Multi-environment trial

Usage

data("sharma.met")

Format

A data frame with 126 observations on the following 5 variables.

gen: genotype
loc: location
year: year
rep: replicate
yield: yield

Details

Yield of 7 genotypes, 3 years, 2 locations per year, 3 replicates.

Might be simulated data.

Source

Jawahar R. Sharma. 1988. Statistical and Biometrical Techniques in Plant Breeding. New Age International Publishers.

References

Andrea Onofri, 2020. Fitting complex mixed models with nlme: Example #5. https://www.statforbiology.com/2020/stat_met_jointreg/

Examples

if (FALSE) { # \dontrun{
  library(agridat)
  data(sharma.met)
  dat <- sharma.met
  dat$env = paste0(dat$year, dat$loc) # Define environment
  
  # Calculate environment index as loc mean - overall mean ---
  libs(dplyr)
  dat <- group_by(dat, env)
  dat <- mutate(dat, eix = mean(yield)-mean(dat$yield))
  
  libs(nlme)

 ## Finlay-Wilkinson model plot-level model ---
  m1fw <- lme(yield ~ gen/eix - 1, 
              random = list(env = pdIdent(~ gen - 1),
                            env = pdIdent(~ rep - 1)), 
              data=dat)
  summary(m1fw)$tTable # Match Sharma table 9.6
  VarCorr(m1fw)
  
  ## Eberhart-Russell plot-level model ---
  # Use pdDiag to get variance for each genotype
  m1er <- lme(yield ~ gen/eix - 1, 
              random = list(env = pdDiag(~ gen - 1),
                            env = pdIdent(~ rep - 1)), 
              data=dat)
  summary(m1er)$tTable # same as FW
  VarCorr(m1er) # genotype variances differ

  
  # Calculate GxE cell means and environment index ---
  dat2 <- group_by(dat, gen, env)
  dat2 <- summarize(dat2, yield=mean(yield))
  dat2 <- group_by(dat2, env)
  dat2 <- mutate(dat2, eix=mean(yield)-mean(dat2$yield))
  
  ## Finlay-Wilkinson cell-means model ---
  m2fw <- lm(yield ~ gen/eix - 1, data=dat2)
  summary(m2fw)
  
  ## Eberhart-Russell cell-means model ---
  # Note, using varIdent(form=~1) is same as FW model
  m2er <- gls(yield ~ gen/eix - 1, 
              weights=varIdent(form=~1|gen), data=dat)
  summary(m2er)$tTable
  sigma <- summary(m2er)$sigma
  sigma2i <- (c(1, coef(m2er$modelStruct$varStruct, uncons = FALSE)) * sigma)^2
  names(sigma2i)[1] <- "A"
  sigma2i # shifted from m1er because variation from reps was swept out
  
} # }