Multi-environment trial of cucumbers in a latin square design

Cucumber yields in latin square design at two locs.

Format

A data frame with 32 observations on the following 5 variables.

loc: location
gen: genotype/cultivar
row: row
col: column
yield: weight of marketable fruit per plot

Details

Conducted at Clemson University in 1985. four cucumber cultivars were grown in a latin square design at Clemson, SC, and Tifton, GA.

Separate variances are modeled each location.

Plot dimensions are not given.

Bridges (1989) used this data to illustrate fitting a heterogeneous mixed model.

Used with permission of William Bridges.

Source

William Bridges (1989). Analysis of a plant breeding experiment with heterogeneous variances using mixed model equations. Applications of mixed models in agriculture and related disciplines, S. Coop. Ser. Bull, 45--51.

Examples

# \dontrun{

  library(agridat)
  data(bridges.cucumber)
  dat <- bridges.cucumber
  dat <- transform(dat, rowf=factor(row), colf=factor(col))

  libs(desplot)
  desplot(dat, yield~col*row|loc,
          # aspect unknown
          text=gen, cex=1,
          main="bridges.cucumber")

  # Graphical inference test for heterogenous variances
  libs(nullabor)
  # Create a lineup of datasets
  fun <- null_permute("loc")
  dat20 <- lineup(fun, dat, n=20, pos=9)

  # Now plot
  libs(lattice)
  bwplot(yield ~ loc|factor(.sample), dat20,
         main="bridges.cucumber - graphical inference")

  libs(asreml) # asreml4
    
  ## Random row/col/resid. Same as Bridges 1989, p. 147
  m1 <- asreml(yield ~ 1 + gen + loc + loc:gen,
               random = ~ rowf:loc + colf:loc, data=dat)
#> Model fitted using the gamma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:53 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -69.1828       62.4832     24 17:07:53    0.0
#>  2      -68.2565       48.7835     24 17:07:53    0.0
#>  3      -67.6053       38.4916     24 17:07:53    0.0
#>  4      -67.3668       32.3653     24 17:07:53    0.0
#>  5      -67.3559       31.5313     24 17:07:53    0.0
#>  6      -67.3558       31.4799     24 17:07:53    0.0
  
  libs(lucid)
  lucid::vc(m1)
#>    effect component std.error z.ratio bound %ch
#>  rowf:loc     31.62     23.02     1.4     P   0
#>  colf:loc     18.08     15.33     1.2     P   0
#>   units!R     31.48     12.85     2.4     P   0
  ##   effect component std.error z.ratio bound 
  ## rowf:loc     31.62     23.02     1.4     P   0
  ## colf:loc     18.08     15.32     1.2     P   0
  ## units(R)     31.48     12.85     2.4     P   0
  
  ## Random row/col/resid at each loc. Matches p. 147
  m2 <- asreml(yield ~ 1 + gen + loc + loc:gen,
               random = ~ at(loc):rowf + at(loc):colf, data=dat,
               resid = ~ dsum( ~ units|loc))
#> Multi-section model using the sigma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:54 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -68.5253           1.0     24 17:07:54    0.0
#>  2      -66.8318           1.0     24 17:07:54    0.0
#>  3      -66.4698           1.0     24 17:07:54    0.0
#>  4      -66.3601           1.0     24 17:07:54    0.0
#>  5      -66.3562           1.0     24 17:07:54    0.0
  lucid::vc(m2)
#>                 effect component std.error z.ratio bound %ch
#>  at(loc, Clemson):rowf     32.32    36.54     0.88     P 0.1
#>   at(loc, Tifton):rowf     30.92    28.46     1.1      P 0.4
#>  at(loc, Clemson):colf     22.55    28.78     0.78     P 0  
#>   at(loc, Tifton):colf     13.62    14.59     0.93     P 0  
#>          loc_Clemson!R     46.85    27.05     1.7      P 0  
#>           loc_Tifton!R     16.11     9.298    1.7      P 0  
  ##                effect component std.error z.ratio bound 
  ## at(loc, Clemson):rowf     32.32    36.58     0.88     P   0
  ##  at(loc, Tifton):rowf     30.92    28.63     1.1      P   0
  ## at(loc, Clemson):colf     22.55    28.78     0.78     P   0
  ##  at(loc, Tifton):colf     13.62    14.59     0.93     P   0
  ##        loc_Clemson(R)     46.85    27.05     1.7      P   0
  ##         loc_Tifton(R)     16.11     9.299    1.7      P   0
  
  predict(m2, data=dat, classify='loc:gen')$pvals
#> Multi-section model using the sigma parameterization.
#> ASReml 4.1.0 Mon Jan 11 17:07:54 2021
#>           LogLik        Sigma2     DF     wall    cpu
#>  1      -66.3562           1.0     24 17:07:54    0.0
#>  2      -66.3562           1.0     24 17:07:54    0.0
#>  3      -66.3562           1.0     24 17:07:54    0.0
#> 
#> 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.
#> - The ignored set: rowf,colf
#> 
#> 
#>       loc      gen predicted.value std.error    status
#> 1 Clemson   Dasher        45.55000  5.042806 Estimable
#> 2 Clemson Guardian        31.62500  5.042806 Estimable
#> 3 Clemson Poinsett        21.42500  5.042806 Estimable
#> 4 Clemson   Sprint        25.95000  5.042806 Estimable
#> 5  Tifton   Dasher        50.48460  3.893635 Estimable
#> 6  Tifton Guardian        38.71697  3.893635 Estimable
#> 7  Tifton Poinsett        33.01487  3.893635 Estimable
#> 8  Tifton   Sprint        39.17952  3.893635 Estimable
  ##       loc      gen predicted.value std.error    status
  ## 1 Clemson   Dasher            45.6      5.04 Estimable
  ## 2 Clemson Guardian            31.6      5.04 Estimable
  ## 3 Clemson Poinsett            21.4      5.04 Estimable
  ## 4 Clemson   Sprint            26        5.04 Estimable
  ## 5  Tifton   Dasher            50.5      3.89 Estimable
  ## 6  Tifton Guardian            38.7      3.89 Estimable
  ## 7  Tifton Poinsett            33        3.89 Estimable
  ## 8  Tifton   Sprint            39.2      3.89 Estimable
  
  # Is a heterogeneous model justified? Maybe not.
  # m1$loglik
  ## -67.35585
  # m2$loglik
  ## -66.35621

# }