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2 Some theory 24Kenward and Roger AdjustmentsIn moderately sized analyses, ASReml will also include the denominator degreesof freedom (DenDF, denoted by ν 2i , Kenward and Roger, 1997) and a probablityvalue if these can be computed. They will be for the conditional Wald F-statisticif it is reported. The !DDF i (see page 68) qualifier can be used to suppress theDenDF calculation (!DDF -1) or request a particular algorithmic method: !DDF1 for numerical derivatives, !DDF 2 for algebraic derivatives. The value in theprobability column (either P inc or P con) is computed from an F ν1i ,ν 2ireferencedistribution. An approximation is used for computational convenience when calculatingthe DenDF for Conditional F statistics using numerical derivatives. TheDenDF reported then relates to a maximal conditional incremental model (MCIM)which, depending on the model order, may not always coincide with the maximalconditional model (MCM) under which the conditional F statistic is calculated.The MCIM model omits terms fitted after any terms ignored for theconditional test (I after . in marginality pattern). In the example above, MCIMignores variety.sow when calculating DenDF for the test of water and ignoreswater.sow when calculating DenDF for the test of variety. When DenDF is notavailable, it is often possible, though anti-conservative to use the residual degreesof freedom for the denominator.Kenward and Roger (1997) pursued the concept of construction of Wald-type teststatistics through an adjusted variance matrix of ˆτ . They argued that it is usefulto consider an improved estimator of the variance matrix of ˆτ which has less biasand accounts for the variability in estimation of the variance parameters. Thereare two reasons for this. Firstly, the small sample distribution of Wald tests issimplified when the adjusted variance matrix is used. Secondly, if measures ofprecision are required for ˆτ or effects therein, those obtained from the adjustedvariance matrix will generally be preferred. Unfortunately the Wald statistics arecurrently computed using an unadjusted variance matrix.Approximate stratum variancesASReml reports approximate stratum variances and degrees of freedom for simplevariance components models. For the linear mixed-effects model with variancecomponents (setting σ 2 = 1) where G = ⊕q Hj=1 γ jI bj , it is often possibleto consider a natural ordering of the variance component parameters includingσ 2 . Based on an idea due to Thompson (1980), ASReml computes approximatestratum degrees of freedom and stratum variances by a modified Cholesky diagonalisationof the average information matrix. That is, if F is the average informationmatrix for σ, let U be an upper triangular matrix such that F = U ′ U.
2 Some theory 25We defineU c = D c Uwhere D c is a diagonal matrix whose elements are given by the inverse elementsof the last column of U ie d cii = 1/u ir , i = 1, . . . , r. The matrix U c is thereforeupper triangular with the elements in the last column equal to one. If the vectorσ is ordered in the “natural” way, with σ 2 being the last element, then we candefine the vector of so called “pseudo” stratum variance components byThenceξ = U c σvar (ξ) = D 2 cThe diagonal elements can be manipulated to produce effective stratum degreesof freedom Thompson (1980) vizν i = 2ξ 2 i /d 2 ciiIn this way the closeness to an orthogonal block structure can be assessed.
Page 1 and 2: ASRemlUser GuideRelease 2.0A R Gilm
Page 3 and 4: Published by:E-mail:Website:VSN Int
Page 5 and 6: PrefaceiiASReml is one of several u
Page 7 and 8: ContentsPrefaceiList of TablesxviiL
Page 9 and 10: Contentsvi3.3 The ASReml data file
Page 11 and 12: ContentsviiiCombining rows from sep
Page 13 and 14: Contentsx7.6 Variance structure qua
Page 15 and 16: Contentsxii12.2 The command line .
Page 17 and 18: Contentsxiv15 Examples 24115.1 Intr
Page 19: List of Tablesxvi7.3 Details of the
Page 22 and 23: List of Figuresxix15.8 Rice bloodwo
Page 24 and 25: 1 Introduction 21.1 What ASReml can
Page 26 and 27: 1 Introduction 41.4 How to use this
Page 28 and 29: 2 Some theoryThe linear mixed model
Page 30 and 31: 2 Some theory 8laid out in a rectan
Page 32 and 33: 2 Some theory 10product of matrices
Page 34 and 35: 2 Some theory 12where H = R + ZGZ
Page 36 and 37: 2 Some theory 14where y i is the
Page 38 and 39: 2 Some theory 162.4 Combining varia
Page 40 and 41: 2 Some theory 18balanced one-way cl
Page 42 and 43: 2 Some theory 20L, r × p, and l, r
Page 44 and 45: 2 Some theory 22the terms A, B, C,
Page 48 and 49: 3 A guided tourIntroductionNebraska
Page 50 and 51: 3 A guided tour 28column rectangula
Page 52 and 53: 3 A guided tour 30(see Chapter 2) t
Page 54 and 55: 3 A guided tour 32els. Similarly fo
Page 56 and 57: 3 A guided tour 34mand to run nin89
Page 58 and 59: 3 A guided tour 36* SYNTAX change:
Page 60 and 61: 3 A guided tour 38repl 3 -0.8713 1.
Page 62 and 63: 3 A guided tour 40title linenin all
Page 64 and 65: 4 Data file preparation 424.1 Intro
Page 66 and 67: 4 Data file preparation 44Fixed for
Page 68 and 69: 5 Command file: Reading the data 46
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5 Command file: Reading the data 74
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6 Command file: Specifying theterms
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6 Command file: Specifying the term
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7 Command file: Specifying variance
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8 Command file: Multivariate analys
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9 Command file: Genetic analysisInt
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9 Command file: Genetic analysis 15
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10 Tabulation of the data andpredic
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10 Tabulation of the data and predi
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11 Functions of variancecomponentsI
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11 Functions of variance components
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11 Functions of variance components
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12 Command file: Running the jobInt
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12 Command file: Running the job 17
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13 Description of output filesIntro
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13 Description of output files 190A
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13 Description of output files 192i
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13 Description of output files 194f
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13 Description of output files 196.
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13 Description of output files 198o
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13 Description of output files 200E
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13 Description of output files 202t
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13 Description of output files 204|
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NIN alliance trial 1989 9a 1Residua
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13 Description of output files 208w
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13 Description of output files 210T
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14 Error messagesIntroductionCommon
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14 Error messages 214filename!last
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14 Error messages 216variety !AQUAL
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14 Error messages 2188. misspelt va
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14 Error messages 220Missing/faulty
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14 Error messages 222Last line read
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14 Error messages 224Model specific
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14 Error messages 226:11 column 11
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14 Error messages 22814.5 Informati
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14 Error messages 230List of warnin
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14 Error messages 232Alphabetical l
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15 Examples 24215.1 IntroductionIn
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15 Examples 244For simple variance
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15 Examples 2460.2_cwt Marvellous 1
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15 Examples 248The input file conta
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15 Examples 250Source Model terms G
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15 Examples 252ltage example 5−3
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15 Examples 254The focus is modelli
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15 Examples 256y1 y3 y5 y7 y10 ~ Tr
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15 Examples 258power model shown in
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15 Examples 260Residual US=UnStr 2
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15 Examples 262the current model).
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15 Examples 264Slate Hall example f
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15 Examples 266Predicted values of
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15 Examples 268wheat.asd !skip 1 !D
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Tullibigeal trial i2 1Variogram of
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15 Examples 272column evaluated at
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15 Examples 274this is for the pair
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15 Examples 276Table 15.8: Estimate
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15 Examples 278(and in fact necessa
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15 Examples 280Tr.run 22 0 US .79 .
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15 Examples 282Interpretation of re
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15 Examples 284The independence of
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15 Examples 286Note that the data f
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15 Examples 288Table 15.11 Orange d
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15 Examples 290217Predicted values
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15 Examples 292105Residual0-5-10200
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15 Examples 294Table 15.13: REML es
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15 Examples 29615*0. #Asreml will e
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15 Examples 298Covariance/Variance/
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15 Examples 300Eigen values 4.382 0
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15 Examples 302Animal modelIn this
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15 Examples 304additive genetic var
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BibliographyAbramowitz, M. and Steg
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Bibliography 308Gilmour, A. R., Cul
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Bibliography 310Schall, R. (1991).
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IndexABORTASR.NOW, 65FINALASR.NOW,
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Index 314free format, 42functions o
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Index 316!==, 53!>, 53!>=, 53!*, 53
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Index 318!STEP, 71!SUBSET, 71!SUB,
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Index 320parameter, 7variance compo
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