ASReml-S reference manual - VSN International

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8.6 Spatial analysis of a field experiment 96the coding of the replicates and lattice blocks. The columns in the data frame are:> shf names(shf)[1] "Rep" "RowBlk" "ColBlk" "Row" "Column" "Variety" "yield"Lattice block numbering is typically coded within replicates, however, in this example thelattice row and column blocks were both numbered from 1 to 30. The terms in the linearmodel are therefore simply RowBlk and ColBlk. The factorsRow and Column indicate thespatial layout of the plots.Table 8.6. Field layout of Slate Hall Farm experimentColumn - Replicate levelsRow 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 1 1 1 1 1 2 2 2 2 2 3 3 3 3 32 1 1 1 1 1 2 2 2 2 2 3 3 3 3 33 1 1 1 1 1 2 2 2 2 2 3 3 3 3 34 1 1 1 1 1 2 2 2 2 2 3 3 3 3 35 1 1 1 1 1 2 2 2 2 2 3 3 3 3 36 4 4 4 4 4 5 5 5 5 5 6 6 6 6 67 4 4 4 4 4 5 5 5 5 5 6 6 6 6 68 4 4 4 4 4 5 5 5 5 5 6 6 6 6 69 4 4 4 4 4 5 5 5 5 5 6 6 6 6 610 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6Column - Rowblk levelsRow 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 1 1 1 1 1 11 11 11 11 11 21 21 21 21 212 2 2 2 2 2 12 12 12 12 12 22 22 22 22 223 3 3 3 3 3 13 13 13 13 13 23 23 23 23 234 4 4 4 4 4 14 14 14 14 14 24 24 24 24 245 5 5 5 5 5 15 15 15 15 15 25 25 25 25 256 6 6 6 6 6 16 16 16 16 16 26 26 26 26 267 7 7 7 7 7 17 17 17 17 17 27 27 27 27 278 8 8 8 8 8 18 18 18 18 18 28 28 28 28 289 9 9 9 9 9 19 19 19 19 19 29 29 29 29 2910 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30Column - Colblk levelsRow 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152 1 2 3 4 5 6 7 8 9 10 11 12 13 14 153 1 2 3 4 5 6 7 8 9 10 11 12 13 14 154 1 2 3 4 5 6 7 8 9 10 11 12 13 14 155 1 2 3 4 5 6 7 8 9 10 11 12 13 14 156 16 17 18 19 20 21 22 23 24 25 26 27 28 29 307 16 17 18 19 20 21 22 23 24 25 26 27 28 29 308 16 17 18 19 20 21 22 23 24 25 26 27 28 29 309 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3010 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Three models are considered: two spatial and the traditional lattice analysis for comparativepurposes. In the first model we fit a separable first order autoregressive processto the variance structure of the plot errors. Gilmour et al. [1997] suggest this is often auseful model to commence the spatial modelling process. The form of the variance matrixfor the plot errors (R-structure) is given byσ 2 Σ = σ 2 (Σ c ⊗ Σ r ) (8.7)where Σ c and Σ r are 15 × 15 and 10 × 10 matrix functions of the column (φ c ) and row(φ r ) autoregressive parameters respectively.Gilmour et al. [1997] recommend revision of the current spatial model based on the use ofdiagnostics such as the sample variogram of the residuals. This diagnostic and a summaryof row and column residual trends are produced by the plot() method for asreml objects.The separable autoregressive error model is fitted by:
8.6 Spatial analysis of a field experiment 97> barley1.asr summary(barley1.asr)$loglik[1] -700.3225> summary(barley1.asr)$varcompgamma component std.error z.ratio constraintR!variance 1.0000000 3.873880e+04 7.747479e+03 5.000181 PositiveR!Row.ar1 0.4585092 4.585092e-01 8.259184e-02 5.551507 UnconstrainedR!Column.ar1 0.6837766 6.837766e-01 6.329681e-02 10.802701 Unconstrained> wald(barley1.asr)Wald tests for fixed effectsResponse: yieldTerms added sequentially; adjusted for those aboveDf Sum of Sq Wald statistic Pr(Chisq)(Intercept) 1 33004556 852 < 2.2e-16 ***Variety 24 12119586 313 < 2.2e-16 ***residual (MS) 38739> plot(barley1.asr, option = ”v”)plots the sample variogram shown in Figure 8.5.0.80.60.40.21412108Column6684224RowFig. 8.5. Sample variogram of the AR1×AR1 model for the Slate Hall data
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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
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 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 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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ASReml-S reference manual - VSN International

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