APPLIED MULTIVARIATE STATISTICS: WITH SAS® SOFTWARE

6.2. The Mixed Effects Linear Model

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)=σ²G₁. 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)=σ²R_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 ...