ASReml-S reference manual - VSN International

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8.8 Paired Case-Control Study 112...84 sye TKM6 9.807568 0.8056834 Estimable85 sye WC1403 9.287950 0.8057545 Estimable86 sye WC140311 8.923817 0.8056858 Estimable87 sye YRK1 8.335681 0.8190248 Estimable88 sye YRK3 8.113448 0.8190248 Estimable$"trait:Variety"$avsed:[1] 1.214741These predictions are on the square root scale; it is straightforward to back-transformthe predicted means to the original scale of measurement. Approximate standard errorson th eoriginal scale can be calculated from a Taylor series approximation. That is,if x is a random variable with E(x) = θ, and y = g(x) is some function of x, thenvar(y) = (dy/dx) 2 θvar(x). See Kendall and Stuart [1969] pp 231, for example. In thiscase, g(x) = x 2 and g ′ (x) = dy/dx = 2x. The following code calculates the transformedpredictions and approximate standard errors:> pv pv$rootwt pv$approxSE pv$est.status pvtrait Variety predicted.value standard.error rootwt approxSE1 syc AliCombo 14.953229 0.9180964 223.5991 27.457012 syc Amaroo 16.161198 0.9180985 261.1843 29.675143 syc Balilla 14.420236 0.9185701 207.9432 26.491994 syc Bluebelle 13.103132 0.9309747 171.6921 24.397375 syc Bogan 15.768223 0.9548522 248.6368 30.11265...84 sye TKM6 9.807568 0.8056834 96.1884 15.8035985 sye WC1403 9.287950 0.8057545 86.2660 14.9676286 sye WC140311 8.923817 0.8056858 79.6345 14.3795987 sye YRK1 8.335681 0.8190248 69.4836 13.6542688 sye YRK3 8.113448 0.8190248 65.8280 13.29023Interpretation of resultsRecall that the primary interest is varietal tolerance to bloodworms. This could be definedin various ways: One option is to consider the regression implicit in the variance structurefor the trait by variety effects. The variance structure can arise from a regression of treatedvariety effects on control effects, namelywhere the slope β = σ vct /σ 2 v c.u vt= βu vc + ɛTolerance can be defined in terms of the deviations from regression, ɛ. Varieties withlarge positive deviations have greatest tolerance to bloodworms. Note that this is similarto the original approach except that the regression has been conducted at the genotypicrather than the phenotypic level. In Figure 8.9 the BLUPs for treated have been plottedagainst the BLUPs for control for each variety and the fitted regression line (slope = 0.61)has been drawn. Varieties with large positive deviations from the regression line includeYRK3, Calrose, HR19 and WC1403.
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.
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Analysis of mixed modelsfor S langu
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D.G. ButlerQueensland Department of
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ContentsPreface . . . . . . . . . .
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ContentsviiB Available variance mod
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List of Figures1.1 Weekly body weig
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1.3 Data sets used 21.2.2 Help and
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1.3 Data sets used 41.3.2 Repeated
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1.3 Data sets used 6101 Sire 1 0102
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2.1 The linear mixed model 8Direct
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2.2 Estimation 10There is a corresp
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2.2 Estimation 12where H ij = ∂ 2
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2.5 Inference for random effects 14
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2.6 Inference for fixed effects 16T
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2.6 Inference for fixed effects 18t
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3Fitting the mixed model3.1 Introdu
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3.3 Introducing the asreml function
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3.6 Getting help3.7 The asreml func
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3.8 Fixed terms 26na.method.Xkeep.o
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3.8 Fixed terms 28Summary of reserv
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3.10 Conditional factors: the at()
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Table 3.2. Families and link functi
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3.15 Multivariate analysis 34R!trai
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Source df F_inc F_con MSource df dd
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4.1.1 Specifying variance models in
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4.2 A sequence of structures for th
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Σ = [σ ij ] :{σii = σ 2 , ∀i
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4.4 Variance model functions 44init
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The Matérn class4.4 Variance model
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4.4 Variance model functions 48Chol
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Required argumentsobj4.5 Rules for
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4.7 Constraining variance parameter
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5Genetic analysis5.1 IntroductionIn
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5.2 Pedigree, G-inverse objects and
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5.4 Using Pedigree and G-inverse ob
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6Prediction from the linear model6.
Page 74 and 75: Optional argumentslevels6.2 The pre
Page 76 and 77: 6.2 The predict method 64The predic
Page 78 and 79: 6.4 Complicated weighting 666.4 Com
Page 80 and 81: 7The asreml class and related metho
Page 82 and 83: maxiter maximum number of iteration
Page 84 and 85: 7.3 Methods and related functions 7
Page 88 and 89: pedigree7.3 Methods and related fun
Page 92 and 93: 8Examples8.1 IntroductionThis secti
Page 94 and 95: 8.2 Split Plot Design 82In this exa
Page 96 and 97: 8.3 Unbalanced nested design 84[4,]
Page 98 and 99: 8.3 Unbalanced nested design 86adju
Page 100 and 101: 8.4 Sources of variability in unbal
Page 102 and 103: 8.5 Balanced repeated measures 902
Page 104 and 105: 8.5 Balanced repeated measures 92Ta
Page 106 and 107: 8.5 Balanced repeated measures 94wh
Page 108 and 109: 8.6 Spatial analysis of a field exp
Page 110 and 111: 8.6 Spatial analysis of a field exp
Page 112 and 113: Variety predicted.value standard.er
Page 114 and 115: 8.7 Unreplicated early generation v
Page 116 and 117: 8.7 Unreplicated early generation v
Page 118 and 119: 8.8 Paired Case-Control Study 106Th
Page 120 and 121: Terms added sequentially; adjusted
Page 122 and 123: 8.8 Paired Case-Control Study 110[
Page 126 and 127: 8.9 Balanced longitudinal data - Ra
Page 134 and 135: A.3 Aliasing and singularities 122W
Page 136 and 137: Table B.1: Details of the available
Page 138 and 139: B Available variance models 126Deta
Page 140 and 141: ReferencesG. E. P. Box. Analysis of
Page 142 and 143: References 130W. W. Stroup, P. S. B
Page 144 and 145: Index 132F statistics, 17fa(,k), 49
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ASReml-S reference manual - VSN International

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