ASReml-S reference manual - VSN International

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3Fitting the mixed model3.1 IntroductionThis chapter begins with a brief introduction covering data frame preparation, fittingthe linear model and the fitted asreml object followed by a detailed description of theasreml function call and some technical details of model fitting, including the treatmentof missing values, and setting initial values for variance parameters. The basic conceptsare illustrated using a real example and pointers to following chapters are given. Forconsistency, the same data are also used for illustration in later chapters where possible.Advanced topics such as models for variance components or genetic models are consideredin later chapters. Chapter 8 gives a lengthy set of additional worked examples.3.2 The data frameData for analysis using asreml are generally contained in a text file or a spreadsheet andare read into a data frame using the appropriate S-PLUS functions. Variates and factorsin the data frame are then resolved through the data argument of the asreml functioncall.The first 25 lines of the comma separated text file nin89.csv containing the NIN fieldtrial data described in Section 1.3.1 are reproduced below. Note that the data are infield order (rows within columns) and a header line (first row) is included. In this casethere are 11 comma separated data fields (Variety. . . Column) and the complete file has224 data rows, one for each variety in each replicate.Variety,Id,pid,raw,Rep,nloc,yield,lat,long,Row,ColumnLANCER,1,1101,585,1,4,29.25,4.3,19.2,16,1BRULE,2,1102,631,1,4,31.55,4.3,20.4,17,1REDLAND,3,1103,701,1,4,35.05,4.3,21.6,18,1CODY,4,1104,602,1,4,30.1,4.3,22.8,19,1ARAPAHOE,5,1105,661,1,4,33.05,4.3,24,20,1NE83404,6,1106,605,1,4,30.25,4.3,25.2,21,1NE83406,7,1107,704,1,4,35.2,4.3,26.4,22,1NE83407,8,1108,388,1,4,19.4,8.6,1.2,1,2CENTURA,9,1109,487,1,4,24.35,8.6,2.4,2,2SCOUT66,10,1110,511,1,4,25.55,8.6,3.6,3,2COLT,11,1111,502,1,4,25.1,8.6,4.8,4,2NE83498,12,1112,492,1,4,24.6,8.6,6,5,2
NE84557,13,1113,509,1,4,25.45,8.6,7.2,6,2NE83432,14,1114,268,1,4,13.4,8.6,8.4,7,2NE85556,15,1115,633,1,4,31.65,8.6,9.6,8,2NE85623,16,1116,513,1,4,25.65,8.6,10.8,9,2CENTURAK78,17,1117,632,1,4,31.6,8.6,12,10,2NORKAN,18,1118,446,1,4,22.3,8.6,13.2,11,2KS831374,19,1119,684,1,4,34.2,8.6,14.4,12,2..3.2 The data frame 21This is typical of the required format: a matrix of observations with a row for eachsampling unit and columns containing variates, covariates, factors, weights and identitiesin any convenient order. An optional, though recommended, header line can be used toname the data columns and missing values are denoted by NA.3.2.1 Creating a data frame from a text fileA data frame is normally created from a text file data source using an S-PLUS functioncall like:> nin89 nin89 nin89 nin89$ID
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 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
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7.3 Methods and related functions 7
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pedigree7.3 Methods and related fun
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8Examples8.1 IntroductionThis secti
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8.2 Split Plot Design 82In this exa
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8.3 Unbalanced nested design 84[4,]
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8.3 Unbalanced nested design 86adju
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8.4 Sources of variability in unbal
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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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Page 130 and 131:
Page 132 and 133:
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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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