ZA.AMMI {ammistability}

Absolute Value of the Relative Contribution of IPCs to the Interaction

Description

ZA.AMMI computes the Absolute Value of the Relative Contribution of IPCs to the Interaction (\(\textrm{Z}_{\textrm{a}}\)) (Zali et al. 2012) considering all significant interaction principal components (IPCs) in the AMMI model. Using \(\textrm{Z}_{\textrm{a}}\), the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

ZA.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 Absolute Value of the Relative Contribution of IPCs to the Interaction (\(Za\)) (Zali et al. 2012) is computed as follows:

\[Za = \sum_{i=1}^{N'}\left | \theta_{n}\gamma_{in} \right |\]

Where, \(N'\) is the number of significant IPCAs (number of IPC that were retained in the AMMI model via F tests); \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(\theta_{n}\) is the percentage sum of squares explained by the \(n\)th principal component interaction effect..

Value

A data frame with the following columns:

Za

The Za values.

SSI

The computed values of simultaneous selection index for yield and stability.

rZa

The ranks of Za 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

Zali H, Farshadfar E, Sabaghpour SH, Karimizadeh R (2012). “Evaluation of genotype × environment interaction in chickpea using measures of stability from AMMI model.” Annals of Biological Research, 3(7), 3126–3136.

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)
ZA.AMMI(model)

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

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

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