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_iand 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" <[EMAIL PROTECTED]>
To: "R help list" <r-help@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
[EMAIL PROTECTED]
<http://callisto.si.usherb.ca:8080/bshipley/> http://callisto.si.usherb.ca:8080/bshipley/
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