Multi-environment trial of corn, incomplete-block design

Multi-environment trial of corn, incomplete-block designlocation.

Format

A data frame with 1152 observations on the following 7 variables.

county

county

row

row

col

column

rep

rep

block

incomplete block

yield

yield

gen

genotype, 1-64

Details

Multi-environment trial of 64 corn hybrids in six counties in North Carolina. Each location had 3 replicates in in incomplete-block design with an 18x11 lattice of plots whose length-to-width ratio was about 2:1.

Note: In the original data, each county had 6 missing plots. This data has rows for each missing plot that uses the same county/block/rep to fill-out the row, sets the genotype to G01, and sets the yield to missing. These missing values were added to the data so that asreml could more easily do AR1xAR1 analysis using rectangular regions.

Each location/panel is:

Field length: 18 rows * 2 units = 36 units.

Field width: 11 plots * 1 unit = 11 units.

Retrieved from https://web.archive.org/web/19990505223413/www.stat.duke.edu/~higdon/trials/nc.dat

Used with permission of David Higdon.

Source

Julian Besag and D Higdon, 1999. Bayesian Analysis of Agricultural Field Experiments, Journal of the Royal Statistical Society: Series B, 61, 691–746. Table 1. https://doi.org/10.1111/1467-9868.00201

Examples

if (FALSE) { # \dontrun{

  library(agridat)
  data(besag.met)
  dat <- besag.met

  libs(desplot)
  desplot(dat, yield ~ col*row|county,
          aspect=36/11, # true aspect
          out1=rep, out2=block,
          main="besag.met")


  # Average reps
  datm <- aggregate(yield ~ county + gen, data=dat, FUN=mean)
  
  # Sections below fit heteroskedastic variance models (variance for each variety)
  # asreml takes 1 second, lme 73 seconds, SAS PROC MIXED 30 minutes



  # lme
  # libs(nlme)
  # m1l <- lme(yield ~ -1 + gen, data=datm, random=~1|county,
  #            weights = varIdent(form=~ 1|gen))
  # m1l$sigma^2 * c(1, coef(m1l$modelStruct$varStruct, unc = FALSE))^2
  ##           G02    G03    G04    G05    G06    G07    G08
  ##  91.90 210.75  63.03 112.05  28.39 237.36  72.72  42.97
  ## ... etc ...
  
  if(require("asreml", quietly=TRUE)) {
   libs(asreml, lucid)

   # Average reps
   datm <- aggregate(yield ~ county + gen, data=dat, FUN=mean)
   #  asreml Using 'rcov' ALWAYS requires sorting the data
   datm <- datm[order(datm$gen),]
   
   m1 <- asreml(yield ~ gen, data=datm,
                random = ~ county,
                residual = ~ dsum( ~ units|gen))
   vc(m1)[1:7,]
   ##      effect component std.error z.ratio bound 
   ##    county   1324       836.1      1.6     P 0.2
   ## gen_G01!R     91.98     58.91     1.6     P 0.1
   ## gen_G02!R    210.6     133.6      1.6     P 0.1
   ## gen_G03!R     63.06     40.58     1.6     P 0.1
   ## gen_G04!R    112.1      71.59     1.6     P 0.1
   ## gen_G05!R     28.35     18.57     1.5     P 0.2
   ## gen_G06!R    237.4     150.8      1.6     P 0  
  
   # We get the same results from asreml & lme
   # plot(m1$vparameters[-1],
   #      m1l$sigma^2 * c(1, coef(m1l$modelStruct$varStruct, unc = FALSE))^2)
   
   # The following example shows how to construct a GxE biplot
   # from the FA2 model.
   
   
   dat <- besag.met
   dat <- transform(dat, xf=factor(col), yf=factor(row))
   dat <- dat[order(dat$county, dat$xf, dat$yf), ]
   
   # First, AR1xAR1
   m1 <- asreml(yield ~ county, data=dat,
                random = ~ gen:county,
                residual = ~ dsum( ~ ar1(xf):ar1(yf)|county))
   # Add FA1
   m2 <- update(m1, random=~gen:fa(county,1)) # rotate.FA=FALSE
   # FA2
   m3 <- update(m2, random=~gen:fa(county,2))
   asreml.options(extra=50)
   m3 <- update(m3, maxit=50)
   asreml.options(extra=0)
   
   # Use the loadings to make a biplot
   vars <- vc(m3)
   psi <- vars[grepl("!var$", vars$effect), "component"]
   la1 <- vars[grepl("!fa1$", vars$effect), "component"]
   la2 <- vars[grepl("!fa2$", vars$effect), "component"]
   mat <- as.matrix(data.frame(psi, la1, la2))
   # I tried using rotate.fa=FALSE, but it did not seem to
   # give orthogonal vectors.  Rotate by hand.
   rot <- svd(mat[,-1])$v # rotation matrix
   lam <- mat[,-1] 
   colnames(lam) <- c("load1", "load2")
   
   co3 <- coef(m3)$random # Scores are the GxE coefficients
   ix1 <- grepl("_Comp1$", rownames(co3))
   ix2 <- grepl("_Comp2$", rownames(co3))
   sco <- matrix(c(co3[ix1], co3[ix2]), ncol=2, byrow=FALSE)
   sco <- sco 
   dimnames(sco) <- list(levels(dat$gen) , c('load1','load2'))
   rownames(lam) <- levels(dat$county)
   sco[,1:2] <- -1 * sco[,1:2]
   lam[,1:2] <- -1 * lam[,1:2]
   biplot(sco, lam, cex=.5, main="FA2 coefficient biplot (asreml)")
   # G variance matrix
   gvar <- lam 
  
   # Now get predictions and make an ordinary biplot
   p3 <- predict(m3, data=dat, classify="county:gen")
   p3 <- p3$pvals
   libs("gge")  
   bi3 <- gge(p3, predicted.value ~ gen*county, scale=FALSE)
   if(interactive()) dev.new()
   # Very similar to the coefficient biplot
   biplot(bi3, stand=FALSE, main="SVD biplot of FA2 predictions")
  }
  
} # }