ASReml-S reference manual - VSN International

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Σ = [σ ij ] :{σii = σ 2 , ∀iσ ij = σ ji , i ≠ j.4.4 Variance model functions 42Note that if Σ is a correlation model, a homogeneous variance model (with one extraparameter) is formed as σ 2 IΣ.For example, the homogeneous variance model corresponding to id() is idv() where Σ =σ 2 I ω (or Σ = γI ω ).4.3.3 Heterogeneous variance modelsThe third variance model is the heterogeneous variance model in which the diagonalelements are positive but differ. That is,{σii = σi 2Σ = [σ ij ] :, i = 1 . . . ωσ ij = σ ji , i ≠ j.For the models defined in terms of correlation matrices, allowance for unequal variancescan be made by applying a diagonal matrix d of standard errors to the correlation matrixto generate a heterogeneous variance model. That is D 1/2 ΣD 1/2 In this case, ω extraparameters are added to the vector of initial values.For example, the heterogeneous variance model corresponding to id() is idh() where Σ =diag(σ 1 , . . . , σ ω ).4.3.4 Positive definite matricesFormation of the mixed model equations (MME) requires the inversion of the variancematrix in the R and G structures. We therefore require these matrices to be either negativedefinite or positive definite. They must not be singular. Negative definite matriceswill have negative elements on the diagonal of the matrix and/or its inverse. The exceptionis the fa model which has been specifically designed to fit singular matrices[Thompson et al., 2003].4.4 Variance model functionsasreml has a wide range of variance models which can be used to specify the variancematrix of terms in the random and rcov formulae. The following considers the variousmodels in terms of functional groups and describes their syntax and application.In general, the correlation models described in the following sections have correspondingvariance models whose names are simply derived by appending ”v” or ”h” to thecorrelation function name. In the former case this yields a homogeneous variance modelwhile the latter gives the corresponding heterogeneous model. For example, for the simplecorrelation model cor(), there also exists the variance functions corv() and corh(). Theexistence or otherwise of such models is noted for each functional group in the sectiondetailing initial model parameter values.
4.4 Variance model functions 434.4.1 Default identityid(obj)idv(obj, init=NA)idh(obj, init=NA)Required argumentsobja factor in the data frame.Optional argumentsinita vector of initial parameter values. This vector can have an optional namesattribute to set the boundary constraint for each parameter. In this case, thename of each element may be one of ”P”, ”U” or ”F” for positive, unconstrainedor fixed, respectively.modelnumber of parametersf form: f() fv() fh()id 0 1 nDetailsasreml uses the id() correlation model or the idv() simple variance component model,depending on context (see the rules for combining variance models in Section 4.5), forterms in the random or rcov formulae that have no variance model explititly specified.4.4.2 Time series type modelsar1(obj, init=NA)ar2(obj, init=NA)ar3(obj, init=NA)sar(obj, init=NA)sar2(obj, init=NA)ma1(obj, init=NA)ma2(obj, init=NA)arma(obj, init=NA)DescriptionIncludes autoregressive models of order 1, 2 and 3 (ar1, ar2 and ar3), symmetric autoregressive(sar), constrained autoregressive order 3 (sar2), moving average models of order1 and 2 (ma1, ma2) and the autoregressive-moving average model (arma).Required argumentsobja factor in the data frame.Optional arguments
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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 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 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
Page 100 and 101: 8.4 Sources of variability in unbal
Page 102 and 103: 8.5 Balanced repeated measures 902
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8.5 Balanced repeated measures 92Ta
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8.5 Balanced repeated measures 94wh
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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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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
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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