ASReml-S reference manual - VSN International

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4.1.1 Specifying variance models in asreml4.2 A sequence of structures for the NIN field trial data 38Variance models are specified with special model functions in the random and rcov formulae.Scaled identity defaults are used if no variance model is explicitly specified. TableB.1 presents the complete range of variance models available in asreml and details ofindividual (variance model) function calls are given in Section 4.4. Most of the modelslisted in Table B.1 are correlation models (id() to agau()) but these are easily generalisedto• homogeneous variance models by appending a v to the function name, for example,converting id() to idv() to specify IID errors,• heterogeneous variance models by appending h to the function name, for example,converting id() to idh() to specify independent but heterogeneous errors.Rules for combining variance models and methods for setting initial values are given inSection 4.5.4.2 A sequence of structures for the NIN field trial dataBy way of introduction, seven variance structures of increasing complexity are consideredfor the NIN field trial data (see Section 1.3.1). This is to give a general feel for variancemodelling in asreml from a practical perspective and some idea of the types of modelsthat are possible (Table B.1).This section illustrates:• changes to u and e and the assumptions regarding the variance these terms,• the impact this has on the random formula for specifying the G structures for u andthe rcov formulae for specifying the R structure(s) for the residuals in e.Model 1: randomised complete block (RCB) analysis - blocks fixed> rcb.asr rcb.asr rcb.asr
Model 1a: RCB analysis - blocks random4.2 A sequence of structures for the NIN field trial data 39> rcb.asr rcb.asr$gammas[”Replicate”]*rcb.asr$sigmThis is done automatically by the summary method (summary.asreml()) where both variancecomponents and variance ratios are returned.In asreml, the IID variance structure is the default for the extra random terms in themodel and does not need to be formally specified in the random formula.All random terms other than residual error must appear in the random formula (seeSection 3.9).Model 1b: RCB analysis with G and R structures> rcb.asr sp.asr
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 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 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
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
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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
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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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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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ASReml-S reference manual - VSN International

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