ASReml-S reference manual - VSN International

More documents

Recommendations

Info

8.3 Unbalanced nested design 84[4,] 7.682954 7.682954 7.682954 NA 9.715025 9.715025 9.715025 9.715025[5,] 9.715025 9.715025 9.715025 9.715025 NA 7.682954 7.682954 7.682954[6,] 9.715025 9.715025 9.715025 9.715025 7.682954 NA 7.682954 7.682954[7,] 9.715025 9.715025 9.715025 9.715025 7.682954 7.682954 NA 7.682954[8,] 9.715025 9.715025 9.715025 9.715025 7.682954 7.682954 7.682954 NA[9,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[10,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[11,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[12,] 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025 9.715025[,9] [,10] [,11] [,12][1,] 9.715025 9.715025 9.715025 9.715025[2,] 9.715025 9.715025 9.715025 9.715025[3,] 9.715025 9.715025 9.715025 9.715025[4,] 9.715025 9.715025 9.715025 9.715025[5,] 9.715025 9.715025 9.715025 9.715025[6,] 9.715025 9.715025 9.715025 9.715025[7,] 9.715025 9.715025 9.715025 9.715025[8,] 9.715025 9.715025 9.715025 9.715025[9,] NA 7.682954 7.682954 7.682954[10,] 7.682954 NA 7.682954 7.682954[11,] 7.682954 7.682954 NA 7.682954[12,] 7.682954 7.682954 7.682954 NA$‘Variety:Nitrogen‘$avsedmin mean max7.682954 9.160824 9.715025For the first two predictions, the average SED is calculated from the average variance ofdifferences.8.3 Unbalanced nested designThis example illustrates some further aspects of testing fixed effects in linear mixedmodels. It differs from the previous split plot example in that it is unbalanced, so morecare is required in assessing the significance of fixed effects.The experiment was reported by Dempster et al. [1984] and was designed to comparethe effect of three doses of an experimental compound (control, low and high) on thematernal performance of rats. Thirty female rats (Dams) were randomly split into threegroups of 10 and each group randomly assigned to the three different doses. All pups ineach litter were weighed. The litters differed both in total size and composition of malesand females. Thus the additional covariate littersize was included in the analysis. Thedifferential effect of the compound on male and female pups was also of interest.Three litters had to be dropped from the experiment, which meant that one dose had only7 dams. The analysis must account for the presence of between dam variation, but mustalso recognise the stratification of the experimental units (pups within litters) and therestricted randomisation of the doses to the dams. An indicative ANOVA decompositionfor this experiment is given in Table 8.2.The Dose and littersize effects are implicitly tested against the residual dam variation,while the remaining effects are tested against the residual within litter variation. Theasreml call is:> rats.asr
Table 8.2. Rat data: ANOVA decompositionstratum decomposition type df or ne8.3 Unbalanced nested design 85(Intercept) fixed 1damsDose fixed 2littersize fixed 1Dam random 27dams:pupsSex fixed 1Dose:Sex fixed 2errorrandomThe abbreviated output from asreml convergence monitoring, followed by variance component(from summary()) and Wald tests (from wald()) tables are:> rats.asr$monitor[,(-2:-5)]1 6 7 final constraintloglik 74.2174175 87.2397736 87.2397915 87.2397915 S2 0.1967003 0.1653213 0.1652993 0.1652993 df 315.0000000 315.0000000 315.0000000 315.0000000 Dam 0.1000000 0.5854392 0.5866881 0.5866742 PositiveR!variance 1.0000000 1.0000000 1.0000000 1.0000000 Positive>> summary(rats.asr)$varcompgamma component std.error z.ratio constraintDam 0.5866742 0.09697687 0.03318527 2.922287 PositiveR!variance 1.0000000 0.16529935 0.01367005 12.092083 Positive> wald(rats.asr,denDF="default",ssType="conditional")$WaldDf denDF F_inc F_con Margin Pr(Intercept) 1 32.0 9049.0000 1099.0000 0.000000e+00littersize 1 31.5 27.9900 46.2500 B 1.690248e-07Dose 2 23.9 12.1500 11.5100 A 3.132302e-04Sex 1 299.8 57.9600 57.9600 A 0.000000e+00Dose:Sex 2 302.1 0.3984 0.3984 B 6.733474e-01$stratumVariancesdf Variance Dam R!varianceDam 22.56348 1.2776214 11.46995 1R!variance 292.43652 0.1652996 0.00000 1>The incremental Wald tests indicate that the interaction between Dose and Sex is notsignificant. Since these tests are sequential then the test for the Dose:Sex term is appropriateas it respects marginality with both the main effects of dose and sex fitted beforethe inclusion of the interaction.The conditional F-test helps assess the significance of the other terms in the model. Itconfirms littersize is significant after the other terms, that dose is significant when
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 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 94 and 95: 8.2 Split Plot Design 82In this exa
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
Page 144 and 145: Index 132F statistics, 17fa(,k), 49
show all

ASReml-S reference manual - VSN International

Create successful ePaper yourself

Delete template?

Save as template?