Incomplete block alpha design

data("burgueno.alpha")

Format

A data frame with 48 observations on the following 6 variables.

rep: rep, 3 levels
block: block, 12 levels
row: row
col: column
gen: genotype, 16 levels
yield: yield

Details

A field experiment with 3 reps, 4 blocks per rep, laid out as an alpha design.

The plot size is not given.

Electronic version of the data obtained from CropStat software.

Used with permission of Juan Burgueno.

Source

J Burgueno, A Cadena, J Crossa, M Banziger, A Gilmour, B Cullis. 2000. User's guide for spatial analysis of field variety trials using ASREML. CIMMYT. https://books.google.com/books?id=PR_tYCFyLCYC&pg=PA1

Examples

# \dontrun{

  library(agridat)
  data(burgueno.alpha)
  dat <- burgueno.alpha

  libs(desplot)
  desplot(dat, yield~col*row,
          out1=rep, out2=block, # aspect unknown
          text=gen, cex=1,shorten="none",
          main='burgueno.alpha')


  libs(lme4,lucid)
  # Inc block model
  m0 <- lmer(yield ~ gen + (1|rep/block), data=dat)
  vc(m0) # Matches Burgueno p. 26
#>        grp        var1 var2   vcov sdcor
#>  block:rep (Intercept) <NA>  86900 294.8
#>        rep (Intercept) <NA> 200900 448.2
#>   Residual        <NA> <NA> 133200 365  
  ##        grp        var1 var2   vcov sdcor
  ##  block:rep (Intercept) <NA>  86900 294.8
  ##        rep (Intercept) <NA> 200900 448.2
  ##   Residual        <NA> <NA> 133200 365  


  libs(asreml) # asreml4
    
  dat <- transform(dat, xf=factor(col), yf=factor(row))
  dat <- dat[order(dat$xf, dat$yf),]                 
  
  # Sequence of models on page 36
  
  m1 <- asreml(yield ~  gen, data=dat)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -232.128      424504.3     32 17:07:56    0.0
  m1$loglik # -232.13
#> [1] -232.1277
  
  m2 <- asreml(yield ~  gen, data=dat,
               random = ~ rep)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -226.562      282408.0     32 17:07:56    0.0
#>  2      -225.458      258453.6     32 17:07:56    0.0
#>  3      -224.388      235077.8     32 17:07:56    0.0
#>  4      -223.676      216846.8     32 17:07:56    0.0
#>  5      -223.503      209444.3     32 17:07:56    0.0
#>  6      -223.483      206934.7     32 17:07:56    0.0
#>  7      -223.482      206516.9     32 17:07:56    0.0
  m2$loglik # -223.48
#> [1] -223.4824
  
  # Inc Block model
  m3 <- asreml(yield ~  gen, data=dat,
               random = ~ rep/block)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -225.610      246800.7     32 17:07:56    0.0
#>  2      -223.872      199712.8     32 17:07:56    0.0
#>  3      -222.453      162923.0     32 17:07:56    0.0
#>  4      -221.644      140326.6     32 17:07:56    0.0
#>  5      -221.443      135401.9     32 17:07:56    0.0
#>  6      -221.417      133560.7     32 17:07:56    0.0
#>  7      -221.417      133229.8     32 17:07:56    0.0
  m3$loglik # -221.42
#> [1] -221.4167
  m3$coef$fixed # Matches solution on p. 27
#>                     bu
#> gen_G01        0.00000
#> gen_G02     -284.28340
#> gen_G03      493.85828
#> gen_G04      699.29379
#> gen_G05      863.39910
#> gen_G06       30.97441
#> gen_G07     -115.81504
#> gen_G08      157.76411
#> gen_G09      407.24195
#> gen_G10      777.17723
#> gen_G11     1038.46296
#> gen_G12      648.02712
#> gen_G13      248.18656
#> gen_G14      405.45778
#> gen_G15      942.48436
#> gen_G16      453.78449
#> (Intercept)  907.97831
#> attr(,"terms")
#>                   tname  n
#> gen                 gen 16
#> (Intercept) (Intercept)  1
  
  # AR1xAR1 model
  m4 <- asreml(yield ~ 1 + gen, data=dat,
               resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -229.632      369295.0     32 17:07:56    0.0
#>  2      -225.313      310549.6     32 17:07:56    0.0
#>  3      -222.576      315026.1     32 17:07:56    0.0
#>  4      -221.714      350768.1     32 17:07:56    0.0
#>  5      -221.498      390126.2     32 17:07:56    0.0
#>  6      -221.475      406435.9     32 17:07:56    0.0
#>  7      -221.473      412526.0     32 17:07:56    0.0
#>  8      -221.472      414688.0     32 17:07:56    0.0
  m4$loglik # -221.47
#> [1] -221.4725
  plot(varioGram(m4), main="burgueno.alpha") # Figure 1
  
  m5 <- asreml(yield ~ 1 + gen, data=dat,
               random= ~ yf, resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -226.301      279679.7     32 17:07:56    0.0
#>  2      -223.503      233517.8     32 17:07:56    0.0
#>  3      -221.336      202245.4     32 17:07:56    0.0
#>  4      -220.254      181270.7     32 17:07:56    0.0
#>  5      -220.081      172053.0     32 17:07:56    0.0
#>  6      -220.068      170878.3     32 17:07:56    0.0
#>  7      -220.068      170961.0     32 17:07:56    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m5$loglik # -220.07
#> [1] -220.0677
  
  m6 <- asreml(yield ~ 1 + gen + pol(yf,-2), data=dat,
               resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -205.690      156958.0     30 17:07:56    0.0
#>  2      -205.189      156511.0     30 17:07:56    0.0
#>  3      -204.651      170349.2     30 17:07:56    0.0
#>  4      -204.640      171539.3     30 17:07:56    0.0
#>  5      -204.639      171955.1     30 17:07:56    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m6$loglik # -204.64
#> [1] -204.6394
  
  m7 <- asreml(yield ~ 1 + gen + lin(yf), data=dat,
               random= ~ spl(yf), resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:56 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -213.764      161236.1     31 17:07:57    0.0
#>  2      -213.161      158001.3     31 17:07:57    0.0
#>  3      -212.686      158486.3     31 17:07:57    0.0
#>  4      -212.518      161586.3     31 17:07:57    0.0
#>  5      -212.512      160691.0     31 17:07:57    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m7$loglik # -212.51
#> [1] -212.5125
  
  m8 <- asreml(yield ~ 1 + gen + lin(yf), data=dat,
               random= ~ spl(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -214.401      162571.5     31 17:07:57    0.0
#>  2      -214.190      158323.8     31 17:07:57    0.0
#>  3      -214.000      153413.7     31 17:07:57    0.0
#>  4      -213.916      149071.2     31 17:07:57    0.0
#>  5      -213.914      148249.7     31 17:07:57    0.0
  m8$loglik # -213.91
#> [1] -213.9141
  
  # Polynomial model with predictions
  m9 <- asreml(yield ~ 1 + gen + pol(yf,-2) + pol(xf,-2), data=dat,
               random= ~ spl(yf),
               resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -192.357      124656.6     28 17:07:57    0.0 (1 restrained)
#>  2      -191.606      114513.8     28 17:07:57    0.0
#>  3      -191.493      114311.7     28 17:07:57    0.0
#>  4      -191.452      115391.7     28 17:07:57    0.0
#>  5      -191.446      114966.4     28 17:07:57    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m9 <- update(m9)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -191.443      115328.5     28 17:07:57    0.0
#>  2      -191.443      115251.7     28 17:07:57    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m9$loglik # -191.44 vs -189.61
#> [1] -191.4426
  p9 <- predict(m9, classify="gen:xf:yf", levels=list(xf=1,yf=1)) 
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -191.442      115160.3     28 17:07:57    0.0
#>  2      -191.442      115178.5     28 17:07:57    0.0
#>  3      -191.442      115210.1     28 17:07:57    0.0
  p9
#> $pvals
#> 
#> Notes:
#> - The predictions are obtained by averaging across the hypertable
#>   calculated from model terms constructed solely from factors in
#>   the averaging and classify sets.
#> - Use 'average' to move ignored factors into the averaging set.
#> 
#> 
#>    gen     xf     yf predicted.value std.error    status
#> 1  G01 order1 order1        1967.154  265.0976 Estimable
#> 2  G02 order1 order1        2018.990  282.6813 Estimable
#> 3  G03 order1 order1        2374.678  233.9746 Estimable
#> 4  G04 order1 order1        2539.440  238.5453 Estimable
#> 5  G05 order1 order1        2817.841  261.9213 Estimable
#> 6  G06 order1 order1        2134.310  260.1078 Estimable
#> 7  G07 order1 order1        2028.879  287.5826 Estimable
#> 8  G08 order1 order1        2205.963  271.0232 Estimable
#> 9  G09 order1 order1        2346.313  251.1598 Estimable
#> 10 G10 order1 order1        2831.710  233.6259 Estimable
#> 11 G11 order1 order1        2868.783  238.5870 Estimable
#> 12 G12 order1 order1        2685.266  246.1334 Estimable
#> 13 G13 order1 order1        2202.347  277.7411 Estimable
#> 14 G14 order1 order1        2633.541  285.9366 Estimable
#> 15 G15 order1 order1        2798.175  270.0601 Estimable
#> 16 G16 order1 order1        2365.906  238.3437 Estimable
#> 
#> $avsed
#>  overall 
#> 275.0335 
#> 
  
  m10 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -218.438      319937.6     30 17:07:57    0.0
#>  2      -214.809      284438.5     30 17:07:57    0.0
#>  3      -212.478      301889.6     30 17:07:57    0.0
#>  4      -211.749      343343.7     30 17:07:57    0.0
#>  5      -211.575      384479.3     30 17:07:57    0.0
#>  6      -211.559      399834.4     30 17:07:57    0.0
#>  7      -211.557      405022.4     30 17:07:57    0.0
  m10$loglik # -211.56
#> [1] -211.5574
  
  m11 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                random= ~ spl(yf),
                resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -210.199      166458.9     30 17:07:57    0.0
#>  2      -209.562      164032.3     30 17:07:57    0.0
#>  3      -209.064      166788.1     30 17:07:57    0.0
#>  4      -208.901      173307.2     30 17:07:57    0.0
#>  5      -208.898      172903.8     30 17:07:57    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m11$loglik # -208.90
#> [1] -208.8981
  
  m12 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                random= ~ spl(yf)+spl(xf),
                resid = ~ar1(xf):ar1(yf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#> Spline: design points closer than 0.0007 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -208.573      135590.1     30 17:07:57    0.0 (1 restrained)
#>  2      -207.575      121857.9     30 17:07:57    0.0
#>  3      -207.068      114896.2     30 17:07:57    0.0
#>  4      -206.844      112501.6     30 17:07:57    0.0
#>  5      -206.826      111035.7     30 17:07:57    0.0
#>  6      -206.825      111519.0     30 17:07:57    0.0
#> Warning: Some components changed by more than 1% on the last iteration.
  m12$loglik # -206.82
#> [1] -206.8252
  
  m13 <- asreml(yield ~ 1 + gen + lin(yf)+lin(xf), data=dat,
                random= ~ spl(yf)+spl(xf))
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:57 2021
#> Spline: design points closer than 0.0005 have been merged.
#> Spline: design points closer than 0.0007 have been merged.
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -208.583      129506.5     30 17:07:57    0.0
#>  2      -208.160      124731.6     30 17:07:57    0.0
#>  3      -207.765      118920.6     30 17:07:57    0.0
#>  4      -207.541      113114.9     30 17:07:57    0.0
#>  5      -207.517      111017.9     30 17:07:57    0.0
#>  6      -207.516      110690.9     30 17:07:57    0.0
  m13$loglik # -207.52
#> [1] -207.5164

# }