Let y_{i} be the p_{i} × 1 vector of repeated measures on the i^{th} subject. Then consider a mixed effects model described as

where X_{i} and Z_{i} are the known matrices of orders p_{i} by q and p_{i} by r respectively, and β is the fixed q by 1 vector of unknown (nonrandom) parameters. The r by 1 vectors ν_{i} are random effects with E(ν_{i})=0, and D(ν_{i})=σ^{2}G_{1}. Finally ϵ_{i} are the p_{i} by 1 vectors of random errors whose elements are no longer required to be uncorrelated. We assume that E(ϵ_{i})=0, D(ϵ_{i})=σ^{2}R_{i}, cov (ν_{i},ν_{i})=0, cov (ϵ_{i},ϵ_{i})= 0, cov (ϵ_{i},ν_{i}′)=0 for all i ≠ i′, and cov (ν_{i},ϵ_{i})=0. Such assumptions seem to be reasonable in repeated ...

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