agridat (version 1.23)

snijders.fusarium: Fusarium infection in wheat varieties

Description

Infection in wheat by different strains of Fusarium.

Format

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

gen

wheat genotype

strain

fusarium strain

year

year

y

percent infected

Details

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.

References

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

Examples

if (FALSE) {

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

# 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.

}