SIPC.AMMI: Sums of the Absolute Value of the IPC Scores

In ajaygpb/AMMIStbp: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

Sums of the Absolute Value of the IPC Scores

Description

SIPC.AMMI computes the Sums of the Absolute Value of the IPC Scores (ASI) \insertCitesneller_repeatability_1997ammistability 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. \loadmathjax

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 (\mjseqnSIPC) \insertCitesneller_repeatability_1997ammistability is computed as follows:

\mjsdeqn

SIPC = \sum_n=1^N' \left | \lambda_n^0.5\gamma_in \right |

OR

\mjsdeqn

SIPC = \sum_n=1^N'\left | PC_n \right |

Where, \mjseqnN' is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \mjseqn\lambda_n is the singular value for \mjseqnnth IPC and correspondingly \mjseqn\lambda_n^2 is its eigen value; \mjseqn\gamma_in is the eigenvector value for \mjseqnith genotype; and \mjseqnPC_1, \mjseqnPC_2, \mjseqn\cdots, \mjseqnPC_n are the scores of 1st, 2nd, ..., and \mjseqnnth 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

\insertAllCited

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)

ajaygpb/AMMIStbp documentation built on Aug. 21, 2023, 7:59 p.m.