FA.AMMI: Stability Measure Based on Fitted AMMI Model

Description Usage Arguments Details Value References See Also Examples

View source: R/FA.AMMI.R

Description

FA.AMMI computes the Stability Measure Based on Fitted AMMI Model (FA) (Raju, 2002) 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.

Usage

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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 (FA) is computed as follows:

FA = N'n=1 λ2nγ2in

Where, N' is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); λn is the singular value for nth IPC and correspondingly λ2n is its eigen value; and γin is the eigenvector value for ith genotype.

When N' is replaced by 1 (only first IPC axis is considered for computation), then the parameter FP can be estimated (Zali et al., 2012).

FP =λ21γ2i1

When N' is replaced by 2 (only first two IPC axes are considered for computation), then the parameter B can be estimated (Zali et al., 2012).

B = 2n=1 λ2nγ2in

When N' is replaced by N (All the IPC axes are considered for computation), then the parameter estimated is equivalent to Wricke's ecovalence (W(AMMI)) (Wricke, 1962; Zali et al., 2012).

W(AMMI) = Nn=1 λ2nγ2in

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

\insertRef

wricke_method_1962ammistability

\insertRef

raju_study_2002ammistability

\insertRef

zali_evaluation_2012ammistability

See Also

AMMI, SSI

Examples

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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 Jan. 27, 2020, 8:53 a.m.