ASReml-S reference manual - VSN International

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1.3 Data sets used 6101 Sire 1 0102 Sire 1 0103 Sire 1 0104 Sire 1 0105 Sire 1 0106 Sire 1 0107 Sire 1 0108 Sire 1 0109 Sire 2 0110 Sire 2 0111 Sire 2 0112 Sire 2 0113 Sire 2 0114 Sire 2 0115 Sire 2 0116 Sire 2 0117 Sire 3 0118 Sire 3 0119 Sire 3 0120 Sire 3 0where unknown parents are denoted here by 0. In this example the columns of the pedigreefile harvey.ped are fully contained within the data file harvey.dat .
2Some theory2.1 The linear mixed model2.1.1 IntroductionIf y denotes the n × 1 vector of observations, the linear mixed model can be written asy = Xτ + Zu + e (2.1)where τ is the p×1 vector of fixed effects, X is an n×p design matrix of full column rankwhich associates observations with the appropriate combination of fixed effects, u is theq × 1 vector of random effects, Z is the n × q design matrix which associates observationswith the appropriate combination of random effects, and e is the n × 1 vector of residualerrors.The model (2.1) is called a linear mixed modelassumed [ ] ([ ]u 0∼ N , θe 0or linear mixed effects model. It is])(2.2)[G(γ) 00 R(φ)where the matrices G and R are functions of parameters γ and φ, respectively. Theparameter θ is a variance parameter which we will refer to as the scale parameter. Inmixed effects models with more than one residual variance, arising for example in theanalysis of data with more than one section (see below) or variate, the parameter θ isfixed to one. In mixed effects models with a single residual variance then θ is equal tothe residual variance (σ 2 ). In this case R must be correlation matrix (see Table 2.1 for adiscussion).2.1.2 Direct product structuresTo undertake variance modelling in asreml it is important to understand the formation ofvariance structures via direct products (⊗). The direct product of two matrices A (m×p)and B (n×q) is⎡⎤a 11B . . . a 1p B.⎢ . .. .⎥⎣a m1B . ⎦. . amp B.
Page 1 and 2: Analysis of mixed modelsfor S langu
Page 3 and 4: D.G. ButlerQueensland Department of
Page 6: ContentsPreface . . . . . . . . . .
Page 10 and 11: ContentsviiB Available variance mod
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 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
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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.
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Optional argumentslevels6.2 The pre
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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
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maxiter maximum number of iteration
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7.3 Methods and related functions 7
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pedigree7.3 Methods and related fun
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8Examples8.1 IntroductionThis secti
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8.2 Split Plot Design 82In this exa
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8.3 Unbalanced nested design 84[4,]
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8.3 Unbalanced nested design 86adju
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8.4 Sources of variability in unbal
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8.5 Balanced repeated measures 902
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8.5 Balanced repeated measures 92Ta
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8.5 Balanced repeated measures 94wh
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8.6 Spatial analysis of a field exp
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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
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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
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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
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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
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References 130W. W. Stroup, P. S. B
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Index 132F statistics, 17fa(,k), 49
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ASReml-S reference manual - VSN International

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