snijders.fusarium {agridat} | R Documentation |
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).
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. http://doi.org/10.1007/BF00215729
Used with permission of Fred van Eeuwijk.
Fred A van Eeuwijk. 1995. Multiplicative interaction in generalized linear models. Biometrics, 51, 1017-1032. http://doi.org/10.2307/2533001
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. require(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 require(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)