ASReml-S reference manual - VSN International

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8.4 Sources of variability in unbalanced data 88gamma component std.error z.ratio constraintSetstat 2.334163e-01 1.193692e-02 8.814339e-03 1.354262 PositiveSetstat:Regulatr 6.018174e-01 3.077697e-02 8.453330e-03 3.640810 PositiveTeststat 6.427520e-02 3.287037e-03 3.337300e-03 0.984939 PositiveSetstat:Teststat 1.011929e-07 5.175009e-09 5.323475e-10 9.721111 BoundaryR!variance 1.000000e+00 5.114004e-02 5.260720e-03 9.721111 PositiveThe convergence criterion was satisfied, however, the variance component estimate forthe Setstat:Teststat term has been fixed at the boundary. The default constraintfor variance components is to ensure that the REML estimate remains positive. If anupdate for any variance component results in a negative value then asreml sets thatvariance component to a small positive value. If this occurs in subsequent iterationsthe parameter is fixed at the boundary. The default parameter constraints (Positivefor variance components) can be altered (to Unconstrained, for example) by changingthe constraint code in the initial value list object(s) for random parameters, that is,the R.param and G.param arguments to asreml. These lists are returned in the asremlobject and are best accessed via the function asreml.gammas.ed(). In this example, thefollowing sequence would achieve this:> temp voltage.asr plot(voltage.asr, option = ”f”)gives a residual plot which indicates two unusual data values (Figure 8.2). These valuesare successive observations, 210 and 211, respectively, being testing stations 2 and 3 forsetting station J, regulator 2. These observations will be retained for consistency withother analyses conducted by Cox and Snell [1981].The model omitting the Setstat:Teststat term:> voltage2.asr summary(voltage2.asr)$varcompgamma component std.error z.ratio constraintSetstat 0.23341667 0.011936975 0.008813969 1.3543246 PositiveSetstat:Regulatr 0.60181723 0.030777054 0.008453248 3.6408553 PositiveTeststat 0.06427521 0.003287047 0.003337314 0.9849378 PositiveR!variance 1.00000000 0.051140201 0.005260744 9.7210963 PositiveThe column labelled z.ratio is calculated to give a guide as to the significance of thevariance components. The statistic is simply the REML estimate of the variance componentdivided by the square root of the diagonal element (for each component) of theinverse of the average information matrix. The diagonal elements of the expected informationmatrix are the asymptotic variances of the REML estimates of the varianceparameters. These statistics cannot be used to test the null hypothesis that the variancecomponent is zero. The conclusions using this crude measure are inconsistent with theconclusions obtained from the REML log-likelihood ratio (Table 8.3).
8.5 Balanced repeated measures 891.51.0Residuals0.50.0−0.5−1.016.0 16.5FittedFig. 8.2. Residuals vs fitted values for the voltage dataTable 8.3. REML log-likelihood ratio test for each variance component in the voltage datatermloglikelihood −2× difference P-value− Setstat 200.31 5.864 .0077− Setstat:Regulatr 184.15 38.19 .0000− Teststat 199.71 7.064 .00398.5 Balanced repeated measuresThe data for this example comes from an experiment conducted at Rothamstead ExperimentalStation, UK, by J. Lamptey. It consists of a total of 5 measurements of height(cm) taken on 14 plants. The 14 plants were either diseased or healthy and were arrangedin a glasshouse in a completely random design. Plant heights were measured 1, 3, 5, 7and 10 weeks after the plants were placed in the glasshouse. There were 7 plants in eachtreatment. The data are illustrated in Figure 8.3.The following illustrates several repeated measures analyses. For some of these it isconvenient to arrange the data in a multivariate form, with 7 columns containing the plantnumber, treatment identification and the 5 heights, respectively, while for other analyses,in particular power models, it is necessary to expand the data frame in a relational senseso that the response, response names and a variate for the time of measurement occupyone column each.The data frame grass is in multivariate form:> grass
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Analysis of mixed modelsfor S langu
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D.G. ButlerQueensland Department of
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ContentsPreface . . . . . . . . . .
Page 10 and 11:
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
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
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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