Multi-environment trial of maize for 9 cultivars at 20 locations.

Maize yields for 9 cultivars at 20 locations.

data("cornelius.maize")

Format

A data frame with 180 observations on the following 3 variables.

env: environment factor, 20 levels
gen: genotype/cultivar, 9 levels
yield: yield, kg/ha

Details

Cell means (kg/hectare) for the CIMMYT EVT16B maize yield trial.

Source

P L Cornelius and J Crossa and M S Seyedsadr. (1996). Statistical Tests and Estimators of Multiplicative Models for Genotype-by-Environment Interaction. Book: Genotype-by-Environment Interaction. Pages 199-234.

References

Forkman, Johannes and Piepho, Hans-Peter. (2014). Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models. Biometrics, 70(3), 639-647. https://doi.org/10.1111/biom.12162

Examples

# \dontrun{

library(agridat)
data(cornelius.maize)
dat <- cornelius.maize

# dotplot(gen~yield|env,dat) # We cannot compare genotype yields easily
# Subtract environment mean from each observation
libs(reshape2)
mat <- acast(dat, gen~env)
#> Using yield as value column: use value.var to override.
mat <- scale(mat, scale=FALSE)
dat2 <- melt(mat)
names(dat2) <- c('gen','env','yield')
libs(lattice)
bwplot(yield ~ gen, dat2,
       main="cornelius.maize - environment centered yields")

if(0){
# This reproduces the analysis of Forkman and Piepho.

test.pc <- function(Y0, type="AMMI", n.boot=10000, maxpc=6) {

  # Test the significance of Principal Components in GGE/AMMI

  # Singular value decomposition of centered/double-centered Y
  Y <- sweep(Y0, 1, rowMeans(Y0)) # subtract environment means
  if(type=="AMMI") {
    Y <- sweep(Y, 2, colMeans(Y0)) # subtract genotype means
    Y <- Y + mean(Y0)
  }
  lam <- svd(Y)$d

  # Observed value of test statistic.
  # t.obs[k] is the proportion of variance explained by the kth term out of
  # the k...M terms, e.g. t.obs[2] is lam[2]^2 / sum(lam[2:M]^2)
  t.obs <- { lam^2/rev(cumsum(rev(lam^2))) } [1:(M-1)]
  t.boot <- matrix(NA, nrow=n.boot, ncol=M-1)

  # Centering rows/columns reduces the rank by 1 in each direction.
  I <- if(type=="AMMI") nrow(Y0)-1 else nrow(Y0)
  J <- ncol(Y0)-1
  M <- min(I, J) # rank of Y, maximum number of components
  M <- min(M, maxpc) # Optional step: No more than 5 components

  for(K in 0:(M-2)){ # 'K' multiplicative components in the svd

    for(bb in 1:n.boot){
      E.b <- matrix(rnorm((I-K) * (J-K)), nrow = I-K, ncol = J-K)
      lam.b <- svd(E.b)$d
      t.boot[bb, K+1] <- lam.b[1]^2 / sum(lam.b^2)
    }

  }

  # P-value for each additional multiplicative term in the SVD.
  # P-value is the proportion of time bootstrap values exceed t.obs
  colMeans(t.boot > matrix(rep(t.obs, n.boot), nrow=n.boot, byrow=TRUE))
}

dat <- cornelius.maize

# Convert to matrix format
libs(reshape2)
dat <- acast(dat, env~gen, value.var='yield')

## R> test.pc(dat,"AMMI")
## [1] 0.0000 0.1505 0.2659 0.0456 0.1086 # Forkman: .00 .156 .272 .046 .111

## R> test.pc(dat,"GGE")
## [1] 0.0000 0.2934 0.1513 0.0461 0.2817 # Forkman: .00 .296 .148 .047 .285

}
# }