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)The AMMI model (An object of class AMMI generated by
AMMI).
The number of principal components to be considered for computation. The default value is the number of significant IPCs.
Type I error probability (Significance level) to be considered to identify the number of significant IPCs.
The method for the computation of simultaneous selection
index. Either "farshadfar" or "rao" (See
SSI).
The ratio of the weights given to the stability components for
computation of SSI when method = "rao" (See
SSI).
A data frame with the following columns:
The MASI values.
The computed values of simultaneous selection index for yield and stability.
The ranks of MASI values.
The ranks of the mean yield of genotypes.
The mean yield of the genotypes.
The names of the genotypes are indicated as the row names of the data frame.
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.
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$ANOVA
#> Analysis of Variance Table
#>
#> Response: Y
#> Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 5 122284 24456.9 257.0382 9.08e-12 ***
#> REP(ENV) 12 1142 95.1 2.5694 0.002889 **
#> GEN 27 17533 649.4 17.5359 < 2.2e-16 ***
#> ENV:GEN 135 23762 176.0 4.7531 < 2.2e-16 ***
#> Residuals 324 11998 37.0
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# IPC F test
model$analysis
#> percent acum Df Sum.Sq Mean.Sq F.value Pr.F
#> PC1 56.3 56.3 31 13368.5954 431.24501 11.65 0.0000
#> PC2 27.1 83.3 29 6427.5799 221.64069 5.99 0.0000
#> PC3 9.4 92.7 27 2241.9398 83.03481 2.24 0.0005
#> PC4 4.3 97.1 25 1027.5785 41.10314 1.11 0.3286
#> PC5 2.9 100.0 23 696.1012 30.26527 0.82 0.7059
# Mean yield and IPC scores
model$biplot
#> type Yield PC1 PC2 PC3 PC4
#> 102.18 GEN 26.31947 -1.50828851 1.258765244 -0.19220309 0.48738861
#> 104.22 GEN 31.28887 0.32517729 -1.297024517 -0.63695749 -0.44159957
#> 121.31 GEN 30.10174 0.95604605 1.143461054 -1.28777348 2.22246913
#> 141.28 GEN 39.75624 2.11153737 0.817810467 1.45527701 0.25257620
#> 157.26 GEN 36.95181 1.05139017 2.461179974 -1.97208942 -1.96538800
#> 163.9 GEN 21.41747 -2.12407441 -0.284381234 -0.21791137 -0.50743629
#> 221.19 GEN 22.98480 -0.84981828 0.347983673 -0.82400783 -0.11451944
#> 233.11 GEN 28.66655 0.07554203 -1.046497338 1.04040485 0.22868362
#> 235.6 GEN 38.63477 1.20102029 -2.816581184 0.80975361 1.02013062
#> 241.2 GEN 26.34039 -0.79948495 0.220768053 -0.98538801 0.30004421
#> 255.7 GEN 30.58975 -1.49543817 -1.186549449 0.92552519 -0.32009239
#> 314.12 GEN 28.17335 1.39335380 -0.332786322 -0.73226877 0.05987348
#> 317.6 GEN 35.32583 1.05170769 0.002555823 -0.81561907 0.58180433
#> 319.20 GEN 38.75767 3.08338144 1.995946966 0.87971668 -1.11908943
#> 320.16 GEN 26.34808 -1.55737097 0.732314249 -0.41432567 1.32097009
#> 342.15 GEN 26.01336 -1.35880873 -0.741980068 0.87480105 -1.12013125
#> 346.2 GEN 23.84175 -2.48453928 -0.397045286 1.07091711 -0.90974484
#> 351.26 GEN 36.11581 1.22670345 1.537183139 1.79835728 -0.03516368
#> 364.21 GEN 34.05974 0.27328985 -0.447941156 0.03139543 0.77920500
#> 402.7 GEN 27.47748 -0.12907269 -0.080086669 0.01934016 -0.36085862
#> 405.2 GEN 28.98663 -1.90936369 0.309047963 0.57682642 0.51163370
#> 406.12 GEN 32.68323 0.90781100 -1.733433781 -0.24223050 -0.38596144
#> 427.7 GEN 36.19020 0.42791957 -0.723190970 -0.85381724 -0.53089914
#> 450.3 GEN 36.19602 1.38026196 1.279525147 0.16025163 0.61270137
#> 506.2 GEN 33.26623 -0.33054261 -0.302588536 -1.58471588 -0.04659416
#> Canchan GEN 27.00126 1.47802905 0.380553178 1.67423900 0.07718375
#> Desiree GEN 16.15569 -3.64968796 1.720025405 0.43761089 0.04648011
#> Unica GEN 39.10400 1.25331924 -2.817033826 -0.99510845 -0.64366599
#> Ayac ENV 23.70254 -2.29611851 0.966037760 1.95959116 2.75548057
#> Hyo-02 ENV 45.73082 3.85283195 -5.093371615 1.16967118 -0.08985538
#> LM-02 ENV 34.64462 -1.14575146 -0.881093222 -4.56547274 0.55159099
#> LM-03 ENV 53.83493 5.34625518 4.265275487 -0.14143931 -0.11714533
#> SR-02 ENV 14.95128 -2.58678337 0.660309540 0.89096920 -3.25055305
#> SR-03 ENV 11.15328 -3.17043379 0.082842050 0.68668051 0.15048221
#> PC5
#> 102.18 -0.04364115
#> 104.22 0.95312506
#> 121.31 -1.30661916
#> 141.28 -0.25996142
#> 157.26 -0.59719268
#> 163.9 0.18563390
#> 221.19 -0.57504816
#> 233.11 0.65754266
#> 235.6 -0.40273415
#> 241.2 0.07555258
#> 255.7 -0.46344763
#> 314.12 0.54406154
#> 317.6 0.39627052
#> 319.20 0.29657050
#> 320.16 2.29506737
#> 342.15 -0.10776433
#> 346.2 -0.12738693
#> 351.26 0.30191335
#> 364.21 -0.95811256
#> 402.7 -0.28473777
#> 405.2 -0.34397623
#> 406.12 -0.49796296
#> 427.7 1.00677993
#> 450.3 -0.34325251
#> 506.2 0.87807441
#> Canchan 0.49381313
#> Desiree -0.86767477
#> Unica -0.90489253
#> Ayac 1.67177210
#> Hyo-02 0.01540152
#> LM-02 0.52350416
#> LM-03 -0.40285728
#> SR-02 1.37283488
#> SR-03 -3.18065538
# G*E matrix (deviations from mean)
array(model$genXenv, dim(model$genXenv), dimnames(model$genXenv))
#> ENV
#> GEN Ayac Hyo-02 LM-02 LM-03 SR-02
#> 102.18 5.5726162 -12.4918224 1.7425251 -2.7070438 2.91734869
#> 104.22 -2.8712076 7.1684102 3.9336218 -4.0358373 0.47881580
#> 121.31 0.3255230 -3.8666836 4.3182811 10.4366135 -11.88343843
#> 141.28 -0.9451837 5.6454825 -9.7806639 14.6463104 -4.80337115
#> 157.26 -10.3149711 -10.6241677 4.2336365 16.8683612 2.71710210
#> 163.9 3.0874931 -6.9416721 3.4963790 -12.5533271 7.01688164
#> 221.19 -0.6041752 -6.0090018 4.0648518 -2.6974743 1.27671246
#> 233.11 2.5837535 6.8277609 -3.4440645 -4.4985717 0.19989490
#> 235.6 -1.7541523 19.8225025 -2.2394463 -5.6643239 -8.11400542
#> 241.2 1.0710975 -5.3831118 5.4253097 -3.2588271 0.46433086
#> 255.7 2.4443155 1.3860497 -1.8857757 -12.9626594 4.31373929
#> 314.12 -3.8812099 6.2098482 2.3577759 5.9071782 -3.92419060
#> 317.6 -1.7450319 3.0388540 3.0448064 5.5211634 -4.79271565
#> 319.20 -6.0155949 2.8477540 -9.7697504 24.8850017 -1.82949467
#> 320.16 10.9481796 -10.2982108 4.9608280 -6.2233088 2.99984918
#> 342.15 0.8508002 -0.3338618 -2.4575390 -10.3783871 7.29753151
#> 346.2 4.7000495 -6.2178087 -2.2612391 -14.9700672 9.90123888
#> 351.26 2.6002030 -0.9918665 -10.8315931 12.7429121 -0.02713985
#> 364.21 -0.4533734 3.2864208 -0.1335527 -0.1592533 -4.82292664
#> 402.7 -1.2134573 -0.0387229 -0.2179557 -0.8774011 1.08032472
#> 405.2 6.6477681 -8.3071271 -0.6159895 -8.8927189 3.52179705
#> 406.12 -6.1296667 12.0703469 1.1195092 -2.2601009 -3.13776595
#> 427.7 -3.1340922 4.3967072 4.2792028 -1.0194744 0.76266844
#> 450.3 -0.5047010 -1.0720791 -3.2821761 12.8806007 -5.04562407
#> 506.2 -1.2991912 -1.5682154 8.3142802 -3.1819279 0.60021498
#> Canchan 1.2929442 5.7152780 -9.3713622 9.0803035 -1.65332869
#> Desiree 9.5767845 -22.3280421 0.2396387 -11.8935722 9.62433886
#> Unica -10.8355195 18.0569790 4.7604622 -4.7341684 -5.13878822
#> ENV
#> GEN SR-03
#> 102.18 4.9663762
#> 104.22 -4.6738028
#> 121.31 0.6697043
#> 141.28 -4.7625741
#> 157.26 -2.8799609
#> 163.9 5.8942454
#> 221.19 3.9690870
#> 233.11 -1.6687730
#> 235.6 -2.0505746
#> 241.2 1.6812008
#> 255.7 6.7043306
#> 314.12 -6.6694018
#> 317.6 -5.0670763
#> 319.20 -10.1179157
#> 320.16 -2.3873373
#> 342.15 5.0214562
#> 346.2 8.8478267
#> 351.26 -3.4925156
#> 364.21 2.2826853
#> 402.7 1.2672123
#> 405.2 7.6462704
#> 406.12 -1.6623226
#> 427.7 -5.2850119
#> 450.3 -2.9760204
#> 506.2 -2.8651608
#> Canchan -5.0638348
#> Desiree 14.7808522
#> Unica -2.1089651
# With default n (N') and default ssi.method (farshadfar)
MASI.AMMI(model)
#> MASI SSI rMASI rY means
#> 102.18 0.91530136 43 20 23 26.31947
#> 104.22 0.40081051 19 6 13 31.28887
#> 121.31 0.63276765 25 10 15 30.10174
#> 141.28 1.21699070 26 25 1 39.75624
#> 157.26 0.91082968 24 19 5 36.95181
#> 163.9 1.19850969 51 24 27 21.41747
#> 221.19 0.49376604 34 8 26 22.98480
#> 233.11 0.30298956 21 4 17 28.66655
#> 235.6 1.02255689 25 21 4 38.63477
#> 241.2 0.46342001 29 7 22 26.34039
#> 255.7 0.90543659 32 18 14 30.58975
#> 314.12 0.79261972 30 12 18 28.17335
#> 317.6 0.59705480 18 9 9 35.32583
#> 319.20 1.82014106 30 27 3 38.75767
#> 320.16 0.89982225 38 17 21 26.34808
#> 342.15 0.79525659 37 13 24 26.01336
#> 346.2 1.40653491 51 26 25 23.84175
#> 351.26 0.82406788 22 14 8 36.11581
#> 364.21 0.19600590 12 2 10 34.05974
#> 402.7 0.07586154 20 1 19 27.47748
#> 405.2 1.07959190 39 23 16 28.98663
#> 406.12 0.69456043 23 11 12 32.68323
#> 427.7 0.32076990 12 5 7 36.19020
#> 450.3 0.85107482 21 15 6 36.19602
#> 506.2 0.25208300 14 3 11 33.26623
#> Canchan 0.85313814 36 16 20 27.00126
#> Desiree 2.10738319 56 28 28 16.15569
#> Unica 1.04376808 24 22 2 39.10400
# With n = 4 and default ssi.method (farshadfar)
MASI.AMMI(model, n = 4)
#> MASI SSI rMASI rY means
#> 102.18 0.91554126 43 20 23 26.31947
#> 104.22 0.40126006 19 6 13 31.28887
#> 121.31 0.63994359 25 10 15 30.10174
#> 141.28 1.21703916 26 25 1 39.75624
#> 157.26 0.91474200 24 19 5 36.95181
#> 163.9 1.19870830 51 24 27 21.41747
#> 221.19 0.49379060 34 8 26 22.98480
#> 233.11 0.30314909 21 4 17 28.66655
#> 235.6 1.02349733 25 21 4 38.63477
#> 241.2 0.46359958 29 7 22 26.34039
#> 255.7 0.90554120 32 18 14 30.58975
#> 314.12 0.79262390 30 12 18 28.17335
#> 317.6 0.59757871 18 9 9 35.32583
#> 319.20 1.82077706 30 27 3 38.75767
#> 320.16 0.90161328 38 17 21 26.34808
#> 342.15 0.79671385 37 13 24 26.01336
#> 346.2 1.40707881 51 26 25 23.84175
#> 351.26 0.82406927 22 14 8 36.11581
#> 364.21 0.19884907 12 2 10 34.05974
#> 402.7 0.07743222 20 1 19 27.47748
#> 405.2 1.07981604 39 23 16 28.98663
#> 406.12 0.69475868 23 11 12 32.68323
#> 427.7 0.32158122 12 5 7 36.19020
#> 450.3 0.85148251 21 15 6 36.19602
#> 506.2 0.25209096 14 3 11 33.26623
#> Canchan 0.85314460 36 16 20 27.00126
#> Desiree 2.10738414 56 28 28 16.15569
#> Unica 1.04413498 24 22 2 39.10400
# With default n (N') and ssi.method = "rao"
MASI.AMMI(model, ssi.method = "rao")
#> MASI SSI rMASI rY means
#> 102.18 0.91530136 1.3969172 20 23 26.31947
#> 104.22 0.40081051 2.2505076 6 13 31.28887
#> 121.31 0.63276765 1.7607970 10 15 30.10174
#> 141.28 1.21699070 1.7014749 25 1 39.75624
#> 157.26 0.91082968 1.7462362 19 5 36.95181
#> 163.9 1.19850969 1.1097764 24 27 21.41747
#> 221.19 0.49376604 1.7481314 8 26 22.98480
#> 233.11 0.30298956 2.5622159 4 17 28.66655
#> 235.6 1.02255689 1.7419553 21 4 38.63477
#> 241.2 0.46342001 1.9229400 7 22 26.34039
#> 255.7 0.90543659 1.5420219 18 14 30.58975
#> 314.12 0.79261972 1.5407527 12 18 28.17335
#> 317.6 0.59705480 1.9777463 9 9 35.32583
#> 319.20 1.82014106 1.5346430 27 3 38.75767
#> 320.16 0.89982225 1.4071180 17 21 26.34808
#> 342.15 0.79525659 1.4682620 13 24 26.01336
#> 346.2 1.40653491 1.1279691 26 25 23.84175
#> 351.26 0.82406788 1.7759790 14 8 36.11581
#> 364.21 0.19600590 3.6263979 2 10 34.05974
#> 402.7 0.07586154 7.3962265 1 19 27.47748
#> 405.2 1.07959190 1.4018946 23 16 28.98663
#> 406.12 0.69456043 1.7756352 11 12 32.68323
#> 427.7 0.32076990 2.7173148 5 7 36.19020
#> 450.3 0.85107482 1.7596054 15 6 36.19602
#> 506.2 0.25208300 3.0408597 3 11 33.26623
#> Canchan 0.85313814 1.4584033 16 20 27.00126
#> Desiree 2.10738319 0.7607639 28 28 16.15569
#> Unica 1.04376808 1.7474547 22 2 39.10400
# Changing the ratio of weights for Rao's SSI
MASI.AMMI(model, ssi.method = "rao", a = 0.43)
#> MASI SSI rMASI rY means
#> 102.18 0.91530136 1.0898268 20 23 26.31947
#> 104.22 0.40081051 1.5492279 6 13 31.28887
#> 121.31 0.63276765 1.3165893 10 15 30.10174
#> 141.28 1.21699070 1.4705116 25 1 39.75624
#> 157.26 0.91082968 1.4376382 19 5 36.95181
#> 163.9 1.19850969 0.8752516 24 27 21.41747
#> 221.19 0.49376604 1.1788734 8 26 22.98480
#> 233.11 0.30298956 1.6345262 4 17 28.66655
#> 235.6 1.02255689 1.4670755 21 4 38.63477
#> 241.2 0.46342001 1.3164054 7 22 26.34039
#> 255.7 0.90543659 1.2315857 18 14 30.58975
#> 314.12 0.79261972 1.1861309 12 18 28.17335
#> 317.6 0.59705480 1.5069682 9 9 35.32583
#> 319.20 1.82014106 1.3802152 27 3 38.75767
#> 320.16 0.89982225 1.0947449 17 21 26.34808
#> 342.15 0.79525659 1.1148160 13 24 26.01336
#> 346.2 1.40653491 0.9281302 26 25 23.84175
#> 351.26 0.82406788 1.4348902 14 8 36.11581
#> 364.21 0.19600590 2.1923580 2 10 34.05974
#> 402.7 0.07586154 3.6910517 1 19 27.47748
#> 405.2 1.07959190 1.1415367 23 16 28.98663
#> 406.12 0.69456043 1.3709472 11 12 32.68323
#> 427.7 0.32076990 1.8410472 5 7 36.19020
#> 450.3 0.85107482 1.4293404 15 6 36.19602
#> 506.2 0.25208300 1.9258290 3 11 33.26623
#> Canchan 0.85313814 1.1289370 16 20 27.00126
#> Desiree 2.10738319 0.6273850 28 28 16.15569
#> Unica 1.04376808 1.4781609 22 2 39.10400
# ASI.AMMI same as MASI.AMMI with n = 2
a <- ASI.AMMI(model)
b <- MASI.AMMI(model, n = 2)
identical(a$ASI, b$MASI)
#> [1] TRUE