Type:	Package
Title:	Additive Main Effects and Multiplicative Interaction Model Stability Parameters
Version:	0.1.4
Description:	Computes various stability parameters from Additive Main Effects and Multiplicative Interaction (AMMI) analysis results such as Modified AMMI Stability Value (MASV), Sums of the Absolute Value of the Interaction Principal Component Scores (SIPC), Sum Across Environments of Genotype-Environment Interaction Modelled by AMMI (AMGE), Sum Across Environments of Absolute Value of Genotype-Environment Interaction Modelled by AMMI (AV_(AMGE)), AMMI Stability Index (ASI), Modified ASI (MASI), AMMI Based Stability Parameter (ASTAB), Annicchiarico's D Parameter (DA), Zhang's D Parameter (DZ), Averages of the Squared Eigenvector Values (EV), Stability Measure Based on Fitted AMMI Model (FA), Absolute Value of the Relative Contribution of IPCs to the Interaction (Za). Further calculates the Simultaneous Selection Index for Yield and Stability from the computed stability parameters. See the vignette for complete list of citations for the methods implemented.
Copyright:	2017-2023, ICAR-DGR
License:	GPL-2 | GPL-3
Encoding:	UTF-8
Depends:	R (≥ 3.5.0)
VignetteBuilder:	knitr
RoxygenNote:	7.2.3
Imports:	agricolae, ggcorrplot, ggplot2, methods, reshape2, stats, Rdpack, mathjaxr
Suggests:	knitr, rmarkdown, pander, XML, httr, RCurl
RdMacros:	Rdpack, mathjaxr
URL:	https://github.com/ajaygpb/ammistability/ https://CRAN.R-project.org/package=ammistability https://ajaygpb.github.io/ammistability/ https://doi.org/10.5281/zenodo.1344756
BugReports:	https://github.com/ajaygpb/ammistability/issues
NeedsCompilation:	no
Packaged:	2023-05-23 05:45:34 UTC; Aravind-DGC
Author:	B. C. Ajay [aut, cre], J. Aravind [aut], R. Abdul Fiyaz [aut], ICAR [cph] (url: https://www.icar.org.in)
Maintainer:	B. C. Ajay <ajaygpb@yahoo.co.in>
Repository:	CRAN
Date/Publication:	2023-05-24 07:40:08 UTC

Sum Across Environments of GEI Modelled by AMMI

Description

AMGE.AMMI computes the Sum Across Environments of Genotype-Environment Interaction (GEI) Modelled by AMMI (AMGE) (Sneller et al. 1997) considering all significant interaction principal components (IPCs) in the AMMI model. Using AMGE, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Sum Across Environments of GEI Modelled by AMMI (\(AMGE\)) (Sneller et al. 1997) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(\delta{jn}\) is the eigenvector value for the \(j\)th environment.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
AMGE.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
AMGE.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
AMGE.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
AMGE.AMMI(model, ssi.method = "rao", a = 0.43)

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

Details

The AMMI Stability Index (\(ASI\)) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017) is computed as follows:

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:

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.

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.

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.

See Also

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))

# With default ssi.method (farshadfar)
ASI.AMMI(model)

# With  ssi.method = "rao"
ASI.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
ASI.AMMI(model, ssi.method = "rao", a = 0.43)

AMMI Based Stability Parameter

Description

ASTAB.AMMI computes the AMMI Based Stability Parameter (ASTAB) (Rao and Prabhakaran 2005) considering all significant interaction principal components (IPCs) in the AMMI model. Using ASTAB, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The AMMI Based Stability Parameter value (\(ASTAB\)) (Rao and Prabhakaran 2005) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
ASTAB.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
ASTAB.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
ASTAB.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
ASTAB.AMMI(model, ssi.method = "rao", a = 0.43)

Sum Across Environments of Absolute Value of GEI Modelled by AMMI

Description

AVAMGE.AMMI computes the Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE) (Zali et al. 2012) 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.

Usage

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

Arguments

Details

The Sum Across Environments of Absolute Value of GEI Modelled by AMMI (\(AV_{(AMGE)}\)) (Zali et al. 2012) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(\delta{jn}\) is the eigenvector value for the \(j\)th environment.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

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.

See Also

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))

# 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)

Annicchiarico's D Parameter

Description

DA.AMMI computes the Annicchiarico's D Parameter values (\(\textrm{D}_{\textrm{a}}\)) (Annicchiarico 1997) considering all significant interaction principal components (IPCs) in the AMMI model. It is the unsquared Euclidean distance from the origin of significant IPC axes in the AMMI model. Using \(\textrm{D}_{\textrm{a}}\), the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Annicchiarico's D Parameter value (\(D_{a}\)) (Annicchiarico 1997) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
DA.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
DA.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
DA.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
DA.AMMI(model, ssi.method = "rao", a = 0.43)

Zhang's D Parameter

Description

DZ.AMMI computes the Zhang's D Parameter values or AMMI statistic coefficient or AMMI distance or AMMI stability index (\(\textrm{D}_{\textrm{z}}\)) (Zhang et al. 1998) considering all significant interaction principal components (IPCs) in the AMMI model. It is the distance of IPC point from origin in space. Using \(\textrm{D}_{\textrm{z}}\), the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Zhang's D Parameter value (\(D_{z}\)) (Zhang et al. 1998) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Zhang Z, Lu C, Xiang Z (1998). “Analysis of variety stability based on AMMI model.” Acta Agronomica Sinica, 24(3), 304–309.

See Also

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))

# 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)

Averages of the Squared Eigenvector Values

Description

EV.AMMI computes the Sums of the Averages of the Squared Eigenvector Values (EV) (Zobel 1994) considering all significant interaction principal components (IPCs) in the AMMI model. Using EV, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Averages of the Squared Eigenvector Values (\(EV\)) (Zobel 1994) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Zobel RW (1994). “Stress resistance and root systems.” In Proceedings of the Workshop on Adaptation of Plants to Soil Stress. 1-4 August, 1993. INTSORMIL Publication 94-2, 80–99. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
EV.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
EV.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
EV.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
EV.AMMI(model, ssi.method = "rao", a = 0.43)

Stability Measure Based on Fitted AMMI Model

Description

FA.AMMI computes the Stability Measure Based on Fitted AMMI Model (FA) (Raju 2002) considering all significant interaction principal components (IPCs) in the AMMI model. Using FA, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Stability Measure Based on Fitted AMMI Model (\(FA\)) (Raju 2002) is computed as follows:

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; and \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype.

When \(N'\) is replaced by 1 (only first IPC axis is considered for computation), then the parameter \(FP\) can be estimated (Zali et al. 2012).

When \(N'\) is replaced by 2 (only first two IPC axes are considered for computation), then the parameter \(B\) can be estimated (Zali et al. 2012).

When \(N'\) is replaced by \(N\) (All the IPC axes are considered for computation), then the parameter estimated is equivalent to Wricke's ecovalence (\(W_{(AMMI)}\)) (Wricke 1962; Zali et al. 2012).

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Raju BMK (2002). “A study on AMMI model and its biplots.” Journal of the Indian Society of Agricultural Statistics, 55(3), 297–322.

Wricke G (1962). “On a method of understanding the biological diversity in field research.” Zeitschrift fur Pflanzenzuchtung, 47, 92–146.

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.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
FA.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
FA.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
FA.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
FA.AMMI(model, ssi.method = "rao", a = 0.43)

Modified AMMI Stability Index

Description

MASI.AMMI computes the Modified AMMI Stability Index (MASI) (Ajay et al. 2018) from a modified formula of AMMI Stability Index (ASI) (Jambhulkar et al. 2014; Jambhulkar et al. 2015; Jambhulkar et al. 2017). Unlike ASI, MASI calculates stability value considering all significant interaction principal components (IPCs) in the AMMI model. Using MASI, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Modified AMMI Stability Index (\(MASI\)) (Ajay et al. 2018) is computed as follows:

Where, \(PC_{n}\) are the scores of \(n\)th IPC; and \(\theta_{n}\) is the percentage sum of squares explained by the \(n\)th principal component interaction effect.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

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.

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.

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.

See Also

AMMI, ASI.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))

# With default n (N') and default ssi.method (farshadfar)
MASI.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
MASI.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
MASI.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
MASI.AMMI(model, ssi.method = "rao", a = 0.43)

# ASI.AMMI same as MASI.AMMI with n = 2

a <- ASI.AMMI(model)
b <- MASI.AMMI(model, n = 2)

identical(a$ASI, b$MASI)

Modified AMMI Stability Value

Description

MASV.AMMI computes the Modified AMMI Stability Value (MASV) (Zali et al. 2012; Ajay et al. 2019) (Please see Note) from a modified formula of AMMI Stability Value (ASV) (Purchase 1997). This formula calculates AMMI stability value considering all significant interaction principal components (IPCs) in the AMMI model. Using MASV, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Modified AMMI Stability Value (\(MASV\)) (Ajay et al. 2019) is computed as follows:

Where, \(SSIPC_{1}\), \(SSIPC_{2}\), \(\cdots\), \(SSIPC_{n}\) are the sum of squares of the 1st, 2nd, ..., and \(n\)th IPC; and \(PC_{1}\), \(PC_{2}\), \(\cdots\), \(PC_{n}\) are the scores of 1st, 2nd, ..., and \(n\)th IPC.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

Note

In Zali et al. (2012), the formula for both AMMI stability value (ASV) was found to be erroneous, when compared with the original publications (Purchase 1997; Purchase et al. 1999; Purchase et al. 2000).

ASV (Zali et al. 2012) \[ASV = \sqrt{\left ( \frac{SSIPC_{1}}{SSIPC_{2}} \right ) \times (PC_{1})^2 + \left (PC_{2} \right )^2}\]

ASV (Purchase 1997; Purchase et al. 1999; Purchase et al. 2000) \[ASV = \sqrt{\left (\frac{SSIPC_{1}}{SSIPC_{2}} \times PC_{1} \right )^2 + \left (PC_{2} \right )^2}\]

The authors believe that the proposed Modified AMMI stability value (MASV) in Zali et al. (2012) is also erroneous and have implemented the corrected one in MASV.AMMI (Ajay et al. 2019).

MASV (Zali et al. 2012) \[MASV = \sqrt{\sum_{n=1}^{N'-1}\left ( \frac{SSIPC_{n}}{SSIPC_{n+1}} \right ) \times (PC_{n})^2 + \left (PC_{N'} \right )^2}\]

References

Ajay BC, Aravind J, Fiyaz RA, Kumar N, Lal C, Gangadhar K, Kona P, Dagla MC, Bera SK (2019). “Rectification of modified AMMI stability value (MASV).” Indian Journal of Genetics and Plant Breeding (The), 79, 726–731.

Purchase JL (1997). Parametric analysis to describe genotype × environment interaction and yield stability in winter wheat. Ph.D. Thesis, University of the Orange Free State.

Purchase JL, Hatting H, van Deventer CS (1999). “The use of the AMMI model and AMMI stability value to describe genotype x environment interaction and yield stability in winter wheat (Triticum aestivum L.).” In Proceedings of the Tenth Regional Wheat Workshop for Eastern, Central and Southern Africa, 14-18 September 1998. University of Stellenbosch, South Africa.

Purchase JL, Hatting H, van Deventer CS (2000). “Genotype × environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance.” South African Journal of Plant and Soil, 17(3), 101–107.

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.

See Also

AMMI, index.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))

# With default n (N') and default ssi.method (farshadfar)
MASV.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
MASV.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
MASV.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
MASV.AMMI(model, ssi.method = "rao", a = 0.43)

Sums of the Absolute Value of the IPC Scores

Description

SIPC.AMMI computes the Sums of the Absolute Value of the IPC Scores (ASI) (Sneller et al. 1997) considering all significant interaction principal components (IPCs) in the AMMI model. Using SIPC, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

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

Arguments

Details

The Sums of the Absolute Value of the IPC Scores (\(SIPC\)) (Sneller et al. 1997) is computed as follows:

OR

Where, \(N'\) is the number of significant IPCs (number of IPC that were retained in the AMMI model via F tests); \(\lambda_{n}\) is the singular value for \(n\)th IPC and correspondingly \(\lambda_{n}^{2}\) is its eigen value; \(\gamma_{in}\) is the eigenvector value for \(i\)th genotype; and \(PC_{1}\), \(PC_{2}\), \(\cdots\), \(PC_{n}\) are the scores of 1st, 2nd, ..., and \(n\)th IPC.

The closer the SIPC scores are to zero, the more stable the genotypes are across test environments.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.

See Also

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))

# With default n (N') and default ssi.method (farshadfar)
SIPC.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
SIPC.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
SIPC.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
SIPC.AMMI(model, ssi.method = "rao", a = 0.43)

Simultaneous Selection Indices for Yield and Stability

Description

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

Usage

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

Arguments

Details

The SSI according to Rao and Prabhakaran (2005) (\(I_{i}\)) is computed as follows:

Where \(SP_{i}\) is the stability measure of the \(i\)th genotype under AMMI procedure; \(\overline{Y}_{i}\) is mean performance of \(i\)th genotype; \(\overline{Y}_{..}\) is the overall mean; \(T\) is the number of genotypes under test and \(\alpha\) is the ratio of the weights given to the stability components (\(w_{2}\)) and yield (\(w_{1}\)) with a restriction that \(w_{1} + w_{2} = 1\). The weights can be specified as required.

The SSI proposed by Farshadfar (2008) is called the Genotype stability index (\(GSI\)) or Yield stability index (\(YSI\)) (Farshadfar et al. 2011) and is computed by summation of the ranks of the stability index/parameter and the ranks of the mean yields.

Where, \(R_{SP}\) is the stability parameter/index rank of the genotype and \(R_{Y}\) is the mean yield rank of the genotype.

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

Farshadfar E (2008). “Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat.” Pakistan Journal of biological sciences, 11(14), 1791.

Farshadfar E, Mahmodi N, Yaghotipoor A (2011). “AMMI stability value and simultaneous estimation of yield and yield stability in bread wheat (Triticum aestivum L.).” Australian Journal of Crop Science, 5(13), 1837–1844.

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

See Also

AMGE.AMMI, ASI.AMMI, ASTAB.AMMI, AVAMGE.AMMI, DA.AMMI, DZ.AMMI, EV.AMMI, FA.AMMI, MASV.AMMI, SIPC.AMMI, ZA.AMMI

Examples

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)

Absolute Value of the Relative Contribution of IPCs to the Interaction

Description

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.

Usage

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

Arguments

Details

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

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..

Value

A data frame with the following columns:

The names of the genotypes are indicated as the row names of the data frame.

References

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.

See Also

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))

# 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)

Estimate multiple AMMI model Stability Parameters

Description

ammistability computes multiple stability parameters from an AMMI model. Further, the corresponding Simultaneous Selection Indices for Yield and Stability (SSI) are also calculated according to the argument ssi.method. From the results, correlation between the computed indices will also be computed. The resulting correlation matrices will be plotted as correlograms. For visual comparisons of ranks of genotypes for different indices, slopegraphs and heatmaps will also be generated by this function.

Usage

ammistability(
  model,
  n,
  alpha = 0.05,
  ssi.method = c("farshadfar", "rao"),
  a = 1,
  AMGE = TRUE,
  ASI = TRUE,
  ASV = TRUE,
  ASTAB = TRUE,
  AVAMGE = TRUE,
  DA = TRUE,
  DZ = TRUE,
  EV = TRUE,
  FA = TRUE,
  MASI = TRUE,
  MASV = TRUE,
  SIPC = TRUE,
  ZA = TRUE,
  force.grouping = TRUE,
  line.size = 1,
  line.alpha = 0.5,
  line.col = NULL,
  point.size = 1,
  point.alpha = 0.5,
  point.col = NULL,
  text.size = 2
)

Arguments

Details

ammistability computes the following stability parameters from an AMMI model.

Sum Across Environments of GEI Modelled by AMMI (AMGE)

Sneller et al. (1997)

AMMI Stability Index (ASI)

Jambhulkar et al. (2014); Jambhulkar et al. (2015); Jambhulkar et al. (2017)

AMMI Stability Value (ASV)

Purchase (1997); Purchase et al. (1999); Purchase et al. (2000)

AMMI Based Stability Parameter (ASTAB)

Rao and Prabhakaran (2005)

Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE)

Zali et al. (2012)

Annicchiarico's D Parameter (DA)

Annicchiarico (1997)

Zhang's D Parameter (DZ)

Zhang et al. (1998)

Averages of the Squared Eigenvector Values (EV)

Zobel (1994)

Stability Measure Based on Fitted AMMI Model (FA)

Raju (2002)

Modified AMMI Stability Index (MASI)

Ajay et al. (2018)

Modified AMMI Stability Value (MASV)

Zali et al. (2012); Ajay et al. (2019)

Sums of the Absolute Value of the IPC Scores (SIPC)

Sneller et al. (1997)

Absolute Value of the Relative Contribution of IPCs to the Interaction (Za)

Zali et al. (2012)

Value

A list with the following components:

References

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

Ajay BC, Aravind J, Fiyaz RA (2019). “ammistability: R package for ranking genotypes based on stability parameters derived from AMMI model.” Indian Journal of Genetics and Plant Breeding (The), 79(2), 460–466.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62.

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.

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.

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.

Purchase JL (1997). Parametric analysis to describe genotype × environment interaction and yield stability in winter wheat. Ph.D. Thesis, University of the Orange Free State.

Purchase JL, Hatting H, van Deventer CS (1999). “The use of the AMMI model and AMMI stability value to describe genotype x environment interaction and yield stability in winter wheat (Triticum aestivum L.).” In Proceedings of the Tenth Regional Wheat Workshop for Eastern, Central and Southern Africa, 14-18 September 1998. University of Stellenbosch, South Africa.

Purchase JL, Hatting H, van Deventer CS (2000). “Genotype × environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance.” South African Journal of Plant and Soil, 17(3), 101–107.

Raju BMK (2002). “A study on AMMI model and its biplots.” Journal of the Indian Society of Agricultural Statistics, 55(3), 297–322.

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.

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.

Zhang Z, Lu C, Xiang Z (1998). “Analysis of variety stability based on AMMI model.” Acta Agronomica Sinica, 24(3), 304–309.

Zobel RW (1994). “Stress resistance and root systems.” In Proceedings of the Workshop on Adaptation of Plants to Soil Stress. 1-4 August, 1993. INTSORMIL Publication 94-2, 80–99. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln.

See Also

AMMI, AMGE.AMMI, ASI.AMMI, ASTAB.AMMI, AMGE.AMMI, DA.AMMI, DZ.AMMI, EV.AMMI, FA.AMMI, MASV.AMMI, SIPC.AMMI, ZA.AMMI, SSI

Examples

library(agricolae)
data(plrv)

# AMMI model
model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console = FALSE))

ammistability(model, AMGE = TRUE, ASI = FALSE, ASV = TRUE, ASTAB = FALSE,
              AVAMGE = FALSE, DA = FALSE, DZ = FALSE, EV = TRUE,
              FA = FALSE, MASI = FALSE, MASV = TRUE, SIPC = TRUE,
              ZA = FALSE)

Ranks in a data.frame

Description

Ranks in a data.frame

Usage

rankdf(df, increasing = NULL, decreasing = NULL, ...)

Arguments

Value

A data frame with the ranks computed in the columns specified in arguments increasing and decreasing.

Examples

library(agricolae)
data(soil)

dec <- c("pH", "EC")
inc <- c("CaCO3", "MO", "CIC", "P", "K", "sand",
         "slime", "clay", "Ca", "Mg", "K2", "Na", "Al_H", "K_Mg", "Ca_Mg",
         "B", "Cu", "Fe", "Mn", "Zn")

soilrank <- rankdf(soil, increasing = inc, decreasing = dec)
soilrank

Rank Slopegraph

Description

Create a slopegraph or bump chart from a data frame of ranks.

Usage

rankslopegraph(
  df,
  names,
  group,
  force.grouping = TRUE,
  line.size = 1,
  line.alpha = 0.5,
  line.col = NULL,
  point.size = 1,
  point.alpha = 0.5,
  point.col = NULL,
  text.size = 2,
  legend.position = "bottom"
)

Arguments

Value

The slopegraph as a ggplot2 grob.

References

Tufte ER (1986). The Visual Display of Quantitative Information. Graphics Press, Cheshire, CT, USA. ISBN 0-9613921-0-X.

Examples

library(agricolae)
data(soil)

dec <- c("pH", "EC")
inc <- c("CaCO3", "MO", "CIC", "P", "K", "sand",
         "slime", "clay", "Ca", "Mg", "K2", "Na", "Al_H", "K_Mg", "Ca_Mg",
         "B", "Cu", "Fe", "Mn", "Zn")

soilrank <- rankdf(soil, increasing = inc, decreasing = dec)
soilrank
soilslopeg <- rankslopegraph(soilrank, names = "place")
soilslopeg