The general mixed linear model reduces to: y=XB+Z1u1+E where E~N(0,oI)and u1~N(0,oIn) and the covariance matrix of y is now V Z1ZTo]+o0In The complete data loglikelihood is 1=-lbg2)- 1 2 =0 where uo =y-XB-Z1u.The m.1.e.'s are 6=u4 i=0,1 B (XTX)-X(y-Z1u) We need to find the expected values of the sufficient statistics ufui,i=0,1 and y- Ziu conditional on observed data vector y.Since uily is distributed as gi-dimensional multivariate normal N(oZV-(y-XB),a2Ig -aZV-Zi) we have E(ufuily)=(y-XB)TV-ZiZ!V-(y-XB)tr(a?Ia -Z!V-Zi) E(y-Ziuy=XB+00v(y-XB) noting that E(o|y）=oV-1(y-X3) E(uouoly)=ao(y-XB)TV-1ZoZov-(y-XB)tr(ooIa:-aZov-1Zo) where Zo=In. 17The general mixed linear model reduces to: y = Xβ + Z1u1 +  where  ∼ N(0, σ 2 0I) and u1 ∼ N(0, σ 2 1In) and the covariance matrix of y is now V = Z1Z T 1 σ 2 1 + σ 2 0In The complete data loglikelihood is l = − 1 2 q log(2π) − 1 2 X 1 i=0 qi log σ 2 i − 1 2 X 1 i=0 u T i ui σ 2 i where u0 = y − Xβ − Z1u1. The m.l.e.’s are σˆ 2 i = u T i ui qi i = 0, 1 βˆ = (XTX) −XT (y − Z1u1) We need to find the expected values of the sufficient statistics u T i ui , i = 0, 1 and y − Z1u1 conditional on observed data vector y. Since ui |y is distributed as qi-dimensional multivariate normal N(σ 2 i Z T i V −1 (y − Xβ), σ 2 i Iqi − σ 4 i Z T i V −1Zi) we have E(u T i ui | y) = σ 4 i (y − Xβ) TV −1ZiZ T i V −1 (y − Xβ) + tr(σ 2 i Iqi − σ 4 i Z T i V −1Zi) E(y − Z1u1 | y) = Xβ + σ 2 0V −1 (y − Xβ) noting that E(u0 | y) = σ 2 0V −1 (y − Xβ) E(u T 0 u0 | y) = σ 4 0 (y − Xβ) TV −1Z0Z T 0 V −1 (y − Xβ) + tr(σ 2 0Iqi − σ 4 0Z T 0 V −1Z0) where Z0 = In. 17