ASReml-S reference manual - VSN International

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ContentsviiB Available variance models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
List of Tables1.1 Trial layout and allocation of varieties to plots in the NIN field trial . . . . . . 32.1 Combination of G and R structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1 Summary of reserved names and special functions with their typicalusage; fixed (f) or random (r) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Families and link functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1 Sequence of variance structures for the NIN field trial . . . . . . . . . . . . . . . . . . 418.1 A split-plot field trial of oat varieties and nitrogen application . . . . . . . . . . 808.2 Rat data: ANOVA decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 858.3 REML log-likelihood ratio test for each variance component in the voltagedata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898.4 Summary of variance models fitted to the plant data . . . . . . . . . . . . . . . . . . . 928.5 Summary of Wald statistics for fixed effects for variance models fitted tothe plant data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.6 Field layout of Slate Hall Farm experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 968.7 Summary of models fitted to the Slate Hall data . . . . . . . . . . . . . . . . . . . . . . 998.8 Estimated variance components from univariate analyses of bloodwormdata. (a) Model with homogeneous variance for all terms and (b) modelwith heterogeneous variance for interactions involving tmt . . . . . . . . . . . . . . 1098.9 Equivalence of random effects in bivariate and univariate analyses . . . . . . . 1108.10 Estimated variance parameters from bivariate analysis of bloodworm data 1118.11 ANOVA decomposition for the orange data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1178.12 Sequence of models fitted to the orange data . . . . . . . . . . . . . . . . . . . . . . . . . 118A.1 Examples of aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122B.1 Details of the available variance models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Page 1 and 2: Analysis of mixed modelsfor S langu
Page 3 and 4: D.G. ButlerQueensland Department of
Page 6: ContentsPreface . . . . . . . . . .
Page 12 and 13: List of Figures1.1 Weekly body weig
Page 14 and 15: 1.3 Data sets used 21.2.2 Help and
Page 16 and 17: 1.3 Data sets used 41.3.2 Repeated
Page 18 and 19: 1.3 Data sets used 6101 Sire 1 0102
Page 20 and 21: 2.1 The linear mixed model 8Direct
Page 22 and 23: 2.2 Estimation 10There is a corresp
Page 24 and 25: 2.2 Estimation 12where H ij = ∂ 2
Page 26 and 27: 2.5 Inference for random effects 14
Page 28 and 29: 2.6 Inference for fixed effects 16T
Page 30 and 31: 2.6 Inference for fixed effects 18t
Page 32 and 33: 3Fitting the mixed model3.1 Introdu
Page 34 and 35: 3.3 Introducing the asreml function
Page 36 and 37: 3.6 Getting help3.7 The asreml func
Page 38 and 39: 3.8 Fixed terms 26na.method.Xkeep.o
Page 40 and 41: 3.8 Fixed terms 28Summary of reserv
Page 42 and 43: 3.10 Conditional factors: the at()
Page 44 and 45: Table 3.2. Families and link functi
Page 46 and 47: 3.15 Multivariate analysis 34R!trai
Page 48 and 49: Source df F_inc F_con MSource df dd
Page 50 and 51: 4.1.1 Specifying variance models in
Page 52 and 53: 4.2 A sequence of structures for th
Page 54 and 55: Σ = [σ ij ] :{σii = σ 2 , ∀i
Page 56 and 57: 4.4 Variance model functions 44init
Page 58 and 59: The Matérn class4.4 Variance model
Page 60 and 61:
4.4 Variance model functions 48Chol
Page 62 and 63:
Required argumentsobj4.5 Rules for
Page 64 and 65:
4.7 Constraining variance parameter
Page 66 and 67:
5Genetic analysis5.1 IntroductionIn
Page 68 and 69:
5.2 Pedigree, G-inverse objects and
Page 70 and 71:
5.4 Using Pedigree and G-inverse ob
Page 72 and 73:
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
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6.4 Complicated weighting 666.4 Com
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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 86 and 87:
Page 88 and 89:
pedigree7.3 Methods and related fun
Page 90 and 91:
Page 92 and 93:
8Examples8.1 IntroductionThis secti
Page 94 and 95:
8.2 Split Plot Design 82In this exa
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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
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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
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Variety predicted.value standard.er
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8.7 Unreplicated early generation v
Page 116 and 117:
8.7 Unreplicated early generation v
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8.8 Paired Case-Control Study 106Th
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Terms added sequentially; adjusted
Page 122 and 123:
8.8 Paired Case-Control Study 110[
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8.8 Paired Case-Control Study 112..
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8.9 Balanced longitudinal data - Ra
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
A.3 Aliasing and singularities 122W
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Table B.1: Details of the available
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B Available variance models 126Deta
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ReferencesG. E. P. Box. Analysis of
Page 142 and 143:
References 130W. W. Stroup, P. S. B
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Index 132F statistics, 17fa(,k), 49
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