Download pdf guide - VSN International

15 Examples 255The two forms for Σ are given byIt follows thatΣ = σ1 2J + σ2 2I, unitsΣ = σeI 2 + σeρ(J 2 − I), CORU(15.3)σe 2 = σ1 2 + σ2 2ρ =σ 2 1σ 2 1 +σ2 2(15.4)Portions of the two outputs are given below. The REML log-likelihoods for thetwo models are the same and it is easy to verify that the REML estimates ofthe variance parameters satisfy (15.4), viz. σ 2 e = 286.310 ≈ 159.858 + 126.528 =286.386; 159.858/286.386 = 0.558191.## !r units#LogL=-204.593 S2= 224.61 60 df 0.1000 1.000LogL=-201.233 S2= 186.52 60 df 0.2339 1.000LogL=-198.453 S2= 155.09 60 df 0.4870 1.000LogL=-197.041 S2= 133.85 60 df 0.9339 1.000LogL=-196.881 S2= 127.56 60 df 1.204 1.000LogL=-196.877 S2= 126.53 60 df 1.261 1.000Final parameter values 1.2634 1.0000Source Model terms Gamma Component Comp/SE % Cunits 14 14 1.26342 159.858 2.11 0 PVariance 70 60 1.00000 126.528 4.90 0 P## CORU#LogL=-196.975 S2= 264.10 60 df 1.000 0.5000LogL=-196.924 S2= 270.14 60 df 1.000 0.5178LogL=-196.886 S2= 278.58 60 df 1.000 0.5400LogL=-196.877 S2= 286.23 60 df 1.000 0.5580LogL=-196.877 S2= 286.31 60 df 1.000 0.5582Final parameter values 1.0000 0.55819Source Model terms Gamma Component Comp/SE % CVariance 70 60 1.00000 286.310 3.65 0 PResidual CORRelat 5 0.558191 0.558191 4.28 0 UA more realistic model for repeated measures data would allow the correlationsto decrease as the lag increases such as occurs with the first order autoregressivemodel. However, since the heights are not measured at equally spaced time pointswe use the EXP model. The correlation function is given byρ(u) = φ uwhere u is the time lag is weeks. The coding for this is