Download pdf guide - VSN International

15 Examples 287160140oo120oocircumference10080o60o40o20200 400 600 800 1000 1200 1400 1600ageFigure 15.13 Fitted cubic smoothing spline for tree 1We now consider the analysis of the full dataset. Following Verbyla et al. (1999)we consider the analysis of variance decomposition (see Table 15.11) which modelsthe overall and individual curves.An overall spline is fitted as well as tree deviation splines. We note however,that the intercept and slope for the tree deviation splines are assumed to berandom effects. This is consistent with Verbyla et al. (1999). In this sense thetree deviation splines play a role in modelling the conditional curves for each treeand variance modelling. The intercept and slope for each tree are included asrandom coefficients (denoted by RC in Table 15.11). Thus, if U 5×2 is the matrixof intercepts (column 1) and slopes (column 2) for each tree, then we assume thatvar (vec(U)) = Σ ⊗ I 5where Σ is a 2 × 2 symmetric positive definite matrix. Non smooth variationcan be modelled at the overall mean (across trees) level and this is achieved inASReml by inclusion of fac(age) as a random term.