DA.AMMI {ammistability}

Annicchiarico's D Parameter

Description

DA.AMMI computes the Annicchiarico's D Parameter values (\(\textrm{D}_{\textrm{a}}\)) (Annicchiarico 1997) considering all significant interaction principal components (IPCs) in the AMMI model. It is the unsquared Euclidean distance from the origin of significant IPC axes in the AMMI model. Using \(\textrm{D}_{\textrm{a}}\), the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

DA.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 Annicchiarico's D Parameter value (\(D_{a}\)) (Annicchiarico 1997) is computed as follows:

\[D_{a} = \sqrt{\sum_{n=1}^{N'}(\lambda_{n}\gamma_{in})^2}\]

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

Value

A data frame with the following columns:

DA

The DA values.

SSI

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

rDA

The ranks of DA 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

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62.

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)
DA.AMMI(model)

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

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

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