# DZ.AMMI: Zhang's D Parameter In ajaygpb/AMMIStbp: Additive Main Effects and Multiplicative Interaction Model Stability Parameters

## Description

DZ.AMMI computes the Zhang's D Parameter values or AMMI statistic coefficient or AMMI distance or AMMI stability index (\mjseqn\textrmD_\textrmz) \insertCitezhang_analysis_1998ammistability considering all significant interaction principal components (IPCs) in the AMMI model. It is the distance of IPC point from origin in space. Using \mjseqn\textrmD_\textrmz, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method. \loadmathjax

## Usage

 1 DZ.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 Zhang's D Parameter value (\mjseqnD_z) \insertCitezhang_analysis_1998ammistability is computed as follows:

\mjsdeqn

D_z = \sqrt\sum_n=1^N'\gamma_in^2

Where, \mjseqnN' is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); and \mjseqn\gamma_in is the eigenvector value for \mjseqnith genotype.

## Value

A data frame with the following columns:

 DZ The DZ values. SSI The computed values of simultaneous selection index for yield and stability. rDZ The ranks of DZ 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) DZ.AMMI(model) # With n = 4 and default ssi.method (farshadfar) DZ.AMMI(model, n = 4) # With default n (N') and ssi.method = "rao" DZ.AMMI(model, ssi.method = "rao") # Changing the ratio of weights for Rao's SSI DZ.AMMI(model, ssi.method = "rao", a = 0.43)