[R-sig-ME] Question about what is "shrinkage"...

[Emmanuel Curis]

Hello,

I've read several time the term "shrinkage", either on this list or,
even more often, when dealing with population pharmacokinetics, and I
am not quite sure what it means and what is its usage... Could it be
possible to have either some references or some explanations? I give
below a longer version, with how far I could get and where I am
stopped... Thanks in advance for any help!

I've search a little bit on the net; shrinkage seems related to the
fact that after regression, it is possible to obtain more precise, but
slightly biased, estimators of the coefficients, by making them a
little bit smaller than the actual value (hence « shrinkage »).
However, in the discussions especially about PK-pop models, the usage
of "shrinkage" does not seem to me coherent with this meaning...
Instead, it seems to be a property of mixed-models, linked to
variances estimations, and used to check the model quality or validaty
in some way, with sentences like "this model increased the shrinkage"
and mentions of something like "random effects parameters shrinkage"
and "residuals shrinkage" (eta-shrinkage and epsilon-shrinkage)...

My other idea was related to the fact that when modeling a set of
repeated measures on several patients, with a straight line, the set
of slopes shows less variability when using a mixed model on the whole
set, than using separate lines for each patient --- as exemplified for
instance in Douglas Bate's book. Hence, variance of slopes is shrinked
in the mixed model approach compared to the variance obtained from the
sample of all individual slopes. This idea seems closer to the use and
terminology above, but I can't see if shrinkage is a good or bad
thing...

I mean, since one imposes a given distribution, hence a constraint, on
slopes, the fact that variance is smaller is not a surprise and it
could be a drawback of the estimation, leading to underestimation.
Conversely, variance of individual slopes also includes the residual
variability, hence is expected to be higher. Is it true then that the
mixed-model estimation is better? But in that case, how shrinkage can
be used to quantify the correctness of a model?

Thanks in advance,
Best regards,

-- 
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html