ASReml-S reference manual - VSN International

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List of Figures1.1 Weekly body weights of rats. C = Control, X = Thyroxin, T = Thiouracil 46.1 Predict tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648.1 Residual plot for the rat data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868.2 Residuals vs fitted values for the voltage data . . . . . . . . . . . . . . . . . . . . . . . . . 898.3 Trellis plot of plant height for each of 14 plants . . . . . . . . . . . . . . . . . . . . . . . 908.4 residual ∼ Plant | Time for the exp() variance model for the plantdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938.5 Sample variogram of the AR1×AR1 model for the Slate Hall data . . . . . . . 978.6 Sample variogram of the AR1×AR1 model for the Tullibigeal data . . . . . . 1028.7 Sample variogram of the AR1×AR1 + pol(column,-1) model for theTullibigeal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.8 Rice bloodworm data: Plot of square root of root weight for treatedversus control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.9 BLUPs for treated plotted against BLUPs for control . . . . . . . . . . . . . . . . . . 1138.10 Estimated deviations from regression of treated on control for eachvariety plotted against estimate for control . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148.11 Estimated difference between control and treated for each variety plottedagainst estimate for control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148.12 Trellis plot of trunk circumference (mm) for each tree against age in dayssince 1 December 1968. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1158.13 Fitted cubic smoothing spline for tree 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1178.14 Plot of fitted cubic smoothing spline for model 1 . . . . . . . . . . . . . . . . . . . . . . 1198.15 Fitted values adjusted for Season and approximate confidence intervalsfor model 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
1Introduction1.1 What ASReml-S can doASReml-S is designed to fit the general linear mixed model to moderately large data setswith complex variance models. ASReml-S has application in the analysis of• (un)balanced longitudinal data,• repeated measures data (multivariate analysis of variance and spline type models),• (un)balanced designed experiments,• multi-environment trials and meta analysis• regular or irregular spatial data.The computational engine of ASReml-S is the algorithm of Gilmour et al. [1995] adaptedfrom the standalone program ASReml [Gilmour et al., 2002]. The computational efficiencyof ASReml-S arises from using this Average Information REML algorithm (givingquadratic convergence) and sparse matrix operations. However, because of overheads inherentin S language implementations, some very large problems may need to use thestandalone ASReml program to overcome memory limitations.The asreml function returns an object of class asreml. Standard methods resid() andfitted() work with this object and methods for coef(), summary(), plot(), wald() andpredict() also exist.1.2 Getting started1.2.1 InstallationProduction versions of asreml for S language environments are available for several implementationson Microsoft Windows and Linux systems. Installation varies with eachsystem and instructions are contained in a separate document distributed with the archiveor available from the web site. If the instructions are inadequate then please contact VSNInternational at www.VSNi.co.uk for support.
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 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
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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.
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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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