agricolae (version 1.2-0)

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 data to biplot, triplot graphs and analysis.

Usage

AMMI(ENV, GEN, REP, Y, MSE = 0,console=FALSE,PC=FALSE)

Arguments

ENV

Environment

GEN

Genotype

REP

Replication

Y

Response

MSE

Mean Square Error

console

ouput TRUE or FALSE

PC

Principal components ouput TRUE or FALSE

Value

• ANOVA
  analysis of variance general
• genXenv
  class by, genopyte and environment
• analysis
  analysis of variance principal components
• means
  average genotype and environment
• biplot
  data to produce graphics
• PC
  class princomp

Details

additional graphics see help(plot.AMMI).

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,plot.AMMI

Examples

# Full replications
library(agricolae)
# triplot and influence genotype
require(klaR) # type=2
require(spdep) # type=3
# Example 1
data(plrv)
attach(plrv)
model<- AMMI(Locality, Genotype, Rep, Yield, console=FALSE)
model$ANOVA
# see help(plot.AMMI)
detach(plrv)
# biplot
plot(model)
# triplot PC 1,2,3 
plot(model, type=2, number=TRUE)
# biplot PC1 vs Yield 
plot(model, first=0,second=1, number=TRUE)
# Example 2
data(CIC)
data1<-CIC$comas[,c(1,6,7,17,18)]
data2<-CIC$oxapampa[,c(1,6,7,19,20)]
cic <- rbind(data1,data2)
attach(cic)
model<-AMMI(Locality, Genotype, Rep, relative)
detach(cic)
model$ANOVA
plot(model,0,1,angle=20,ecol="brown")
# 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,PC=TRUE)
detach(sinRepAmmi)
# print anova
print(model$ANOVA,na.print = "")
# Biplot with the one restored observed.
plot(model,0,1,type=1)
# with principal components model$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