ASReml-S reference manual - VSN International

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5.4 Using Pedigree and G-inverse objects 58ginvainvinbreedingdeta data frame with 3 columns holding the lower triangle of the inverserelationship matrix in sparse form. The first 2 columns are the rowand column indices of the matrix element, respectively, and the thirdcolumn holds the (inverse) matrix element itself. Sort order is columnswithin rows, that is, the lower triangle row-wise. This data frame hasan attribute rowNames containing the vector of identifiers for the rowsmatrix.the diagonal elements of the inverse relationship matrix.the inbreeding coefficient for each individual, calculated as diag(A −I).the determinant.5.4 Using Pedigree and G-inverse objectsPutting it all together, an analysis of average daily gain (y1 in harvey.dat ) using thepedigree harvey.ped can be obtained from:> harvey.ainv adg.asr summary(adg.asr)$varcompgamma component std.error z.ratio constraintped(Calf) 1.828628 499.5096 500.5393 0.9979427 PositiveR!variance 1.000000 273.1609 410.0210 0.6662119 Positiveand the BLUP estimates by:> summary(adg.asr)$coef.randomsolution std error z ratioped(Calf)_Sire_1 11.0252890 17.44623 0.631958069ped(Calf)_Sire_2 -17.6385364 17.44623 -1.011022518ped(Calf)_Sire_3 6.6132474 18.02693 0.366853786ped(Calf)_Sire_4 -8.0185320 18.76570 -0.427297361ped(Calf)_Sire_5 8.0185320 18.76570 0.427297361ped(Calf)_Sire_6 8.4824687 17.13032 0.495172801ped(Calf)_Sire_7 0.4445043 16.60110 0.026775595ped(Calf)_Sire_8 -26.9640897 16.83823 -1.601361699ped(Calf)_Sire_9 18.0371167 16.60110 1.086501425ped(Calf)_101 -7.3121005 14.75468 -0.495578393ped(Calf)_102 16.3994122 14.75468 1.111471922...ped(Calf)_164 13.7740505 14.28636 0.964140026ped(Calf)_165 7.9907547 14.28636 0.559327589User specified general inverse matrices are included in an analysis in the same way.Consider an easily verified example where we define a general inverse matrix for Sire inthe harvey data as 0.5I 9 .A simple analysis fitting Sire and ignoring the pedigree:> adg1.asr summary(adg1.asr)$varcomp
5.4 Using Pedigree and G-inverse objects 59gamma component std.error z.ratio constraintSire 0.2055558 27.20922 26.59081 1.023256 PositiveR!variance 1.0000000 132.36900 25.00140 5.294463 Positivewhile including the general inverse 0.5I 9 :> sire.giv attr(sire.giv,”rowNames”) ¡- paste(”Sire ”,seq(1,9),sep=””)> adg2.asr summary(adg2.asr)$varcompgamma component std.error z.ratio constraintgiv(Sire) 0.1027814 13.61135 13.20766 1.030565 PositiveR!variance 1.0000000 132.43012 25.01868 5.293250 Positive
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Analysis of mixed modelsfor S langu
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D.G. ButlerQueensland Department of
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ContentsPreface . . . . . . . . . .
Page 10 and 11:
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
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 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
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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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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
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References 130W. W. Stroup, P. S. B
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Index 132F statistics, 17fa(,k), 49
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