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15 Examples 274this is for the paired dataY=syeX=sycY−axis: 1.8957 14.8835 X−axis: 8.2675 23.5051Figure 15.8: Rice bloodworm data: Plot of square root of root weight for treatedversus controlThere is an additional blocking term, however, due to the fact that the bloodwormswithin a run are derived from the same batch of larvae whereas betweenruns the bloodworms come from different sources. This defines a block structureof the formrun/tmt/variety = run + run.tmt + run.tmt.variety( = run + run.tmt + pair.tmt )Combining the two provides the full block structure for the design, namelyrun + run.variety + run.tmt + run.tmt.variety= run + run.variety + run.tmt + units= run + pair + run.tmt + pair.tmtIn line with the aims of the experiment the treatment structure comprises varietyand treatment main effects and treatment by variety interactions. In thetraditional approach the terms in the block structure are regarded as randomand the treatment terms as fixed. The choice of treatment terms as fixed orrandom depends largely on the aims of the experiment. The aim of this exampleis to select the ”best” varieties. The definition of best is somewhat more complexsince it does not involve the single trait sqrt(rootwt) but rather two traits,
15 Examples 275namely sqrt(rootwt) in the presence/absence of bloodworms. Thus to minimiseselection bias the variety main effects and thence the tmt.variety interactionsare taken as random. The main effect of treatment is fitted as fixed to allow forthe likely scenario that rather than a single population of treatment by varietyeffects there are in fact two populations (control and treated) with a differentmean for each. There is evidence of this prior to analysis with the large differencein mean sqrt(rootwt) for the two groups (14.93 and 8.23 for control andtreated respectively). The inclusion of tmt as a fixed effect ensures that BLUPsof tmt.variety effects are shrunk to the correct mean (treatment means ratherthan an overall mean).The model for the data is given byy = Xτ + Z 1 u 1 + Z 2 u 2 + Z 3 u 3 + Z 4 u 4 + Z 5 u 5 + e (15.7)where y is a vector of length n = 264 containing the sqrt(rootwt) values, τcorresponds to a constant term and the fixed treatment contrast and u 1 . . . u 5correspond to random variety, treatment by variety, run, treatment by run andvariety by run effects. The random effects and error are assumed to be independentGaussian variables with zero means and variance structures var (u i ) = σ 2 i I b i(where b i is the length of u i , i = 1 . . . 5) and var (e) = σ 2 I n .The ASReml code for this analysis isBloodworm data Dr M Stevenspair 132rootwtrun 66tmt 2 !Aidvariety 44 !Arice.asd !skip 1 !DOPATH 1!PATH 1sqrt(rootwt) ~ mu tmt !r variety variety.tmt run pair run.tmt0 0 0!PATH 2sqrt(rootwt) ~ mu tmt !r variety tmt.variety run pair tmt.run,uni(tmt,2)0 0 2tmt.variety 22 0 DIAG .1 .1 !GU44 0 0tmt.run 22 0 DIAG .1 .1 !GU66 0 0
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ASRemlUser GuideRelease 2.0A R Gilm
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Published by:E-mail:Website:VSN Int
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PrefaceiiASReml is one of several u
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ContentsPrefaceiList of TablesxviiL
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Contentsvi3.3 The ASReml data file
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ContentsviiiCombining rows from sep
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Contentsx7.6 Variance structure qua
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Contentsxii12.2 The command line .
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Contentsxiv15 Examples 24115.1 Intr
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List of Tablesxvi7.3 Details of the
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List of Figuresxix15.8 Rice bloodwo
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1 Introduction 21.1 What ASReml can
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1 Introduction 41.4 How to use this
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2 Some theoryThe linear mixed model
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2 Some theory 8laid out in a rectan
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2 Some theory 10product of matrices
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2 Some theory 12where H = R + ZGZ
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2 Some theory 14where y i is the
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2 Some theory 162.4 Combining varia
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2 Some theory 18balanced one-way cl
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2 Some theory 20L, r × p, and l, r
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2 Some theory 22the terms A, B, C,
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2 Some theory 24Kenward and Roger A
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3 A guided tourIntroductionNebraska
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3 A guided tour 28column rectangula
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3 A guided tour 30(see Chapter 2) t
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3 A guided tour 32els. Similarly fo
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3 A guided tour 34mand to run nin89
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3 A guided tour 36* SYNTAX change:
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3 A guided tour 38repl 3 -0.8713 1.
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3 A guided tour 40title linenin all
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4 Data file preparation 424.1 Intro
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4 Data file preparation 44Fixed for
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5 Command file: Reading the data 46
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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
Page 246 and 247: 14 Error messages 224Model specific
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Page 250 and 251: 14 Error messages 22814.5 Informati
Page 252 and 253: 14 Error messages 230List of warnin
Page 254 and 255: 14 Error messages 232Alphabetical l
Page 264 and 265: 15 Examples 24215.1 IntroductionIn
Page 266 and 267: 15 Examples 244For simple variance
Page 268 and 269: 15 Examples 2460.2_cwt Marvellous 1
Page 270 and 271: 15 Examples 248The input file conta
Page 272 and 273: 15 Examples 250Source Model terms G
Page 274 and 275: 15 Examples 252ltage example 5−3
Page 276 and 277: 15 Examples 254The focus is modelli
Page 278 and 279: 15 Examples 256y1 y3 y5 y7 y10 ~ Tr
Page 280 and 281: 15 Examples 258power model shown in
Page 282 and 283: 15 Examples 260Residual US=UnStr 2
Page 284 and 285: 15 Examples 262the current model).
Page 286 and 287: 15 Examples 264Slate Hall example f
Page 288 and 289: 15 Examples 266Predicted values of
Page 290 and 291: 15 Examples 268wheat.asd !skip 1 !D
Page 292 and 293: Tullibigeal trial i2 1Variogram of
Page 294 and 295: 15 Examples 272column evaluated at
Page 298 and 299: 15 Examples 276Table 15.8: Estimate
Page 300 and 301: 15 Examples 278(and in fact necessa
Page 302 and 303: 15 Examples 280Tr.run 22 0 US .79 .
Page 304 and 305: 15 Examples 282Interpretation of re
Page 306 and 307: 15 Examples 284The independence of
Page 308 and 309: 15 Examples 286Note that the data f
Page 310 and 311: 15 Examples 288Table 15.11 Orange d
Page 312 and 313: 15 Examples 290217Predicted values
Page 314 and 315: 15 Examples 292105Residual0-5-10200
Page 316 and 317: 15 Examples 294Table 15.13: REML es
Page 318 and 319: 15 Examples 29615*0. #Asreml will e
Page 320 and 321: 15 Examples 298Covariance/Variance/
Page 322 and 323: 15 Examples 300Eigen values 4.382 0
Page 324 and 325: 15 Examples 302Animal modelIn this
Page 326 and 327: 15 Examples 304additive genetic var
Page 328 and 329: BibliographyAbramowitz, M. and Steg
Page 330 and 331: Bibliography 308Gilmour, A. R., Cul
Page 332 and 333: Bibliography 310Schall, R. (1991).
Page 334 and 335: IndexABORTASR.NOW, 65FINALASR.NOW,
Page 336 and 337: Index 314free format, 42functions o
Page 338 and 339: Index 316!==, 53!>, 53!>=, 53!*, 53
Page 340 and 341: Index 318!STEP, 71!SUBSET, 71!SUB,
Page 342: Index 320parameter, 7variance compo
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