ASReml-S reference manual - VSN International

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Table B.1: Details of the available variance modelsB Available variance models 124functionnamedescriptionalgebraicformnumber of parameterscorr hom hetvariance varianceCorrelation modelsid() identity C ii= 1, C ij= 0, i ≠ j 0 1 ωar1() 1 st orderautoregressiveC ii= 1, C i+1,i= φ 1C ij= φ 1C i−1,j, i > j + 1|φ 1| < 11 2 1 + ωar2() 2 nd orderautoregressivear3() 3 rd orderautoregressivesar()symmetricautoregressiveC ii= 1,C i+1,i= φ 1/(1 − φ 2)C ij= φ 1C i−1,j+φ 2C i−2,j, i > j +1|φ 1± φ 2| < 1,|φ 1| < 1, |φ 2| < 1C ii= 1, Ω = 1 − φ 2− φ 3(φ 1+ φ 3),C i+1,i= (φ 1+ φ 2φ 3)/Ω,C i+2,i= (φ 1(φ 1+ φ 3) + φ 2(1 − φ 2))/Ω,C ij= φ 1C i−1,j+ φ 2C i−2,j+ φ 3C i−3,j, i > j + 2|φ 1| < (1 − φ 2), |φ 2| < 1, |φ 3| < 1C ii= 1,C i+1,i= φ 1/(1 + φ 2 1 /4)C ij= φ 1C i−1,j− φ 2 1 /4 C i−2,j ,i > j + 1|φ 1| < 12 3 2 + ω3 4 3 + ω1 2 1 + ωsar2()constrainedautoregressive 3used forcompetitionas for AR3 usingφ 1= γ 1+ 2γ 2,φ 2= −γ 2(2γ 1+ γ 2),φ 3= γ 1γ 2 , 22 3 2 + ωma1() 1 st ordermoving averagema2() 2 nd ordermoving averageC ii= 1,C i+1,i= −θ 1/(1 + θ 2 ) 1C ji= 0, j > i + 2|θ 1| < 1C ii= 1,C i+1,i= −θ 1(1 − θ 2)/(1 + θ 2 + 1 θ2)2C i+2,i= −θ 2/(1 + θ 2 + 1 θ2)2C ji= 0, j > i + 2θ 2± θ 1< 1|θ 1| < 1, |θ 2| < 11 2 1 + ω2 3 2 + ω
B Available variance models 125Details of the available variance modelsfunctionnamedescriptionalgebraicformnumber of parameterscorr hom hetvariance variancearma()autoregressivemoving averageC ii= 1,C i+1,i= (θ − φ)(1 − θφ)/(1 +θ 2 − 2θφ)C ji= φC j−1,i, j > i + 1|θ| < 1, |φ| < 12 3 2 + ωcor()uniformcorrelationC ii= 1, C ij= θ, i ≠ j 1 2 1 + ωcorb()bandedcorrelationC ii= 1C i+j,i= φ j, 1 ≤ j ≤ ω − 1|φ j | < 1ω − 1 ω 2ω − 1corg()generalcorrelationcorgh() = us()C ii= 1C ij= φ ij, i ≠ j|φ ij| < 1ω(ω−1)2ω(ω−1)+1 ω(ω−1)2 2+ ωOne-dimensional equally spaced power modelsexp() exponential C ii= 1C ijgau() gaussian C ii= 1= φ |x i−x j | , i ≠ jx i are coordinates|φ| < 1C ij= φ (x i−x j ) 2x i are coordinates|φ| < 11 2 1 + ω1 2 1 + ωTwo-dimensional irregularly spaced power modelsiexp() isotropic exponentialigau() isotropic gaussianieuc() isotropic euclideanC ii= 1C ij= φ |x i−x j |+|y i −y j |x and y vectors of coordinates|φ| < 1C ii= 1C ij= φ (x i−x j ) 2 +(y i −y j ) 2x and y vectors of coordinates|φ| < 1C ii= 1C ij= φ√(xi −x j ) 2 +(y i −y j ) 2x and y vectors of coordinates|φ| < 11 2 1 + ω1 2 1 + ω1 2 1 + ω
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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
Page 86 and 87: 7.3 Methods and related functions 7
Page 88 and 89: pedigree7.3 Methods and related fun
Page 90 and 91: 7.3 Methods and related functions 7
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 134 and 135: A.3 Aliasing and singularities 122W
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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