ASReml-S reference manual - VSN International

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8.3 Unbalanced nested design 86adjusted for littersize and sex but ignoring dose.sex, and that sex is significantwhen adjusted for littersize and dose but ignoring dose.sex. These tests respectmarginality to the dose.sex interaction.A plot of residuals vs fitted values> plot(rats.asr, option =”f”)is shown in Figure 8.1. Before proceeding we note the possibility of several outliers, inparticular unit 66. The weight of this female rat, within litter 9 is only 3.68, compared toweights of 7.26 and 6.58 for two other female sibling pups. This weight appears erroneous,but without knowledge of the actual experiment we retain the observation.10Residuals−1−2−35.0 5.5 6.0 6.5 7.0 7.5FittedFig. 8.1. Residual plot for the rat dataWe refit the model without the Dose:Sex term.> rats2.asr summary(rats2.asr)$varcompgamma component std.error z.ratio constraintDam 0.595157 0.09791776 0.03341462 2.930386 PositiveR!variance 1.000000 0.16452427 0.01356057 12.132547 Positive> wald(rats2.asr,denDF="default",ssType="conditional")$WaldDf denDF F_inc F_con Margin Pr(Intercept) 1 32.0 8981.00 1093.00 0.000000e+00littersize 1 31.4 27.85 46.43 A 1.643469e-07
8.4 Sources of variability in unbalanced data 87Dose 2 24.0 12.05 11.42 A 3.278549e-04Sex 1 301.7 58.27 58.27 A 0.000000e+00$stratumVariancesdf Variance Dam R!varianceDam 22.60301 1.2878697 11.47231 1R!variance 294.39699 0.1645245 0.00000 1>Note that the variance parameters are re-estimated, though there is little change fromthe previous analysis.The impact of (wrongly) dropping dam from this model is shown below:> rats3.asr wald(rats3.asr,denDF="default",ssType="conditional")$WaldDf denDF F_inc F_con Margin Pr(Intercept) 1 317 47080.00 3309.00 0.000000e+00littersize 1 317 68.48 146.50 A 0.000000e+00Dose 2 317 60.99 58.43 A 0.000000e+00Sex 1 317 24.52 24.52 A 2.328158e-06$stratumVariancesNULL>Even if a random term is not ’significant’, it should not be dropped from the model ifit represents a strata of the design as in this case. The impact of deleting Dam on thesignificance tests for the fixed effects is substantial and not surprising. This reinforcesthe importance of preserving the strata of the design when assessing the significance offixed effects.8.4 Sources of variability in unbalanced dataThis example illustrates an approach to the analysis of unbalanced data where the mainaim is to determine the sources of variation rather than assess the significance of imposedtreatments. The data are taken from Cox and Snell [1981] and involve an experiment toexamine the variability in the production of car voltage regulators. Standard productionof regulators involves two steps: 1) Regulators are taken from the production line andpassed to a setting station which adjusts the regulator to operate within a specifiedrange of voltages, and, 2) from the setting station the regulator is then passed to atesting station where it is tested and returned if outside the required range.A total of 64 regulators was tested at four testing stations (Teststat). The voltagefor individual regulators was set at a total of 10 setting stations (Setstat). A variablenumber of regulators (between 4 to 8) were set at each station, however each regulatorwas tested at every testing station. The asreml function call is:> voltage.asr summary(voltage.asr)$varcomp
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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
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 94 and 95: 8.2 Split Plot Design 82In this exa
Page 96 and 97: 8.3 Unbalanced nested design 84[4,]
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
Page 144 and 145: Index 132F statistics, 17fa(,k), 49
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ASReml-S reference manual - VSN International

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