this kind of data negative? Besides, I
wonder that whether the negative shinkage indicate the model
misspecification? How important is shinkage to diagnose a model? Is it more
used to evaluate the relationship between the covariate and parameters or to
choose a model?
Thanks!
Li Mengyao
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