MASI.AMMI {ammistability}

Modified AMMI Stability Index

Description

MASI.AMMI computes the Modified AMMI Stability Index (MASI) (Ajay et al. 2018) from a modified formula of AMMI Stability Index (ASI) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017). Unlike ASI, MASI calculates stability value considering all significant interaction principal components (IPCs) in the AMMI model. Using MASI, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

MASI.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 Index (\(MASI\)) (Ajay et al. 2018) is computed as follows:

\[MASI = \sqrt{ \sum_{n=1}^{N'} PC_{n}^{2} \times \theta_{n}^{2}}\]

Where, \(PC_{n}\) are the scores of \(n\)th IPC; and \(\theta_{n}\) is the percentage sum of squares explained by the \(n\)th principal component interaction effect.

Value

A data frame with the following columns:

MASI

The MASI values.

SSI

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

rMASI

The ranks of MASI 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

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

Jambhulkar NN, Bose LK, Pande K, Singh ON (2015). “Genotype by environment interaction and stability analysis in rice genotypes.” Ecology, Environment and Conservation, 21(3), 1427–1430.

Jambhulkar NN, Bose LK, Singh ON (2014). “AMMI stability index for stability analysis.” In Mohapatra T (ed.), CRRI Newsletter, January-March 2014, volume 35(1), 15. Central Rice Research Institute, Cuttack, Orissa.

Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017). “Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.” Oryza, 54(2), 236–240.

See Also

AMMI, ASI.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)
MASI.AMMI(model)

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

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

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

# ASI.AMMI same as MASI.AMMI with n = 2

a <- ASI.AMMI(model)
b <- MASI.AMMI(model, n = 2)

identical(a$ASI, b$MASI)