SIPC.AMMI {ammistability}

Sums of the Absolute Value of the IPC Scores

Description

SIPC.AMMI computes the Sums of the Absolute Value of the IPC Scores (ASI) (Sneller et al. 1997) considering all significant interaction principal components (IPCs) in the AMMI model. Using SIPC, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

SIPC.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 Sums of the Absolute Value of the IPC Scores (\(SIPC\)) (Sneller et al. 1997) is computed as follows:

\[SIPC = \sum_{n=1}^{N'} \left | \lambda_{n}^{0.5}\gamma_{in} \right |\]

OR

\[SIPC = \sum_{n=1}^{N'}\left | PC_{n} \right |\]

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; \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(PC_{1}\), \(PC_{2}\), \(\cdots\), \(PC_{n}\) are the scores of 1st, 2nd, ..., and \(n\)th IPC.

The closer the SIPC scores are to zero, the more stable the genotypes are across test environments.

Value

A data frame with the following columns:

SIPC

The SIPC values.

SSI

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

rSIPC

The ranks of SIPC 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

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.

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)
SIPC.AMMI(model)

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

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

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