From the above we can derive the following EM-type algorithms for this case: Basic EM Algorithm Step 1 (E-step)Set V()=Z1Zo+In and for i=0,1 calculate )=E(ufuily)B= oi(y-XB()TV(Z:Z!V((y-XB) +tr(o01-4zV0-'z)i=0,1 i()=E(y-Ziuly)B=B=0) XB()+00v)'(y-XB()) Step 2(M-step) +w=s9/gi=0,1 B+)=(XTX）-1X'o0 ECM Algorithm Step 1 (E-step)Set V()=Z1Z+In and,for i=0,1 calculate s=E(uulw)）lg=B,=29 02(y-XB()TV()'Z:Z:V()(y-XB) +tr(2 Ia-ZV()Z) Step 2(M-step) Partition the parameter vector 0=(00,o,B)as 01=(00,o)and 02=B CM-step 1 Maximize complete data log likelihood over 01 2+”=s9/4i=0,1 CM-step 2 Calculate B(+1)as B(+1)=(XTX)-1XTw(+1) where o+1)=XB+3+V+)-'(gy-XB9) 18From the above we can derive the following EM-type algorithms for this case: Basic EM Algorithm Step 1 (E-step) Set V (t) = Z1Z 0 1σ 2 (t) 1 + σ 2 (t) 0 In and for i = 0, 1 calculate sˆ (t) i = E(u T i ui |y) | β=β (t) , σ 2 i =σ 2(t) i = σ 4 (t) i (y − Xβ (t) ) TV (t)ZiZ T i V (t) (y − Xβ (t) ) + tr(σ 2 (t) i Iqi − σ 4 (t) i Z T i V (t)−1 Zi) i = 0, 1 wˆ (t) = E(y − Z1u1|y) | β=β (t) , σ 2 i =σ 2 (t) i = Xβ (t) + σ 2 (t) 0 V (t)−1 (y − Xβ (t) ) Step 2 (M-step) σ 2 (t+1) i = sˆ (t) i /qi i = 0, 1 β (t+1) = (XTX) −1X0wˆ (t) ECM Algorithm Step 1 (E-step) Set V (t) = Z1Z 0 1σ 2 (t) 1 + σ 2 (t) 0 In and, for i = 0, 1 calculate sˆ (t) i = E(u T i ui |y) | β=β (t) , σ 2 i =σ 2 (t) i = σ 4 (t) i (y − Xβ (t) ) TV (t)−1 ZiZiV (t)−1 (y − Xβ) + tr(σ 2 (t) i Iqi − σ 4 (t) i Z T i V (t)−1 Zi) Step 2 (M-step) Partition the parameter vector θ = (σ 2 0 , σ 2 1 , β) as θ1 = (σ 2 0 , σ 2 1 ) and θ2 = β CM-step 1 Maximize complete data log likelihood over θ1 σ 2 (t+1) i = sˆ (t) i /qi i = 0, 1 CM-step 2 Calculate β (t+1) as β (t+1) = (XTX) −1XT wˆ (t+1) where wˆ (t+1) = Xβ (t) + σ 2 (t+1) 0 V (t+1)−1 (y − Xβ (t) ) 18