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

if (FALSE) { # \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")

  if(require("asreml", quietly=TRUE)) {
    libs(asreml,lucid)
    
    ## 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)
  
    lucid::vc(m1)
    ##   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))
    lucid::vc(m2)
    ##                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
    ##       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
  }
  
} # }