ASReml-S reference manual - VSN International

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8.2 Split Plot Design 82In this example there are four terms included in the summary. The overall mean(Intercept) is included though it is of no interest for these data. The tests are sequential,that is the effect of each term is assessed by the change in sums of squares achievedby adding the term to the current model, given those terms appearing above the currentterm are already included. For example, the effect of Nitrogen is assessed by calculatingthe change in sums of squares for the two models (Intercept)+Variety+Nitrogenand (Intercept)+Variety. No refitting occurs, that is the variance parameters are heldconstant at the REML estimates obtained from the currently specified fixed model.The usual ANOVA divides into three strata, with treatment effects separating into differentstrata as a consequence of the balanced design and the confounding of main effectsof Variety with whole-plots. It is straightforward to derive the ANOVA estimates of thestratum variances from the above REML estimates. That is,blocks = 12˜σ 2 b + 4˜σ 2 w + ˜σ 2 = 3175.1blocks.wplots = 4˜σ 2 w + ˜σ 2 = 601.3residual = ˜σ 2 = 177.1The incremental Wald tests have an asymptotic χ 2 distribution, with degrees of freedom(df) given by the number of estimable effects (the number in the df column). The denominatordegrees of freedom for testing fixed effects and approximate stratumm variancesare returned by:> wald(oats.asr, denDF="default")$WaldTestsDf denDF F inc Pr(Intercept) 1 5 245.1000 0.000000e+00Variety 2 10 1.4850 2.723869e-01Nitrogen 3 45 37.6900 4.034452e-08Variety:Nitrogen 6 45 0.3028 9.321988e-01$stratumVariancesdf Variance Blocks Blocks:Wplots R!varianceBlocks 5 3175.0556 12 4 1Blocks:Wplots 10 601.3306 0 4 1R!variance 45 177.0833 0 0 1This is a simple problem for balanced designs, such as the split plot design, but it is notstraightforward to determine the relevant denominator df in unbalanced designs, such asthe rat data set described in the next section.Tables of predicted means for the Variety, Nitrogen and Variety:Nitrogen effects canbe obtained from the predict method:> oats.pv oats.pv$predictions$Nitrogen$Nitrogen$pvalsNotes:
8.2 Split Plot Design 83- Variety is averaged over fixed levels- Blocks terms are ignored unless specifically included- Wplots terms are ignored unless specifically included- The cells of the hypertable are calculated from all model terms constructedsolely from factors in the averaging and classify sets.Nitrogen predicted.value standard.error est.status1 0.2_cwt 98.88889 7.17471 Estimable2 0.4_cwt 114.22222 7.17471 Estimable3 0.6_cwt 123.38889 7.17471 Estimable4 0_cwt 79.38889 7.17471 Estimable$Nitrogen$avsed[1] 4.435755$Variety$Variety$pvalsNotes:- Nitrogen is averaged over fixed levels- Blocks terms are ignored unless specifically included- Wplots terms are ignored unless specifically included- The cells of the hypertable are calculated from all model terms constructedsolely from factors in the averaging and classify sets.Variety predicted.value standard.error est.status1 Golden_rain 104.5000 7.797539 Estimable2 Marvellous 109.7917 7.797539 Estimable3 Victory 97.6250 7.797539 Estimable$Variety$avsed[1] 7.078904$‘Variety:Nitrogen‘$‘Variety:Nitrogen‘$pvalsNotes:Variety Nitrogen predicted.value standard.error est.status1 Golden_rain 0.2_cwt 98.50000 9.106977 Estimable2 Golden_rain 0.4_cwt 114.66667 9.106977 Estimable3 Golden_rain 0.6_cwt 124.83333 9.106977 Estimable4 Golden_rain 0_cwt 80.00000 9.106977 Estimable5 Marvellous 0.2_cwt 108.50000 9.106977 Estimable6 Marvellous 0.4_cwt 117.16667 9.106977 Estimable7 Marvellous 0.6_cwt 126.83333 9.106977 Estimable8 Marvellous 0_cwt 86.66667 9.106977 Estimable9 Victory 0.2_cwt 89.66667 9.106977 Estimable10 Victory 0.4_cwt 110.83333 9.106977 Estimable11 Victory 0.6_cwt 118.50000 9.106977 Estimable12 Victory 0_cwt 71.50000 9.106977 Estimable$‘Variety:Nitrogen‘$sed[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8][1,] NA 7.682954 7.682954 7.682954 9.715025 9.715025 9.715025 9.715025[2,] 7.682954 NA 7.682954 7.682954 9.715025 9.715025 9.715025 9.715025[3,] 7.682954 7.682954 NA 7.682954 9.715025 9.715025 9.715025 9.715025
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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()
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 88 and 89: pedigree7.3 Methods and related fun
Page 92 and 93: 8Examples8.1 IntroductionThis secti
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 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
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Index 132F statistics, 17fa(,k), 49
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ASReml-S reference manual - VSN International

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