# MASV.AMMI: Modified AMMI Stability Value In ajaygpb/AMMIStbp: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

## Description

`MASV.AMMI` computes the Modified AMMI Stability Value (MASV) (Zali et al., 2012; Ajay et al., 2019; Please see Note) from a modified formula of AMMI Stability Value (ASV) (Purchase et al. 1997). 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`.

## Usage

 `1` ```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 (MASV) is computed as follows (Ajay et al., 2019):

MASV = √[∑N'-1n=1((SSIPCnSSIPCn+1) × PC1)2 + (PCN')2]

Where, SSIPC1, SSIPC2, …, SSIPCn are the sum of squares of the 1st, 2nd, ..., and nth IPC; and PC1, PC2, …, PCn are the scores of 1st, 2nd, ..., and nth 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 Zali et al., (2012), the formula for both AMMI stability value (ASV) was found to be erroneous, when compared with the original publications (Purchase 1997; Purchase et al., 1999; Purchase et al., 2000).

ASV (Zali et al., 2012)

ASV = √[(SSIPC1 ⁄ SSIPC2) × (PC1)2 + (PC2)2]

ASV (Purchase 1997; Purchase et al., 1999; Purchase et al., 2000)

ASV = √[((SSIPC1SSIPC2) × PC1)2 + (PC2)2]

The authors believe that the proposed Modified AMMI stability value (MASV) in Zali et al., (2012) is also erroneous and have implemented the corrected one in `MASV.AMMI` (Ajay et al., 2019).

MASV (Zali et al., 2012)

MASV = √[∑N'-1n=1(SSIPCnSSIPCn+1) × (PC1)2 + (PCN')2]

## References

\insertRef

purchase_parametric_1997ammistability

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purchase_use_1999ammistability

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purchase_genotype_2000ammistability

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zali_evaluation_2012ammistability

\insertRef

ajay_rectification_2019ammistability

`AMMI`, `index.AMMI`, `SSI`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```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) ```