Abstract #300025

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JSM 2003 Abstract #300025
Activity Number: 18
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: ENAR
Abstract - #300025
Title: Unbiased Estimation for Linear Mixed Effects Models in Small Samples
Author(s): Eugene Demidenko*+
Companies: Dartmouth Medical School
Address: HB 7927, Hanover, NH, 03756-1000,
Keywords: LME ; Variance components ; MINQUE ; Growth curve ; Random effects ; Mixed effects
Abstract:

We deal with linear mixed effects (LME or repeated measurements) model in the Laird and Ware (1982) formulation y=Xa+Zb+e where y is the nx1 vector of the dependent variable, X is the nxm design matrix of fixed effects, a is the mx1 vector of unknown parameters, Z is the nxk matrix of random effects, b is the kx1 vector of random effects, e is the nx1 error term. The subscript I at y, X, Z, b, e is omitted for simplicity of notation. Typically, parameter a is estimated by maximum likelihood. We, however, develop a noniterative unbiased estimation of a and variance parameters s2=var(e) and D=cov(b) using MINQUE theory. We prove that MLE/RMLE is unbiased for a but biased for s2 and D when data are not balanced. Several important special cases of the LME, such as balanced growth curve model, are considered. Statistical simulations confirm that the noniterative estimators for s2 and matrix D often outperform standard MLEs.

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