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Infection in wheat by different strains of Fusarium.

A data frame with 204 observations on the following 4 variables.

`gen`

wheat genotype

`strain`

fusarium strain

`year`

year

`y`

percent infected

The data are the percent of leaf area affected by Fusarium head blight, averaged over 4-5 reps, for 17 winter wheat genotypes.

Van Eeuwijk fit a generalized ammi-2 model to this data. It is a generalized model in the sense that a link function is used, and is a non-linear AMMI model in that there are main effects for variety and year-strain, but additional multiplicative effects for the interactions.

Note, the value for strain F348 in 1988, gen SVP75059-32 should be 28.3 (as shown in VanEeuwijk 1995) and not 38.3 (as shown in Snijders 1991).

Used with permission of Fred van Eeuwijk.

Snijders, CHA and Van Eeuwijk, FA. 1991. Genotype x strain interactions for resistance to Fusarium head blight caused by Fusarium culmorum in winter wheat. Theoretical and Applied Genetics, 81, 239–244. Table 1. https://doi.org/10.1007/BF00215729

Fred A van Eeuwijk. 1995.
Multiplicative interaction in generalized linear models.
*Biometrics*, 51, 1017-1032.
https://doi.org/10.2307/2533001

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 59 60 | ```
library(agridat)
data(snijders.fusarium)
dat <- snijders.fusarium
aggregate(y ~ strain + year, dat, FUN=mean) # Match means in Snijders table 1
dat <- transform(dat, y=y/100, year=factor(year), yrstr=factor(paste0(year,"-",strain)))
# Strain F329 shows little variation across years. F39 shows a lot.
libs(lattice)
dotplot(gen~y|strain, data=dat, group=year,
main="snijders.fusarium : infection by strain",
xlab="Fraction infected", ylab="variety",
auto.key=list(columns=3))
# Logit transform
dat <- transform(dat, logit=log(y/(1-y)))
m1 <- aov(logit ~ yrstr + gen, data=dat) # Match SS in VanEeuwijk table 4
anova(m1) # Match SS in VanEeuwijk table 4
m2 <- aov(logit ~ year*strain + gen + gen:year + gen:strain, data=dat)
anova(m2) # Match to VanEeuwijk table 5
## Not run:
# GLM on untransformed data using logit link, variance mu^2(1-mu)^2
libs(gnm) # for 'wedderburn' family
m2 <- glm(y ~ yrstr + gen, data=dat, family="wedderburn")
anova(m2) # Main effects match VanEeuwijk table 6
# Generalized AMMI-2 model. Matches VanEeuwijk table 6
bilin2 <- gnm(y ~ yrstr + gen + instances(Mult(yrstr, gen), 2),
data=dat, family = wedderburn)
# plot(bilin2,1) # Resid vs fitted plot matches VanEeuwijk figure 3c
## anova(bilin2)
## Df Deviance Resid. Df Resid. Dev
## NULL 203 369.44
## yrstr 11 150.847 192 218.60
## gen 16 145.266 176 73.33
## Mult(yrstr, gen, inst = 1) 26 26.128 150 47.20
## Mult(yrstr, gen, inst = 2) 24 19.485 126 27.72
# Manually extract coordinates for biplot
cof <- coef(bilin2)
y1 <- cof[29:40]
g1 <- cof[41:57]
y2 <- cof[58:69]
g2 <- cof[70:86]
g12 <- cbind(g1,g2)
rownames(g12) <- substring(rownames(g12), 29)
y12 <- cbind(y1,y2)
rownames(y12) <- substring(rownames(y12), 31)
g12[,1] <- -1 * g12[,1]
y12[,1] <- -1 * y12[,1]
# GAMMI biplot. Inner-products of points projected onto
# arrows match VanEeuwijk figure 4. Slight rotation of graph is ignorable.
biplot(y12, g12, cex=.75, main="snijders.fusarium") # Arrows to genotypes.
## End(Not run)
``` |

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