agricolae (version 1.0-4)

AMMI: AMMI Analysis

Description

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 biplot, triplot graphs and analysis.

Usage

AMMI(ENV, GEN, REP, Y, MSE = 0, number=TRUE,graph="biplot",...)

Arguments

ENV

Environment

GEN

Genotype

REP

Replication

Y

Response

MSE

Mean Square Error

number

TRUE or FALSE

graph

"biplot" or "triplot"

...

plot graphics parameters

Value

• ENV
  Factor
• GEN
  Factor
• REP
  Numeric
• Y
  Numeric
• MSE
  Numeric
• number
  TRUE or FALSE
• graph
  "biplot" or "triplot"
• ...
  others parameters

Details

additional biplot.

References

GGE Biplot Analysis: A graphical tool for breeder, geneticists, and agronomists. Weikai Yan and Manjit S. Kang. www.crepress.com 2003, Principles and procedures of statistics: a biometrical approach Steel & Torry & Dickey. Third Edition 1997

See Also

lineXtester

Examples

# Full replications
library(agricolae)
library(klaR)
# Example 1
data(ltrv)
#startgraph
# biplot
model<- AMMI(ltrv[,2], ltrv[,1], ltrv[,3], ltrv[,5],xlim=c(-3,3),ylim=c(-4,4),
graph="biplot")
model<- AMMI(ltrv[,2], ltrv[,1], ltrv[,3], ltrv[,5],xlim=c(-3,3),ylim=c(-4,4),
graph="biplot",number=FALSE)
# triplot
model<- AMMI(ltrv[,2], ltrv[,1], ltrv[,3], ltrv[,5],graph="triplot")
model<- AMMI(ltrv[,2], ltrv[,1], ltrv[,3], ltrv[,5],graph="triplot",number=FALSE)
#endgraph
# Example 2
data(CIC)
attach(CIC)
#startgraph
par(cex=0.6)
model<-AMMI(Environment, Genotype, Rep, Relative,xlim=c(-0.6,0.6),
ylim=c(-1.5e-8,1.5e-8))
#endgraph
pc<- princomp(model$genXenv, cor = FALSE)
pc$loadings
summary(pc)
model$biplot
detach(CIC)
# Example 3
# Only means. Mean square error is well-known.
data(sinRepAmmi)
attach(sinRepAmmi)
REP <- 3
MSerror <- 93.24224
#startgraph
model<-AMMI(ENV, GEN, REP, YLD, MSerror,xlim=c(-8,6),ylim=c(-6,6))
#endgraph
pc<- princomp(model$genXenv, cor = FALSE)
pc$loadings
summary(pc)
model$biplot
detach(sinRepAmmi)
# Biplot with the one restored observed.
rm(REP)
bplot<-model$biplot[,1:4]
attach(bplot)
#startgraph
par(cex=0.8)
plot(YLD,CP1,cex=0.0,text(YLD,CP1,labels=row.names(bplot),col="blue"),
 main="AMMI BIPLOT",frame=TRUE)
media<-mean(YLD)
abline(h=0,v= media,lty=2,col="red")
amb<-subset(bplot,type=="ENV")
detach(bplot)
attach(amb)
s <- seq(length(YLD))
arrows(media, 0, 0.9*(YLD[s]-media)+media, 0.9*CP1[s], col= "brown",
lwd=1.8,length=0.1)
#endgraph
detach(amb)
# Principal components by means of the covariance 
# It is to compare results with AMMI
cova<-cov(model$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