ASReml-S reference manual - VSN International

8.9 Balanced longitudinal data - Random coefficients and cubic smoothing splines 11321Exposed BLUP0-1-2-2 -1 0 1 2 3Control BLUPFig. 8.9. BLUPs for treated plotted against BLUPs for controlAn alternative definition of tolerance is the simple difference between treated and controlBLUPs for each variety, namely δ = u vc − u vt . Unless β = 1 the two measures ɛ andδ have very different interpretations. The key difference is that ɛ is a measure which isindependent of inherent vigour whereas δ is not. To see this considerwhereascov (ɛ) u ′ v c= cov (u vt − βu vc ) u ′ v(c= σ vct − σ )v ctσv 2 σv 2 cc= 0The independence of ɛ and cov u (δ) u ′ v c= cov (u vc − u vt ) u ′ vc and dependence v c= ( betweenσv 2 )δ and u vc is clearly illustratedin Figures 8.10 and 8.11. In this example thectwo − σ vctmeasures I44 have provided very differentrankings of the varieties. The choice of tolerance measure depends on the aim of theexperiment. In this experiment the aim was to identify tolerance which is independentof inherent vigour so the deviations from regression is preferred.I 448.9 Balanced longitudinal data - Random coefficients and cubicsmoothing splinesThis section illustrates the use of random coefficients and cubic smoothing splines forthe analysis of balanced longitudinal data.