ASReml-S reference manual - VSN International

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Index 132F statistics, 17fa(,k), 49Fisher-scoring algorithm, 12fitted(), 23fixedargument, 22model formula, 26fixed effects, 7fixed terms, 26covariates, 28primary, 26sparse, 28formulafixed model, 26G structure, 9, 29, 37ginverse, 69GLM, 31GLMM, 32grid, 69group, 69help, 24heterogeneityerror variance, 9heterogeneous variance models, 42homogeneous variance models, 41hypothesis testingrandom effects, 14identifiable, 14IID, 8inbreeding, 57incremental Wald statistics, 17information matrixexpected, 12observed, 11initial values, 29inverse coefficient matrix, 23isotropic covariance model, 9kriging, 45kronecker product, 9likelihoodlog residual, 11residual, 11linear mixed model, 7link(), 51longitudinal databalanced example, 113marginal distribution, 11Matérn variance structure, 47matrixaverage information, 23inverse coefficient, 23maxiter, 70mbf, 69MET, 9meta analysis, 9methods, 23missing valuescovariates, 28, 31design factors, 31response, 31mixedeffects, 7model, 7mixed model equations, 13modelcorrelation, 10covariance, 10model formularandom, 29multi-environment trial, 9multivariate analysis, 33NA, 21na.method.Y, 31Nebraska Intrastate Nursery, 2nonidentifiable, 14objective function, 13observed information matrix, 11operator+, 22∼ , 22ordering of terms, 121overspecified, 14P, 29parameterscale, 7variance, 7plot(), 23positive definite matrix, 42power, 125Predictprwts, 66prediction, 60predictpoints, 69prior mean, 13productdirect, 9kronecker, 9pworkspace, 70pwrpoints, 69R structure, 8, 29, 37randomargument, 22effects, 7correlated, 13model formula, 29regressions, 51terms, 29random coefficients, 113
Index 133random regression, 10RCB, 29design, 3rcov, 23, 30argument, 22read.table(), 21REML, 11, 14log-likelihood, 23REMLRT, 14resid(), 23residualerror, 7likelihood, 11residual variance, 7residual maximum likelihood, 11scale parameter, 7score, 11section, 8separability, 9shrinkage, 13singularities, 121sparse equations, 121sparse matrix methods, 12spatialanalysis, 9, 95example, 95model, 39spline.step, 69splinepoints, 68splinescale, 69split plot, 80stepsize, 70summary(), 23summary.asreml(), 23tests of hypotheses, 14, 16trace, 69trait, 33U, 29unbalanced datasources of variability, 87unbalanced nested design, 84unreplicated trial, 100varianceparameter, 7, 11estimation, 12residual, 7variance functionaexp(), 126agau(), 126ante(,k), 126ante(,k), 49ar1(), 30, 124ar2(), 124ar3(), 124arma(), 125chol(,k), 126cir(), 126cor(), 125corb(), 125corg(), 125diag(), 126exp(), 125gau(), 125giv(), 127id(), 124idh(), 126ieuc(), 125iexp(), 125igau(), 125isp(), 126ma1(), 124ma2(), 124mtrn(), 126ped(), 127sar(), 124sar2(), 124us(), 126variance modelcombining, 14, 50correlation, 41heterogeneous, 42homogenous, 41specification, 37variogram, 16Wald statistics, 35Wald test, 17wald(), 23weighted analysis, 31weights, 31workspace, 70
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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.
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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
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 124 and 125: 8.8 Paired Case-Control Study 112..
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
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