MASV.AMMI: Modified AMMI Stability Value

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

Modified AMMI Stability Value

Description

MASV.AMMI computes the Modified AMMI Stability Value (MASV) \insertCitezali_evaluation_2012,ajay_rectification_2019ammistability (Please see Note) from a modified formula of AMMI Stability Value (ASV) \insertCitepurchase_parametric_1997ammistability. This formula calculates AMMI stability value considering all significant interaction principal components (IPCs) in the AMMI model. Using MASV, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method. \loadmathjax

Usage

MASV.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 Modified AMMI Stability Value (\mjseqnMASV) \insertCiteajay_rectification_2019ammistability is computed as follows:

\mjsdeqn

MASV = \sqrt\sum_n=1^N'-1\left (\fracSSIPC_nSSIPC_n+1 \times PC_n \right )^2 + \left (PC_N' \right )^2

Where, \mjseqnSSIPC_1, \mjseqnSSIPC_2, \mjseqn\cdots, \mjseqnSSIPC_n are the sum of squares of the 1st, 2nd, ..., and \mjseqnnth IPC; and \mjseqnPC_1, \mjseqnPC_2, \mjseqn\cdots, \mjseqnPC_n are the scores of 1st, 2nd, ..., and \mjseqnnth IPC.

Value

A data frame with the following columns:

MASV	The MASV values.
SSI	The computed values of simultaneous selection index for yield and stability.
rMASV	The ranks of MASV 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.

Note

In \insertCitezali_evaluation_2012;textualammistability, the formula for both AMMI stability value (ASV) was found to be erroneous, when compared with the original publications \insertCitepurchase_parametric_1997,purchase_use_1999,purchase_genotype_2000ammistability.

ASV \insertCitezali_evaluation_2012ammistability \mjsdeqnASV = \sqrt\left ( \fracSSIPC_1SSIPC_2 \right ) \times (PC_1)^2 + \left (PC_2 \right )^2

ASV \insertCitepurchase_parametric_1997,purchase_use_1999,purchase_genotype_2000ammistability \mjsdeqnASV = \sqrt\left (\fracSSIPC_1SSIPC_2 \times PC_1 \right )^2 + \left (PC_2 \right )^2

The authors believe that the proposed Modified AMMI stability value (MASV) in \insertCitezali_evaluation_2012;textualammistability is also erroneous and have implemented the corrected one in MASV.AMMI \insertCiteajay_rectification_2019ammistability.

MASV \insertCitezali_evaluation_2012ammistability \mjsdeqnMASV = \sqrt\sum_n=1^N'-1\left ( \fracSSIPC_nSSIPC_n+1 \right ) \times (PC_n)^2 + \left (PC_N' \right )^2

References

\insertAllCited

See Also

AMMI, index.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)
MASV.AMMI(model)

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

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

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

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