ZA.AMMI {ammistability} | R Documentation |

`ZA.AMMI`

computes the Absolute Value of the Relative Contribution of
IPCs to the Interaction (\(\textrm{Z}_{\textrm{a}}\))
(Zali et al. 2012) considering all significant
interaction principal components (IPCs) in the AMMI model. Using
\(\textrm{Z}_{\textrm{a}}\), the Simultaneous Selection Index for Yield
and Stability (SSI) is also calculated according to the argument
`ssi.method`

.

ZA.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)

`model` |
The AMMI model (An object of class |

`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 |

`a` |
The ratio of the weights given to the stability components for
computation of SSI when |

The Absolute Value of the Relative Contribution of IPCs to the Interaction (\(Za\)) (Zali et al. 2012) is computed as follows:

\[Za = \sum_{i=1}^{N'}\left | \theta_{n}\gamma_{in} \right |\]Where, \(N'\) is the number of significant IPCAs (number of IPC that were retained in the AMMI model via F tests); \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(\theta_{n}\) is the percentage sum of squares explained by the \(n\)th principal component interaction effect..

A data frame with the following columns:

`Za` |
The Za values. |

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

`rZa` |
The ranks of Za 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.

Zali H, Farshadfar E, Sabaghpour SH, Karimizadeh R (2012).
“Evaluation of genotype × environment interaction in chickpea using measures of stability from AMMI model.”
*Annals of Biological Research*, **3**(7), 3126–3136.

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) ZA.AMMI(model) # With n = 4 and default ssi.method (farshadfar) ZA.AMMI(model, n = 4) # With default n (N') and ssi.method = "rao" ZA.AMMI(model, ssi.method = "rao") # Changing the ratio of weights for Rao's SSI ZA.AMMI(model, ssi.method = "rao", a = 0.43)

[Package *ammistability* version 0.1.2 Index]