Estimate multiple AMMI model Stability Parameters — ammistability • ammistability

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

model: The AMMI model (An object of class AMMI generated by AMMI).
n: The number of principal components to be considered for computation. The default value is the number of significant IPCs.
alpha: Type I error probability (Significance level) to be considered to identify the number of significant IPCs.
ssi.method: The method for the computation of simultaneous selection index. Either "farshadfar" or "rao" (See SSI).
a: The ratio of the weights given to the stability components for computation of SSI when method = "rao" (See SSI).
AMGE: If TRUE, computes AMGE (see Details). Default is TRUE.
ASI: If TRUE, computes ASI (see Details). n = 2 will be used in this case. Default is TRUE.
ASV: If TRUE, computes ASV (see Details). n = 2 will be used in this case. Default is TRUE.
ASTAB: If TRUE, computes ASTAB (see Details). Default is TRUE.
AVAMGE: If TRUE, computes AVAMGE (see Details). Default is TRUE.
DA: If TRUE, computes DA (see Details). Default is TRUE.
DZ: If TRUE, computes DZ (see Details). Default is TRUE.
EV: If TRUE, computes EV (see Details). Default is TRUE.
FA: If TRUE, computes FA (see Details). Default is TRUE.
MASI: If TRUE, computes MASI (see Details). Default is TRUE.
MASV: If TRUE, computes MASV (see Details). Default is TRUE.
SIPC: If TRUE, computes SIPC (see Details). Default is TRUE.
ZA: If TRUE, computes ZA (see Details). Default is TRUE.
force.grouping: If TRUE, genotypes will be considered as a grouping variable for plotting the slopegraphs. (Each genotype will be represented by a different colour in the slopegraphs). Default is TRUE.
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 TRUE. Overrides colouring by force.grouping argument.
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 TRUE. Overrides colouring by force.grouping argument.
text.size: Size of text annotations plotted in the slopegraphs. Must be numeric.

Value

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.

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)

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.

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)
#> Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
#> ℹ Please use tidy evaluation idioms with `aes()`.
#> ℹ See also `vignette("ggplot2-in-packages")` for more information.
#> ℹ The deprecated feature was likely used in the ggcorrplot package.
#>   Please report the issue at <https://github.com/kassambara/ggcorrplot/issues>.
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> ℹ The deprecated feature was likely used in the ammistability package.
#>   Please report the issue at <https://github.com/ajaygpb/ammistability/issues>.
#> $Details
#> $Details$`Stability parameters estimated`
#> [1] "AMGE" "ASV"  "EV"   "MASV" "SIPC"
#> 
#> $Details$`SSI method`
#> [1] "Farshadfar (2008)"
#> 
#> 
#> $`Stability Parameters`
#>    genotype    means          AMGE       ASV           EV      MASV      SIPC
#> 1    102.18 26.31947 -5.329071e-15 3.3801820 0.0232206231 4.7855876 2.9592568
#> 2    104.22 31.28887  1.776357e-15 1.4627695 0.0175897578 3.8328358 2.2591593
#> 3    121.31 30.10174  8.881784e-16 2.2937918 0.0342010876 4.0446758 3.3872806
#> 4    141.28 39.75624  3.552714e-15 4.4672401 0.0529036285 5.1867706 4.3846248
#> 5    157.26 36.95181 -2.664535e-15 3.2923168 0.0965635719 7.6459224 5.4846596
#> 6     163.9 21.41747 -5.329071e-15 4.4269636 0.0236900961 4.4977055 2.6263670
#> 7    221.19 22.98480 -2.220446e-15 1.8014494 0.0127574566 2.1905344 2.0218098
#> 8    233.11 28.66655  2.553513e-15 1.0582263 0.0211138628 3.1794345 2.1624442
#> 9     235.6 38.63477  3.552714e-15 3.7647078 0.0723274691 8.4913020 4.8273551
#> 10    241.2 26.34039 -1.998401e-15 1.6774241 0.0153823821 2.0338659 2.0056410
#> 11    255.7 30.58975 -1.776357e-15 3.3289736 0.0317506280 4.7013868 3.6075128
#> 12   314.12 28.17335  3.552714e-15 2.9170536 0.0170302467 3.1376678 2.4584089
#> 13    317.6 35.32583  2.664535e-15 2.1874274 0.0136347120 2.3345492 1.8698826
#> 14   319.20 38.75767  7.105427e-15 6.7164864 0.0855988994 8.6398087 5.9590451
#> 15   320.16 26.34808 -1.776357e-15 3.3208950 0.0180662044 3.8822326 2.7040109
#> 16   342.15 26.01336 -1.776357e-15 2.9219360 0.0225156118 3.6438425 2.9755899
#> 17    346.2 23.84175 -5.329071e-15 5.1827747 0.0459434537 5.3987165 3.9525017
#> 18   351.26 36.11581  2.220446e-15 2.9786832 0.0639652186 5.4005468 4.5622439
#> 19   364.21 34.05974  1.221245e-15 0.7236998 0.0018299284 1.4047546 0.7526264
#> 20    402.7 27.47748 -3.330669e-16 0.2801470 0.0001339385 0.3537818 0.2284995
#> 21    405.2 28.98663 -2.664535e-15 3.9832546 0.0229492190 4.1095727 2.7952381
#> 22   406.12 32.68323  3.552714e-15 2.5631734 0.0264692745 5.3218165 2.8834753
#> 23    427.7 36.19020  3.552714e-15 1.1467970 0.0135698145 2.4124676 2.0049278
#> 24    450.3 36.19602  1.776357e-15 3.1430174 0.0216161656 4.6608954 2.8200387
#> 25    506.2 33.26623 -7.632783e-16 0.7511331 0.0318266934 1.9330143 2.2178470
#> 26  Canchan 27.00126  3.996803e-15 3.0975884 0.0461305761 3.6665608 3.5328212
#> 27  Desiree 16.15569 -1.243450e-14 7.7833445 0.0901534938 9.0626072 5.8073242
#> 28    Unica 39.10400  8.881784e-15 3.8380782 0.0770659860 8.5447632 5.0654615
#> 
#> $`Simultaneous Selection Indices`
#>    genotype    means AMGE_SSI ASV_SSI EV_SSI MASV_SSI SIPC_SSI
#> 1    102.18 26.31947     26.0      43     37       42       39
#> 2    104.22 31.28887     29.5      19     21       25       22
#> 3    121.31 30.10174     29.0      25     34       29       33
#> 4    141.28 39.75624     24.0      26     23       21       23
#> 5    157.26 36.95181     10.5      22     33       29       31
#> 6     163.9 21.41747     30.0      51     42       43       38
#> 7    221.19 22.98480     33.0      34     29       31       32
#> 8    233.11 28.66655     36.0      21     27       26       24
#> 9     235.6 38.63477     27.0      25     28       29       28
#> 10    241.2 26.34039     30.0      29     28       26       27
#> 11    255.7 30.58975     24.0      33     31       32       34
#> 12   314.12 28.17335     41.0      30     25       26       28
#> 13    317.6 35.32583     29.0      18     14       15       12
#> 14   319.20 38.75767     30.0      30     29       30       31
#> 15   320.16 26.34808     31.0      39     30       34       33
#> 16   342.15 26.01336     34.0      37     36       34       41
#> 17    346.2 23.84175     28.0      51     45       47       46
#> 18   351.26 36.11581     26.0      22     31       31       31
#> 19   364.21 34.05974     25.0      12     12       12       12
#> 20    402.7 27.47748     32.0      20     20       20       20
#> 21    405.2 28.98663     21.5      39     29       31       29
#> 22   406.12 32.68323     35.0      23     28       33       27
#> 23    427.7 36.19020     30.0      12     11       14       11
#> 24    450.3 36.19602     22.5      22     17       23       20
#> 25    506.2 33.26623     23.0      14     29       14       19
#> 26  Canchan 27.00126     46.0      35     41       31       39
#> 27  Desiree 16.15569     29.0      56     55       56       55
#> 28    Unica 39.10400     30.0      24     27       28       27
#> 
#> $`SP Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV   -0.28 1.00**   <NA>   <NA>   <NA>
#> EV     0.03 0.70** 1.00**   <NA>   <NA>
#> MASV   0.01 0.81** 0.90** 1.00**   <NA>
#> SIPC   0.01 0.81** 0.96** 0.94** 1.00**
#> 
#> $`SSI Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV    0.14 1.00**   <NA>   <NA>   <NA>
#> EV     0.11 0.84** 1.00**   <NA>   <NA>
#> MASV   0.09 0.92** 0.90** 1.00**   <NA>
#> SIPC   0.14 0.89** 0.96** 0.95** 1.00**
#> 
#> $`SP and SSI Correlation`
#>             AMGE    ASV     EV   MASV   SIPC AMGE_SSI ASV_SSI EV_SSI MASV_SSI
#> AMGE      1.00**   <NA>   <NA>   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> ASV        -0.28 1.00**   <NA>   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> EV          0.03 0.70** 1.00**   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> MASV        0.01 0.81** 0.90** 1.00**   <NA>     <NA>    <NA>   <NA>     <NA>
#> SIPC        0.01 0.81** 0.96** 0.94** 1.00**     <NA>    <NA>   <NA>     <NA>
#> AMGE_SSI    0.26  -0.10  -0.30  -0.26  -0.25   1.00**    <NA>   <NA>     <NA>
#> ASV_SSI  -0.68** 0.71**   0.21   0.35   0.34     0.14  1.00**   <NA>     <NA>
#> EV_SSI   -0.62** 0.64** 0.48**  0.47* 0.53**     0.11  0.84** 1.00**     <NA>
#> MASV_SSI -0.63** 0.73**  0.40* 0.54** 0.51**     0.09  0.92** 0.90**   1.00**
#> SIPC_SSI -0.60** 0.70**  0.45* 0.50** 0.54**     0.14  0.89** 0.96**   0.95**
#>          SIPC_SSI
#> AMGE         <NA>
#> ASV          <NA>
#> EV           <NA>
#> MASV         <NA>
#> SIPC         <NA>
#> AMGE_SSI     <NA>
#> ASV_SSI      <NA>
#> EV_SSI       <NA>
#> MASV_SSI     <NA>
#> SIPC_SSI   1.00**
#> 
#> $`SP Correlogram`

#> 
#> $`SSI Correlogram`

#> 
#> $`SP and SSI Correlogram`

#> 
#> $`SP Slopegraph`

#> 
#> $`SSI Slopegraph`

#> 
#> $`SP Heatmap`

#> 
#> $`SSI Heatmap`

#>