ASReml-S reference manual - VSN International

More documents

Recommendations

Info

B Available variance models 126Details of the available variance modelsfunctionnamedescriptionalgebraicformnumber of parameterscorr hom hetvariance varianceisp() spherical C ij= 1 − 3 2 θ ij + 1 2 θ3 ij0 < φ 11 2 1 + ωcir()circular (Websterand Oliver [2001])C ij= 1− 2 (θ π ij√1 − θ2ij+ sin −1 θ ij )1 2 1 + ω0 < φ 1aexp() anisotropic exponentialC ii= 1C ij= φ |x i−x j |1 φ |y i−y j |2x and y vectors of coordinates|φ 1| < 1, |φ 2| < 12 3 2+ωagau()anisotropicgaussianC ii= 1C ij= φ (x i−x j ) 21 φ (y i−y j ) 22x and y vectors of coordinates|φ 1| < 1, |φ 2| < 12 3 2 + ωmtrn() Matérn withfirst 1 ≤ k ≤ 5parametersspecified by theuserC ij=Matérn: see Section 4.4.3φ > 0 range, ν shape(0.5)δ > 0 anisotropy ratio(1),α anisotropy angle(0),λ(1|2) metric(2)k k+1 k + ωHeterogeneous variance modelsdiag() diagonal = idh() Σ ii= φ iΣ ij= 0, i ≠ j - - ωus()unstructuredgeneral covariancematrixΣ ij = φ ij- -ω(ω+1)2ante(,k)chol(,k)antedependenceorder k1 ≤ order ≤ω − 1choleskyorder k1 ≤ order ≤ω − 1fa(,k) factor analyticorder kΣ −1 = UDU ′D ii= d i, D ij= 0, i ≠ jU ii= 1, U ij= u ij, 1 ≤ j − i ≤orderU ij = 0, i > jΣ = LDL ′D ii= d i, D ij= 0, i ≠ jL ii= 1, L ij= l ij, 1 ≤ i−j ≤ orderΣ = ΓΓ ′ + Ψ,Γ contains covariance factorsΨ contains specific variance- - (k + 1)(ω − k/2)- - (k + 1)(ω − k/2)- - kω + ω
B Available variance models 127Details of the available variance modelsfunctionnamedescriptionalgebraicformnumber of parameterscorr hom hetvariance varianceInverse relationship matricesgiv() generalised inverse - 1 -ped() inverse relationship matrix derived from pedigree - 1 -
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 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 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 136 and 137: Table B.1: Details of the available
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
show all

ASReml-S reference manual - VSN International

Create successful ePaper yourself

Delete template?

Save as template?