[R] shrinkage estimates in lme

[Dimitris Rizopoulos]

What exactly do you mean by slope estimates? Marginal or 
subject-specific?

Presuming that you mean the fixed-effects (since you refer to OLS) 
then these are unbiased since they are Weighted Least Squares 
estimators based on the marginal model. They are unbiased even in the 
case where you misspecify the correlation structure. Moreover if you 
use a reasonably well chosen covariance structure then they are also 
very efficient.

The subject-specific fitted values are shrunken toward the mean in the 
sense:

\hat{y}_i = \sum_i V_i^{-1}X_i\hat{\bfbeta} + (I-\sum_i V_i^{-1})y_i

and thus it is a weighted average of the population average profile 
X_i\hat{\bfbeta} and the observed data y_i with weights \sum_i 
V_i^{-1} and (I-\sum_i V_i^{-1}), respectively (where \sum_i V_i^{-1} 
is the residual covariance matrix).

I hope this helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat/
     http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Bill Shipley" <bill.shipley at usherbrooke.ca>
To: "R help list" <r-help at stat.math.ethz.ch>
Sent: Tuesday, February 15, 2005 5:17 PM
Subject: [R] shrinkage estimates in lme


Hello.  Slope estimates in lme are shrinkage estimates which pull the
OLS slope estimates towards the population estimates, the degree of
which depends on the group sample size and the distance between the
group-based estimate and the overall population estimate.  Although
these shrinkage estimates as said to be more precise with respect to 
the
true values, they are also biased.  So there is a tradeoff between
precision and bias.

Are there rules of thumb to help determine when it is better to use 
the
OLS slope estimates and when to use the mixed model (lme) shrinkage
estimates?  I have 35 groups but the numbers per group vary from over 
50
to as low as 4.

Thanks for any help.



Bill Shipley

Subject Matter Editor, Ecology

North American Editor, Annals of Botany

Département de biologie, Université de Sherbrooke,

Sherbrooke (Québec) J1K 2R1 CANADA

Bill.Shipley at USherbrooke.ca

 <http://callisto.si.usherb.ca:8080/bshipley/>
http://callisto.si.usherb.ca:8080/bshipley/




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