FA.AMMI: Stability Measure Based on Fitted AMMI Model

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

Stability Measure Based on Fitted AMMI Model

Description

FA.AMMI computes the Stability Measure Based on Fitted AMMI Model (FA) \insertCiteraju_study_2002ammistability considering all significant interaction principal components (IPCs) in the AMMI model. Using FA, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method. \loadmathjax

Usage

FA.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 Stability Measure Based on Fitted AMMI Model (\mjseqnFA) \insertCiteraju_study_2002ammistability is computed as follows:

\mjsdeqn

FA = \sum_n=1^N'\lambda_n^2\gamma_in^2

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; and \mjseqn\gamma_in is the eigenvector value for \mjseqnith genotype.

When \mjseqnN' is replaced by 1 (only first IPC axis is considered for computation), then the parameter \mjseqnFP can be estimated \insertCitezali_evaluation_2012ammistability.

\mjsdeqn

FP = \lambda_1^2\gamma_i1^2

When \mjseqnN' is replaced by 2 (only first two IPC axes are considered for computation), then the parameter \mjseqnB can be estimated \insertCitezali_evaluation_2012ammistability.

\mjsdeqn

B = \sum_n=1^2\lambda_n^2\gamma_in^2

When \mjseqnN' is replaced by \mjseqnN (All the IPC axes are considered for computation), then the parameter estimated is equivalent to Wricke's ecovalence (\mjseqnW_(AMMI)) \insertCitewricke_method_1962,zali_evaluation_2012ammistability.

\mjsdeqn

W_(AMMI) = \sum_n=1^N\lambda_n^2\gamma_in^2

Value

A data frame with the following columns:

FA	The FA values.
SSI	The computed values of simultaneous selection index for yield and stability.
rFA	The ranks of FA 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)
FA.AMMI(model)

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

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

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

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