ASI.AMMI {ammistability} R Documentation

## AMMI Stability Index

### Description

ASI.AMMI computes the AMMI Stability Index (ASI) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017) considering the first two interaction principal components (IPCs) in the AMMI model. Using ASI, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

### Usage

ASI.AMMI(model, ssi.method = c("farshadfar", "rao"), a = 1)


### Arguments

 model The AMMI model (An object of class AMMI generated by AMMI). 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 AMMI Stability Index ($$ASI$$) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017) is computed as follows:

$ASI = \sqrt{\left [ PC_{1}^{2} \times \theta_{1}^{2} \right ]+\left [ PC_{2}^{2} \times \theta_{2}^{2} \right ]}$

Where, $$PC_{1}$$ and $$PC_{2}$$ are the scores of 1st and 2nd IPCs respectively; and $$\theta_{1}$$ and $$\theta_{2}$$ are percentage sum of squares explained by the 1st and 2nd principal component interaction effect respectively.

### Value

A data frame with the following columns:

 ASI The ASI values. SSI The computed values of simultaneous selection index for yield and stability. rASI The ranks of ASI 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

Jambhulkar NN, Bose LK, Pande K, Singh ON (2015). “Genotype by environment interaction and stability analysis in rice genotypes.” Ecology, Environment and Conservation, 21(3), 1427–1430. http://www.envirobiotechjournals.com/article_abstract.php?aid=6346&iid=200&jid=3.

Jambhulkar NN, Bose LK, Singh ON (2014). “AMMI stability index for stability analysis.” In Mohapatra T (ed.), CRRI Newsletter, January-March 2014, volume 35(1), 15. Central Rice Research Institute, Cuttack, Orissa. http://www.crri.nic.in/CRRI_newsletter/crnl_jan_mar_14_web.pdf.

Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017). “Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.” Oryza, 54(2), 236–240. doi: 10.5958/2249-5266.2017.00030.3, https://doi.org/10.5958/2249-5266.2017.00030.3.

AMMI, SSI

### Examples

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))