ASReml-S reference manual - VSN International

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Source df F_inc F_con MSource df ddf_inc F_inc P_incSource df ddf_con F_inc F_con M P_con3.16 Testing of terms: the wald() method 36depending on whether conditional F-statistics are reported or whether the denominatordegrees of freedom are calculated. See Section 2.6 for more background on the contentsof this table.The numerator degrees of freedom for each term is easily determined as the numberof non-singular effects involved in the term. However, in general, calculation of the denominatordegrees of freedom is not trivial. asreml will only attempt the calculation ifspecifically requested as it requires further iterations of the model (using update.asreml()).
4Specifying the variance structures4.1 IntroductionThis chapter introduces variance model specification in asreml, a complex aspect of themodelling process. The key concepts are:• The mixed linear modelhas a residual termand random effectswhere in the most complex formsand eachy = Xτ + Zu + ee ∼ N(0, θR)u ∼ N(0, θG)R = ⊕ i R iG = ⊕ j G jR i = R i (φ i )G j = G j (δ j )where φ i and δ j parameterise the respective variance models.• We use the terms R structure and G structure to refer to the matrices R i and G jabove in a syntactic manner, respectively,• R and G structures are typically formed as a direct product of particular variancemodels,• The order of terms in a direct product must agree with the order of effects in thecorresponding model term,• Variance models may be correlation matrices or variance matrices with equal or unequalvariances on the diagonal. A model for a correlation matrix (eg. ar1) can beconverted to an equal variance form (eg. ar1v) and to a heterogeneous variance form(eg. ar1h),• Variances are sometimes estimated as variance component ratios (relative to the overallscale parameter, θ).Chapter 2 gives theoretical details. We begin this chapter by considering an ordered sequenceof variance structures for the NIN variety trial (see Section 4.2) as an introductionto variance modelling in practice; we then consider the topics in detail.
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 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
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
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 128 and 129:
Page 130 and 131:
Page 132 and 133:
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
Page 144 and 145:
Index 132F statistics, 17fa(,k), 49
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