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Four-way factorial agronomic experiment in triticale

1 | ```
data("besag.triticale")
``` |

A data frame with 54 observations on the following 7 variables.

`yield`

yield, g/m^2

`row`

row

`col`

column

`gen`

genotype / variety, 3 levels

`rate`

seeding rate, kg/ha

`nitro`

nitrogen rate, kw/ha

`regulator`

growth regulator, 3 levels

Experiment conducted as a factorial on the yields of triticale. Fully randomized. Plots were 1.5m x 5.5m, but the orientation is not clear.

Besag and Kempton show how accounting for neighbors changes non-significant genotype differences into significant differences.

Julian Besag and Rob Kempton (1986).
Statistical Analysis of Field Experiments Using Neighbouring Plots.
*Biometrics*, 42, 231-251. Table 2.
https://doi.org/10.2307/2531047

None.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | ```
## Not run:
library(agridat)
data(besag.triticale)
dat <- besag.triticale
dat <- transform(dat, rate=factor(rate), nitro=factor(nitro))
dat <- transform(dat, xf=factor(col), yf=factor(row))
libs(desplot)
desplot(dat, yield ~ col*row,
# aspect unknown
main="besag.triticale")
# Besag & Kempton are not perfectly clear on the model, but
# indicate that there was no evidence of any two-way interactions.
# A reduced, main-effect model had genotype effects that were
# "close to significant" at the five percent level.
# The model below has p-value of gen at .04, so must be slightly
# different than their model.
m2 <- lm(yield ~ gen + rate + nitro + regulator + yf, data=dat)
anova(m2)
# Similar, but not exact, to Besag figure 5
dat$res <- resid(m2)
libs(lattice)
xyplot(res ~ col|as.character(row), data=dat,
as.table=TRUE, type="s", layout=c(1,3),
main="besag.triticale")
libs(asreml) # asreml4
# Besag uses an adjustment based on neighboring plots.
# This analysis fits the standard AR1xAR1 residual model
dat <- dat[order(dat$xf, dat$yf), ]
m3 <- asreml(yield ~ gen + rate + nitro + regulator +
gen:rate + gen:nitro + gen:regulator +
rate:nitro + rate:regulator +
nitro:regulator + yf, data=dat,
resid = ~ ar1(xf):ar1(yf))
wald(m3) # Strongly significant gen, rate, regulator
## Df Sum of Sq Wald statistic Pr(Chisq)
## (Intercept) 1 1288255 103.971 < 2.2e-16 ***
## gen 2 903262 72.899 < 2.2e-16 ***
## rate 1 104774 8.456 0.003638 **
## nitro 1 282 0.023 0.880139
## regulator 2 231403 18.676 8.802e-05 ***
## yf 2 3788 0.306 0.858263
## gen:rate 2 1364 0.110 0.946461
## gen:nitro 2 30822 2.488 0.288289
## gen:regulator 4 37269 3.008 0.556507
## rate:nitro 1 1488 0.120 0.728954
## rate:regulator 2 49296 3.979 0.136795
## nitro:regulator 2 41019 3.311 0.191042
## residual (MS) 12391
## End(Not run)
``` |

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