# AVAMGE.AMMI: Sum Across Environments of Absolute Value of GEI Modelled by... In ajaygpb/AMMIStbp: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

## Description

AVAMGE.AMMI computes the Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE) \insertCitezali_evaluation_2012ammistability considering all significant interaction principal components (IPCs) in the AMMI model. Using AVAMGE, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method. \loadmathjax

## Usage

 1 AVAMGE.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 Sum Across Environments of Absolute Value of GEI Modelled by AMMI (\mjseqnAV_(AMGE)) \insertCitezali_evaluation_2012ammistability is computed as follows:

\mjsdeqn

AV_(AMGE) = \sum_j=1^E \sum_n=1^N' \left |\lambda_n \gamma_in \delta_jn \right |

Where, \mjseqnN' is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \mjseqn\lambda_n is the singular value for \mjseqnnth IPC and correspondingly \mjseqn\lambda_n^2 is its eigen value; \mjseqn\gamma_in is the eigenvector value for \mjseqnith genotype; and \mjseqn\deltajn is the eigenvector value for the \mjseqnjth environment.

## Value

A data frame with the following columns:

 AVAMGE The AVAMGE values. SSI The computed values of simultaneous selection index for yield and stability. rAVAMGE The ranks of AVAMGE 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

\insertAllCited

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