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Additive Main Effects and Multiplicative Interaction Models (AMMI) are widely used to analyze main effects and genotype by environment (GEN, ENV) interactions in multilocation variety trials. Furthermore, this function generates data to biplot, triplot graphs and analysis.
AMMI(ENV, GEN, REP, Y, MSE = 0,console=FALSE,PC=FALSE)
analysis of variance general
class by, genopyte and environment
analysis of variance principal components
average genotype and environment
data to produce graphics
class princomp
Environment
Genotype
Replication
Response
Mean Square Error
ouput TRUE or FALSE
Principal components ouput TRUE or FALSE
F. de Mendiburu
additional graphics see help(plot.AMMI).
Crossa, J. 1990. Statistical analysis of multilocation trials. Advances in Agronomy 44:55-85
lineXtester,plot.AMMI
# Full replications
library(agricolae)
# Example 1
data(plrv)
model<- with(plrv,AMMI(Locality, Genotype, Rep, Yield, console=FALSE))
model$ANOVA
# see help(plot.AMMI)
# biplot
plot(model)
# biplot PC1 vs Yield
plot(model, first=0,second=1, number=TRUE)
# Example 2
data(CIC)
data1<-CIC$comas[,c(1,6,7,17,18)]
data2<-CIC$oxapampa[,c(1,6,7,19,20)]
cic <- rbind(data1,data2)
model<-with(cic,AMMI(Locality, Genotype, Rep, relative))
model$ANOVA
plot(model,0,1,angle=20,ecol="brown")
# Example 3
# Only means. Mean square error is well-known.
data(sinRepAmmi)
REP <- 3
MSerror <- 93.24224
#startgraph
model<-with(sinRepAmmi,AMMI(ENV, GEN, REP, YLD, MSerror,PC=TRUE))
# print anova
print(model$ANOVA,na.print = "")
# Biplot with the one restored observed.
plot(model,0,1)
# with principal components model$PC is class "princomp"
pc<- model$PC
pc$loadings
summary(pc)
biplot(pc)
# Principal components by means of the covariance similar AMMI
# It is to compare results with AMMI
cova<-cov(model$genXenv)
values<-eigen(cova)
total<-sum(values$values)
round(values$values*100/total,2)
# AMMI: 64.81 18.58 13.50 3.11 0.00
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