Wheat yield in South Australia with serpentine row/col effects
An RCB experiment of wheat in South Australia, with strong spatial variation and serpentine row/column effects.
A data frame with 330 observations on the following 5 variables.
colcolumn
rowrow
repreplicate factor, 3 levels
genwheat variety, 108 levels
yieldyield
A randomized complete block experiment. There are 108 varieties in 3 reps. Plots are 6 meters long, 0.75 meters wide, trimmed to 4.2 meters lengths before harvest. Trimming was done by spraying the wheat with herbicide. The sprayer travelled in a serpentine pattern up and down columns. The trial was sown in a serpentine manner with a planter that seeds three rows at a time (Left, Middle, Right).
Field width 15 columns * 6 m = 90 m
Field length 22 plots * .75 m = 16.5 m
Used with permission of Arthur Gilmour, in turn with permission from Gil Hollamby.
Arthur R Gilmour and Brian R Cullis and Arunas P Verbyla, 1997. Accounting for natural and extraneous variation in the analysis of field experiments. Journal of Agric Biol Env Statistics, 2, 269-293.
N. W. Galwey. 2014. Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance. Table 10.9
## Not run:
library(agridat)
data(gilmour.serpentine)
dat <- gilmour.serpentine
libs(desplot)
desplot(dat, yield~ col*row,
num=gen, show.key=FALSE, out1=rep,
aspect = 16.5/90, # true aspect
main="gilmour.serpentine")
# Extreme field trend. Blocking insufficient--needs a spline/smoother
# xyplot(yield~col, data=dat, main="gilmour.serpentine")
# ----------------------------------------------------------------------------
libs(asreml,lucid) # asreml4
dat <- transform(dat, rowf=factor(row), colf=factor(10*(col-8)))
dat <- dat[order(dat$rowf, dat$colf), ] # Sort order needed by asreml
# RCB
m0 <- asreml(yield ~ gen, data=dat, random=~rep)
# Add AR1 x AR1
m1 <- asreml(yield ~ gen, data=dat,
resid = ~ar1(rowf):ar1(colf))
# Add spline
m2 <- asreml(yield ~ gen + col, data=dat,
random= ~ spl(col) + colf,
resid = ~ar1(rowf):ar1(colf))
# Figure 4 shows serpentine spraying
p2 <- predict(m2, data=dat, classify="colf")$pvals
plot(p2$predicted, type='b', xlab="column number", ylab="BLUP")
# Define column code (due to serpentine spraying)
# Rhelp doesn't like double-percent modulus symbol, so compute by hand
dat <- transform(dat, colcode = factor(dat$col-floor((dat$col-1)/4)*4 -1))
m3 <- asreml(yield ~ gen + lin(colf) + colcode, data=dat,
random= ~ colf + rowf + spl(colf),
resid = ~ar1(rowf):ar1(colf))
# Figure 6 shows serpentine row effects
p3 <- predict(m3, data=dat, classify="rowf")$pvals
plot(p3$predicted, type='l', xlab="row number", ylab="BLUP")
text(1:22, p3$predicted, c('L','L','M','R','R','M','L','L',
'M','R','R','M','L','L','M','R','R','M','L','L','M','R'))
# Define row code (due to serpentine planting). 1=middle, 2=left/right
dat <- transform(dat, rowcode = factor(row))
levels(dat$rowcode) <- c('2','2','1','2','2','1','2','2','1',
'2','2','1','2','2','1','2','2','1','2','2','1','2')
m6 <- asreml(yield ~ gen + lin(colf) + colcode +rowcode, data=dat,
random= ~ colf + rowf + spl(col),
resid = ~ar1(rowf):ar1(colf))
plot(varioGram(m6), xlim=c(0:17), ylim=c(0,11), zlim=c(0,4000),
main="gilmour.serpentine")
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