EV.AMMI: Averages of the Squared Eigenvector Values

In ammistability: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

Averages of the Squared Eigenvector Values

Description

EV.AMMI computes the Sums of the Averages of the Squared Eigenvector Values (EV) \insertCitezobel_stress_1994ammistability considering all significant interaction principal components (IPCs) in the AMMI model. Using EV, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method. \loadmathjax

Usage

EV.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)

Arguments

model	The AMMI model (An object of class AMMI generated by AMMI).
n	The number of principal components to be considered for computation. The default value is the number of significant IPCs.
alpha	Type I error probability (Significance level) to be considered to identify the number of significant IPCs.
ssi.method	The method for the computation of simultaneous selection index. Either "farshadfar" or "rao" (See SSI).
a	The ratio of the weights given to the stability components for computation of SSI when method = "rao" (See SSI).

Details

The Averages of the Squared Eigenvector Values (\mjseqnEV) \insertCitezobel_stress_1994ammistability is computed as follows:

\mjsdeqn

EV = \sum_n=1^N'\frac\gamma_in^2N'

Where, \mjseqnN' is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); and \mjseqn\gamma_in is the eigenvector value for \mjseqnith genotype.

Value

A data frame with the following columns:

EV	The EV values.
SSI	The computed values of simultaneous selection index for yield and stability.
rEV	The ranks of EV values.
rY	The ranks of the mean yield of genotypes.
means	The mean yield of the genotypes.

The names of the genotypes are indicated as the row names of the data frame.

References

\insertRef

zobel_stress_1994ammistability

See Also

AMMI, SSI

Examples

library(agricolae)
data(plrv)

# AMMI model
model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console = FALSE))

# ANOVA
model$ANOVA

# IPC F test
model$analysis

# Mean yield and IPC scores
model$biplot

# G*E matrix (deviations from mean)
array(model$genXenv, dim(model$genXenv), dimnames(model$genXenv))

# With default n (N') and default ssi.method (farshadfar)
EV.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
EV.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
EV.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
EV.AMMI(model, ssi.method = "rao", a = 0.43)

ammistability documentation built on May 31, 2023, 7:44 p.m.