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15 Examples 254The focus is modelling of the error variance for the data. Specifically we fit themultivariate regression model given byY = DT + E (15.1)where Y 14×5 is the matrix of heights, D 14×2 is the design matrix, T 2×5 is thematrix of fixed effects and E 14×5 is the matrix of errors. The heights taken onthe same plants will be correlated and so we assume thatwhere Σ 5×5 is a symmetric positive definite matrix.var (vec(E)) = I 14 ⊗ Σ (15.2)The variance models used for Σ are given in Table 15.4. These represent somecommonly used models for the analysis of repeated measures data (see Wolfinger,1986). The variance models are fitted by changing the last four lines of the inputfile. The sequence of commands for the first model fitted isy1 y3 y5 y7 y10 ~ Trait tmt Tr.tmt !r units1 2 014TraitTable 15.4 Summary of variance models fitted to the plant datanumber of REMLmodel parameters log-likelihood BICUniform 2 -196.88 401.95Power 2 -182.98 374.15Heterogeneous Power 6 -171.50 367.57Antedependence (order 1) 9 -160.37 357.51Unstructured 15 -158.04 377.50The split plot in time model can be fitted in two ways, either by fitting a unitsterm plus an independent residual as above, or by specifying a CORU variancemodel for the R-structure as followsy1 y3 y5 y7 y10 ~ Trait tmt Tr.tmt1 2 014Trait 0 CORU .5