,
J. Aravind [aut] ,
R. Abdul Fiyaz [aut] ,
ICAR [cph] (https://www.icar.org.in)| Title: | Additive Main Effects and Multiplicative Interaction Model Stability Parameters |
|---|---|
| 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. |
| Authors: | B. C. Ajay [aut, cre] ,
J. Aravind [aut] ,
R. Abdul Fiyaz [aut] ,
ICAR [cph] (https://www.icar.org.in) |
| Maintainer: | B. C. Ajay <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 0.1.4.9000 |
| Built: | 2025-03-03 06:20:32 UTC |
| Source: | https://github.com/ajaygpb/ammistability |
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.
AMGE.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)AMGE.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 Sum Across Environments of GEI Modelled by AMMI (\(AMGE\)) (Sneller et al. 1997) is computed as follows:
\[AMGE = \sum_{j=1}^{E} \sum_{n=1}^{N'} \lambda_{n} \gamma_{in} \delta_{jn}\]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.
A data frame with the following columns:
AMGE |
The AMGE values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rAMGE |
The ranks of AMGE 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.
Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.
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)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)
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.
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 )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 )
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 |
AMGE |
If |
ASI |
If |
ASV |
If |
ASTAB |
If |
AVAMGE |
If |
DA |
If |
DZ |
If |
EV |
If |
FA |
If |
MASI |
If |
MASV |
If |
SIPC |
If |
ZA |
If |
force.grouping |
If |
line.size |
Size of lines plotted in the slopegraphs. Must be numeric. |
line.alpha |
Transparency of lines plotted in the slopegraphs. Must be numeric. |
line.col |
Default is |
point.size |
Size of points plotted in the slopegraphs. Must be numeric. |
point.alpha |
Transparency of points plotted in the slopegraphs. Must be numeric. |
point.col |
Default is |
text.size |
Size of text annotations plotted in the slopegraphs. Must be numeric. |
ammistability computes the following stability parameters from an AMMI
model.
Sneller et al. (1997)
Jambhulkar et al. (2014); Jambhulkar et al. (2015); Jambhulkar et al. (2017)
Purchase (1997); Purchase et al. (1999); Purchase et al. (2000)
Rao and Prabhakaran (2005)
Zali et al. (2012)
Annicchiarico (1997)
Zhang et al. (1998)
Zobel (1994)
Raju (2002)
Ajay et al. (2018)
Zali et al. (2012); Ajay et al. (2019)
Sneller et al. (1997)
Zali et al. (2012)
A list with the following components:
Details |
A data frame indicating the stability parameters computed and the method used for computing the SSI. |
Stability Parameters |
A data frame of computed stability parameters. |
Simultaneous Selection Indices |
A data frame of computed SSIs. |
SP Correlation |
A data frame of correlation between stability parameters. |
SSI Correlation |
A data frame of correlation between SSIs. |
SP and SSI Correlation |
A data frame of correlation between stability parameters and SSIs. |
SP
Correlogram |
Correlogram of stability parameters. |
SSI
Correlogram |
Correlogram of SSIs. |
SP and SSI
Correlogram |
Correlogram of stability parameters and SSIs. |
SP
Slopegraph |
Slopegraph of stability parameter ranks. |
SSI
Slopegraph |
Slopegraph of SSI ranks. |
SP Heatmap |
Heatmap of stability parameter ranks. |
SSI Heatmap |
Heatmap of SSI ranks. |
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.
AMMI,
AMGE.AMMI,
ASI.AMMI,
ASTAB.AMMI,
AMGE.AMMI,
DA.AMMI, DZ.AMMI,
EV.AMMI, FA.AMMI,
MASV.AMMI,
SIPC.AMMI,
ZA.AMMI, SSI
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)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)
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.
ASI.AMMI(model, ssi.method = c("farshadfar", "rao"), a = 1)ASI.AMMI(model, ssi.method = c("farshadfar", "rao"), a = 1)
model |
The AMMI model (An object of class |
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 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.
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.
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.
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)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)
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.
ASTAB.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)ASTAB.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 AMMI Based Stability Parameter value (\(ASTAB\)) (Rao and Prabhakaran 2005) is computed as follows:
\[ASTAB = \sum_{n=1}^{N'}\lambda_{n}\gamma_{in}^{2}\]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.
A data frame with the following columns:
ASTAB |
The ASTAB values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rASTAB |
The ranks of ASTAB 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.
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.
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)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)
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.
AVAMGE.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)AVAMGE.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 Sum Across Environments of Absolute Value of GEI Modelled by AMMI (\(AV_{(AMGE)}\)) (Zali et al. 2012) is computed as follows:
\[AV_{(AMGE)} = \sum_{j=1}^{E} \sum_{n=1}^{N'} \left |\lambda_{n} \gamma_{in} \delta_{jn} \right |\]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.
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.
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) 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)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)
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.
DA.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)DA.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 Annicchiarico's D Parameter value (\(D_{a}\)) (Annicchiarico 1997) is computed as follows:
\[D_{a} = \sqrt{\sum_{n=1}^{N'}(\lambda_{n}\gamma_{in})^2}\]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.
A data frame with the following columns:
DA |
The DA values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rDA |
The ranks of DA 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.
Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62.
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)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)
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.
DZ.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)DZ.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 Zhang's D Parameter value (\(D_{z}\)) (Zhang et al. 1998) is computed as follows:
\[D_{z} = \sqrt{\sum_{n=1}^{N'}\gamma_{in}^{2}}\]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.
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.
Zhang Z, Lu C, Xiang Z (1998). “Analysis of variety stability based on AMMI model.” Acta Agronomica Sinica, 24(3), 304–309.
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)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)
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.
EV.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)EV.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 Averages of the Squared Eigenvector Values (\(EV\)) (Zobel 1994) is computed as follows:
\[EV = \sum_{n=1}^{N'}\frac{\gamma_{in}^2}{N'}\]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.
A data frame with the following columns:
EV |
The EV values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rEV |
The ranks of EV 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.
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.
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)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)
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.
FA.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)FA.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 Stability Measure Based on Fitted AMMI Model (\(FA\)) (Raju 2002) is computed as follows:
\[FA = \sum_{n=1}^{N'}\lambda_{n}^{2}\gamma_{in}^{2}\]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).
\[FP = \lambda_{1}^{2}\gamma_{i1}^{2}\]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).
\[B = \sum_{n=1}^{2}\lambda_{n}^{2}\gamma_{in}^{2}\]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).
\[W_{(AMMI)} = \sum_{n=1}^{N}\lambda_{n}^{2}\gamma_{in}^{2}\]A data frame with the following columns:
FA |
The FA values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rFA |
The ranks of FA 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.
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.
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)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)
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.
MASI.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)MASI.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 Modified AMMI Stability Index (\(MASI\)) (Ajay et al. 2018) is computed as follows:
\[MASI = \sqrt{ \sum_{n=1}^{N'} PC_{n}^{2} \times \theta_{n}^{2}}\]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.
A data frame with the following columns:
MASI |
The MASI values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rMASI |
The ranks of MASI 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.
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.
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)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)
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.
MASV.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)MASV.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 Modified AMMI Stability Value (\(MASV\)) (Ajay et al. 2019) is computed as follows:
\[MASV = \sqrt{\sum_{n=1}^{N'-1}\left (\frac{SSIPC_{n}}{SSIPC_{n+1}} \times PC_{n} \right )^2 + \left (PC_{N'} \right )^2}\]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.
A data frame with the following columns:
MASV |
The MASV values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rMASV |
The ranks of MASV 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.
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) \[MASV = \sqrt{\sum_{n=1}^{N'-1}\left ( \frac{SSIPC_{n}}{SSIPC_{n+1}} \right ) \times (PC_{n})^2 + \left (PC_{N'} \right )^2}\]
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.
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)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)
Ranks in a data.frame
rankdf(df, increasing = NULL, decreasing = NULL, ...)rankdf(df, increasing = NULL, decreasing = NULL, ...)
df |
A data frame. |
increasing |
A character vector of column names of the data frame to be ranked in increasing order. |
decreasing |
A character vector of column names of the data frame to be ranked in decreasing order. |
... |
Additional arguments to be passed on to
|
A data frame with the ranks computed in the columns specified in
arguments increasing and decreasing.
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) soilranklibrary(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
Create a slopegraph or bump chart from a data frame of ranks.
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" )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" )
df |
A data frame of records. |
names |
The name of the column having the names of the records. |
group |
Optional. The name of the column with a grouping variable. |
force.grouping |
If |
line.size |
Size of lines plotted. Must be numeric. |
line.alpha |
Transparency of lines plotted. Must be numeric. |
line.col |
Default is |
point.size |
Size of points plotted. Must be numeric. |
point.alpha |
Transparency of points plotted. Must be numeric. |
point.col |
Default is |
text.size |
Size of text annotations plotted. Must be numeric. |
legend.position |
Position of the legend in the plot. |
The slopegraph as a ggplot2 grob.
Tufte ER (1986). The Visual Display of Quantitative Information. Graphics Press, Cheshire, CT, USA. ISBN 0-9613921-0-X.
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") soilslopeglibrary(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
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.
SIPC.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)SIPC.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 Sums of the Absolute Value of the IPC Scores (\(SIPC\)) (Sneller et al. 1997) is computed as follows:
\[SIPC = \sum_{n=1}^{N'} \left | \lambda_{n}^{0.5}\gamma_{in} \right |\]OR
\[SIPC = \sum_{n=1}^{N'}\left | PC_{n} \right |\]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.
A data frame with the following columns:
SIPC |
The SIPC values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rSIPC |
The ranks of SIPC 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.
Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390.
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)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)
SSI computes the Simultaneous Selection Index for Yield and Stability
(SSI) according to the methods specified in the argument method.
SSI(y, sp, gen, method = c("farshadfar", "rao"), a = 1)SSI(y, sp, gen, method = c("farshadfar", "rao"), a = 1)
y |
A numeric vector of the mean yield/performance of genotypes. |
sp |
A numeric vector of the stability parameter/index of the genotypes. |
gen |
A character vector of the names of the genotypes. |
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 SSI according to Rao and Prabhakaran (2005) (\(I_{i}\)) is computed as follows:
\[I_{i} = \frac{\overline{Y}_{i}}{\overline{Y}_{..}} + \alpha \frac{\frac{1}{SP_{i}}}{\frac{1}{T}\sum_{i=1}^{T}\frac{1}{SP_{i}}}\]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.
| \(\alpha\) | \(w_{1}\) | \(w_{2}\) |
| 1.00 | 0.5 | 0.5 |
| 0.67 | 0.6 | 0.4 |
| 0.43 | 0.7 | 0.3 |
| 0.25 | 0.8 | 0.2 |
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.
\[GSI = YSI = R_{SP} + R_{Y}\]Where, \(R_{SP}\) is the stability parameter/index rank of the genotype and \(R_{Y}\) is the mean yield rank of the genotype.
A data frame with the following columns:
SP |
The stability parameter values. |
SSI |
The computed values of simultaneous selection index for yield and stability. |
rSP |
The ranks of the stability parameter. |
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.
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.
AMGE.AMMI,
ASI.AMMI,
ASTAB.AMMI,
AVAMGE.AMMI,
DA.AMMI, DZ.AMMI,
EV.AMMI, FA.AMMI,
MASV.AMMI,
SIPC.AMMI,
ZA.AMMI
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)$DZ genotypes <- rownames(DZ.AMMI(model)) # With default ssi.method (farshadfar) SSI(y = yield, sp = stab, gen = genotypes) # With ssi.method = "rao" SSI(y = yield, sp = stab, gen = genotypes, method = "rao") # Changing the ratio of weights for Rao's SSI SSI(y = yield, sp = stab, gen = genotypes, method = "rao", a = 0.43)library(agricolae) data(plrv) model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console=FALSE)) yield <- aggregate(model$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)
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)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)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)