ASReml-S reference manual - VSN International

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3.15 Multivariate analysis 34R!trait_wt2:wt0 31.58214 31.58214 11.258510 2.805180 UnconstrainedR!trait_wt2:wt1 69.06071 69.06071 21.681866 3.185183 UnconstrainedR!trait_wt2:wt2 94.76905 94.76905 27.357257 3.464128 UnconstrainedR!trait_wt3:wt0 29.37619 29.37619 14.112774 2.081532 UnconstrainedR!trait_wt3:wt1 64.54345 64.54345 26.334015 2.450954 UnconstrainedR!trait_wt3:wt2 116.35595 116.35595 35.791126 3.250972 UnconstrainedR!trait_wt3:wt3 181.55655 181.55655 52.410398 3.464132 UnconstrainedR!trait_wt4:wt0 24.66071 24.66071 16.328866 1.510253 UnconstrainedR!trait_wt4:wt1 56.72024 56.72024 30.044386 1.887881 UnconstrainedR!trait_wt4:wt2 122.88690 122.88690 41.098144 2.990084 UnconstrainedR!trait_wt4:wt3 207.21310 207.21310 61.801813 3.352864 UnconstrainedR!trait_wt4:wt4 268.40952 268.40952 77.482498 3.464131 UnconstrainedA bivariate exampleThe asreml function call for a basic bivariate analysis of the wether trial data describedin Section 1.3.3 is:> wether.asr wether.asr$monitor[,c(1,’final’,’constraint’)]1 final constraintloglik -886.5213 -723.4616740 S2 1.0000 1.0000000 df 2964.0000 2964.0000000 trait:Team!trait_gfw:gfw 0.4000 0.3744933 Unconstrainedtrait:Team!trait_fdiam:gfw 0.3000 0.3887395 Unconstrainedtrait:Team!trait_fdiam:fdiam 1.3000 1.3653342 Unconstrainedtrait:Tag!trait_gfw:gfw 0.2000 0.2571589 Unconstrainedtrait:Tag!trait_fdiam:gfw 0.2000 0.2195574 Unconstrainedtrait:Tag!trait_fdiam:fdiam 2.0000 1.9208175 UnconstrainedR!variance 1.0000 1.0000000 FixedR!trait_gfw:gfw 0.2000 0.1983514 UnconstrainedR!trait_fdiam:gfw 0.2000 0.1288901 UnconstrainedR!trait_fdiam:fdiam 0.4000 0.4406009 UnconstrainedFinal estimmates of the variance components are given by summary() (illustrated above)and an analysis of variance calculating the approximate denominator degrees of freedomand conditional F-tests can be obtained by:> wald(wth0.asr,denDF=’default’,ssType=’conditional’)Df denDF F_inc F_con Margin Prtrait 2 33.0 5762 5762 A 0trait:Year 4 1162.2 1095 1095 B 03.15.2 Specifying multivariate variance structuresA more sophisticated default error structure is required for multivariate analysis in asreml.Using the notation of Chapter 4, consider a multivariate analysis with n t traits and n
3.16 Testing of terms: the wald() method 35units in which the data are ordered traits within units. An algebraic expression for thevariance matrix in this case isI n ⊗ Σwhere Σ (n t ×n t ) is an unstructured variance matrix.For a standard multivariate analysis• the error structure must be specified as two-dimensional, with independent units andoften an unstructured variance matrix across traits.– the rcov this model is therefore rcov ∼ units:us(trait)– missing values are allowed and must be fitted. asreml automatically includes thespecial factor mv in the sparse formula in such cases.• for the default analysis, that is the response is specified as a matrix, the R structuremust reflect the data order of traits within units which means that the term unitsmust appear before trait in the rcov formula.• variance parameters are variances, not variance ratios.• the error structure is often specified as an unstructured variance matrix but correlationmodels may also be used. asreml attempts to detect such cases and fix or estimatethe residual scale parameter accordingly.For example, with the Wolfinger data the times are equally spaced so we could fit afirst order autoregressive model using:> wolfinger.asr
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 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 98 and 99:
8.3 Unbalanced nested design 86adju
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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
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8.6 Spatial analysis of a field exp
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Variety predicted.value standard.er
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8.7 Unreplicated early generation v
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8.7 Unreplicated early generation v
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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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Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
A.3 Aliasing and singularities 122W
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Table B.1: Details of the available
Page 138 and 139:
B Available variance models 126Deta
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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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