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)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 ASTAB values.
The computed values of simultaneous selection index for yield and stability.
The ranks of ASTAB 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 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.
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$ANOVA
#> Analysis of Variance Table
#>
#> Response: Y
#> Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 5 122284 24456.9 257.0382 9.08e-12 ***
#> REP(ENV) 12 1142 95.1 2.5694 0.002889 **
#> GEN 27 17533 649.4 17.5359 < 2.2e-16 ***
#> ENV:GEN 135 23762 176.0 4.7531 < 2.2e-16 ***
#> Residuals 324 11998 37.0
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# IPC F test
model$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)
ASTAB.AMMI(model)
#> ASTAB SSI rASTAB rY means
#> 102.18 3.89636621 39 16 23 26.31947
#> 104.22 2.19372771 21 8 13 31.28887
#> 121.31 3.87988776 29 14 15 30.10174
#> 141.28 7.24523520 23 22 1 39.75624
#> 157.26 11.05196482 31 26 5 36.95181
#> 163.9 4.64005014 46 19 27 21.41747
#> 221.19 1.52227265 30 4 26 22.98480
#> 233.11 2.18330553 24 7 17 28.66655
#> 235.6 10.03128021 28 24 4 38.63477
#> 241.2 1.65890425 27 5 22 26.34039
#> 255.7 4.50083178 32 18 14 30.58975
#> 314.12 2.58839912 27 9 18 28.17335
#> 317.6 1.77133006 15 6 9 35.32583
#> 319.20 14.26494686 30 27 3 38.75767
#> 320.16 3.13335427 32 11 21 26.34808
#> 342.15 3.16217247 36 12 24 26.01336
#> 346.2 7.47744386 48 23 25 23.84175
#> 351.26 7.10182225 29 21 8 36.11581
#> 364.21 0.27632429 12 2 10 34.05974
#> 402.7 0.02344768 20 1 19 27.47748
#> 405.2 4.07390905 33 17 16 28.98663
#> 406.12 3.88758910 27 15 12 32.68323
#> 427.7 1.43512423 10 3 7 36.19020
#> 450.3 3.56798827 19 13 6 36.19602
#> 506.2 2.71214267 21 10 11 33.26623
#> Canchan 5.13246683 40 20 20 27.00126
#> Desiree 16.47021287 56 28 28 16.15569
#> Unica 10.49672952 27 25 2 39.10400
# With n = 4 and default ssi.method (farshadfar)
ASTAB.AMMI(model, n = 4)
#> ASTAB SSI rASTAB rY means
#> 102.18 4.1339139 36 13 23 26.31947
#> 104.22 2.3887379 21 8 13 31.28887
#> 121.31 8.8192568 38 23 15 30.10174
#> 141.28 7.3090299 22 21 1 39.75624
#> 157.26 14.9147148 31 26 5 36.95181
#> 163.9 4.8975417 45 18 27 21.41747
#> 221.19 1.5353874 29 3 26 22.98480
#> 233.11 2.2356017 24 7 17 28.66655
#> 235.6 11.0719467 29 25 4 38.63477
#> 241.2 1.7489308 27 5 22 26.34039
#> 255.7 4.6032909 30 16 14 30.58975
#> 314.12 2.5919840 27 9 18 28.17335
#> 317.6 2.1098263 15 6 9 35.32583
#> 319.20 15.5173080 30 27 3 38.75767
#> 320.16 4.8783163 38 17 21 26.34808
#> 342.15 4.4168665 39 15 24 26.01336
#> 346.2 8.3050795 47 22 25 23.84175
#> 351.26 7.1030587 28 20 8 36.11581
#> 364.21 0.8834847 12 2 10 34.05974
#> 402.7 0.1536666 20 1 19 27.47748
#> 405.2 4.3356781 30 14 16 28.98663
#> 406.12 4.0365553 24 12 12 32.68323
#> 427.7 1.7169781 11 4 7 36.19020
#> 450.3 3.9433912 17 11 6 36.19602
#> 506.2 2.7143137 21 10 11 33.26623
#> Canchan 5.1384242 39 19 20 27.00126
#> Desiree 16.4723733 56 28 28 16.15569
#> Unica 10.9110354 26 24 2 39.10400
# With default n (N') and ssi.method = "rao"
ASTAB.AMMI(model, ssi.method = "rao")
#> ASTAB SSI rASTAB rY means
#> 102.18 3.89636621 0.9916073 16 23 26.31947
#> 104.22 2.19372771 1.2572096 8 13 31.28887
#> 121.31 3.87988776 1.1154972 14 15 30.10174
#> 141.28 7.24523520 1.3680406 22 1 39.75624
#> 157.26 11.05196482 1.2518822 26 5 36.95181
#> 163.9 4.64005014 0.8103867 19 27 21.41747
#> 221.19 1.52227265 1.0909958 4 26 22.98480
#> 233.11 2.18330553 1.1728390 7 17 28.66655
#> 235.6 10.03128021 1.3115430 24 4 38.63477
#> 241.2 1.65890425 1.1722749 5 22 26.34039
#> 255.7 4.50083178 1.1129205 18 14 30.58975
#> 314.12 2.58839912 1.1194868 9 18 28.17335
#> 317.6 1.77133006 1.4453573 6 9 35.32583
#> 319.20 14.26494686 1.3001667 27 3 38.75767
#> 320.16 3.13335427 1.0250358 11 21 26.34808
#> 342.15 3.16217247 1.0126098 12 24 26.01336
#> 346.2 7.47744386 0.8469106 23 25 23.84175
#> 351.26 7.10182225 1.2507915 21 8 36.11581
#> 364.21 0.27632429 2.9922101 2 10 34.05974
#> 402.7 0.02344768 23.0708927 1 19 27.47748
#> 405.2 4.07390905 1.0727560 17 16 28.98663
#> 406.12 3.88758910 1.1994027 15 12 32.68323
#> 427.7 1.43512423 1.5423074 3 7 36.19020
#> 450.3 3.56798827 1.3259199 13 6 36.19602
#> 506.2 2.71214267 1.2763780 10 11 33.26623
#> Canchan 5.13246683 0.9816986 20 20 27.00126
#> Desiree 16.47021287 0.5583351 28 28 16.15569
#> Unica 10.49672952 1.3245441 25 2 39.10400
# Changing the ratio of weights for Rao's SSI
ASTAB.AMMI(model, ssi.method = "rao", a = 0.43)
#> ASTAB SSI rASTAB rY means
#> 102.18 3.89636621 0.9155436 16 23 26.31947
#> 104.22 2.19372771 1.1221097 8 13 31.28887
#> 121.31 3.87988776 1.0391104 14 15 30.10174
#> 141.28 7.24523520 1.3271348 22 1 39.75624
#> 157.26 11.05196482 1.2250659 26 5 36.95181
#> 163.9 4.64005014 0.7465140 19 27 21.41747
#> 221.19 1.52227265 0.8963051 4 26 22.98480
#> 233.11 2.18330553 1.0370941 7 17 28.66655
#> 235.6 10.03128021 1.2819982 24 4 38.63477
#> 241.2 1.65890425 0.9936194 5 22 26.34039
#> 255.7 4.50083178 1.0470721 18 14 30.58975
#> 314.12 2.58839912 1.0049865 9 18 28.17335
#> 317.6 1.77133006 1.2780410 6 9 35.32583
#> 319.20 14.26494686 1.2793904 27 3 38.75767
#> 320.16 3.13335427 0.9304495 11 21 26.34808
#> 342.15 3.16217247 0.9188855 12 24 26.01336
#> 346.2 7.47744386 0.8072751 23 25 23.84175
#> 351.26 7.10182225 1.2090596 21 8 36.11581
#> 364.21 0.27632429 1.9196572 2 10 34.05974
#> 402.7 0.02344768 10.4311581 1 19 27.47748
#> 405.2 4.07390905 1.0000071 17 16 28.98663
#> 406.12 3.88758910 1.1231672 15 12 32.68323
#> 427.7 1.43512423 1.3357940 3 7 36.19020
#> 450.3 3.56798827 1.2428556 13 6 36.19602
#> 506.2 2.71214267 1.1671018 10 11 33.26623
#> Canchan 5.13246683 0.9239540 20 20 27.00126
#> Desiree 16.47021287 0.5403407 28 28 16.15569
#> Unica 10.49672952 1.2963093 25 2 39.10400