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APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE by Dayanand N. Naik, Ravindra Khattree

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6.2. The Mixed Effects Linear Model

Let yi be the pi × 1 vector of repeated measures on the ith subject. Then consider a mixed effects model described as

where Xi and Zi are the known matrices of orders pi by q and pi by r respectively, and β is the fixed q by 1 vector of unknown (nonrandom) parameters. The r by 1 vectors νi are random effects with Ei)=0, and Di)=σ2G1. Finally ϵi are the pi by 1 vectors of random errors whose elements are no longer required to be uncorrelated. We assume that Ei)=0, Di)=σ2Ri, covii)=0, cov (ϵii)= 0, covii′)=0 for all ii′, and covii)=0. Such assumptions seem to be reasonable in repeated ...

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