# SSI: Simultaneous Selection Indices for Yield and Stability In ajaygpb/AMMIStbp: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

## Description

SSI computes the Simultaneous Selection Index for Yield and Stability (SSI) according to the methods specified in the argument method. \loadmathjax

## Usage

 1 SSI(y, sp, gen, method = c("farshadfar", "rao"), a = 1) 

## Arguments

 y A numeric vector of the mean yield/performance of genotypes. sp A numeric vector of the stability parameter/index of the genotypes. gen A character vector of the names of the genotypes. method The method for the computation of simultaneous selection index. Either "farshadfar" or "rao" (See Details). a The ratio of the weights given to the stability components for computation of SSI when method = "rao" (See Details).

## Details

The SSI according to \insertCiterao_use_2005;textualammistability (\mjseqnI_i) is computed as follows:

\mjsdeqn

I_i = \frac\overlineY_i\overlineY_.. + \alpha \frac\frac1SP_i\frac1T\sum_i=1^T\frac1SP_i

Where \mjseqnSP_i is the stability measure of the \mjseqnith genotype under AMMI procedure; \mjseqn\overlineY_i is mean performance of \mjseqnith genotype; \mjseqn\overlineY_.. is the overall mean; \mjseqnT is the number of genotypes under test and \mjseqn\alpha is the ratio of the weights given to the stability components (\mjseqnw_2) and yield (\mjseqnw_1) with a restriction that \mjseqnw_1 + w_2 = 1. The weights can be specified as required.

 \mjseqn\alpha \mjseqnw_1 \mjseqnw_2 1.00 0.5 0.5 0.67 0.6 0.4 0.43 0.7 0.3 0.25 0.8 0.2

The SSI proposed by \insertCitefarshadfar_incorporation_2008;textualammistability is called the Genotype stability index (\mjseqnGSI) or Yield stability index (\mjseqnYSI) \insertCitefarshadfar_ammi_2011ammistability and is computed by summation of the ranks of the stability index/parameter and the ranks of the mean yields.

\mjsdeqn

GSI = YSI = R_SP + R_Y

Where, \mjseqnR_SP is the stability parameter/index rank of the genotype and \mjseqnR_Y is the mean yield rank of the genotype.

## Value

A data frame with the following columns:

 SP The stability parameter values. SSI The computed values of simultaneous selection index for yield and stability. rSP The ranks of the stability parameter. 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

AMGE.AMMI, ASI.AMMI, ASTAB.AMMI, AVAMGE.AMMI, DA.AMMI, DZ.AMMI, EV.AMMI, FA.AMMI, MASV.AMMI, SIPC.AMMI, ZA.AMMI
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 library(agricolae) data(plrv) model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console=FALSE)) yield <- aggregate(model$means$Yield, by= list(model$means$GEN), FUN=mean, na.rm=TRUE)[,2] stab <- DZ.AMMI(model)\$DZ genotypes <- rownames(DZ.AMMI(model)) # With default ssi.method (farshadfar) SSI(y = yield, sp = stab, gen = genotypes) # With ssi.method = "rao" SSI(y = yield, sp = stab, gen = genotypes, method = "rao") # Changing the ratio of weights for Rao's SSI SSI(y = yield, sp = stab, gen = genotypes, method = "rao", a = 0.43)