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)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 SIPC values.
The computed values of simultaneous selection index for yield and stability.
The ranks of SIPC 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 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.
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$ANOVA
#> Analysis of Variance Table
#>
#> Response: Y
#> Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 5 122284 24456.9 257.0382 9.08e-12 ***
#> REP(ENV) 12 1142 95.1 2.5694 0.002889 **
#> GEN 27 17533 649.4 17.5359 < 2.2e-16 ***
#> ENV:GEN 135 23762 176.0 4.7531 < 2.2e-16 ***
#> Residuals 324 11998 37.0
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# IPC F test
model$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)
SIPC.AMMI(model)
#> SIPC SSI rSIPC rY means
#> 102.18 2.9592568 39 16 23 26.31947
#> 104.22 2.2591593 22 9 13 31.28887
#> 121.31 3.3872806 33 18 15 30.10174
#> 141.28 4.3846248 23 22 1 39.75624
#> 157.26 5.4846596 31 26 5 36.95181
#> 163.9 2.6263670 38 11 27 21.41747
#> 221.19 2.0218098 32 6 26 22.98480
#> 233.11 2.1624442 24 7 17 28.66655
#> 235.6 4.8273551 28 24 4 38.63477
#> 241.2 2.0056410 27 5 22 26.34039
#> 255.7 3.6075128 34 20 14 30.58975
#> 314.12 2.4584089 28 10 18 28.17335
#> 317.6 1.8698826 12 3 9 35.32583
#> 319.20 5.9590451 31 28 3 38.75767
#> 320.16 2.7040109 33 12 21 26.34808
#> 342.15 2.9755899 41 17 24 26.01336
#> 346.2 3.9525017 46 21 25 23.84175
#> 351.26 4.5622439 31 23 8 36.11581
#> 364.21 0.7526264 12 2 10 34.05974
#> 402.7 0.2284995 20 1 19 27.47748
#> 405.2 2.7952381 29 13 16 28.98663
#> 406.12 2.8834753 27 15 12 32.68323
#> 427.7 2.0049278 11 4 7 36.19020
#> 450.3 2.8200387 20 14 6 36.19602
#> 506.2 2.2178470 19 8 11 33.26623
#> Canchan 3.5328212 39 19 20 27.00126
#> Desiree 5.8073242 55 27 28 16.15569
#> Unica 5.0654615 27 25 2 39.10400
# With n = 4 and default ssi.method (farshadfar)
SIPC.AMMI(model, n = 4)
#> SIPC SSI rSIPC rY means
#> 102.18 3.4466455 38 15 23 26.31947
#> 104.22 2.7007589 23 10 13 31.28887
#> 121.31 5.6097497 38 23 15 30.10174
#> 141.28 4.6372010 22 21 1 39.75624
#> 157.26 7.4500476 33 28 5 36.95181
#> 163.9 3.1338033 38 11 27 21.41747
#> 221.19 2.1363292 29 3 26 22.98480
#> 233.11 2.3911278 23 6 17 28.66655
#> 235.6 5.8474857 29 25 4 38.63477
#> 241.2 2.3056852 27 5 22 26.34039
#> 255.7 3.9276052 31 17 14 30.58975
#> 314.12 2.5182824 26 8 18 28.17335
#> 317.6 2.4516869 16 7 9 35.32583
#> 319.20 7.0781345 30 27 3 38.75767
#> 320.16 4.0249810 39 18 21 26.34808
#> 342.15 4.0957211 43 19 24 26.01336
#> 346.2 4.8622465 47 22 25 23.84175
#> 351.26 4.5974075 28 20 8 36.11581
#> 364.21 1.5318314 12 2 10 34.05974
#> 402.7 0.5893581 20 1 19 27.47748
#> 405.2 3.3068718 29 13 16 28.98663
#> 406.12 3.2694367 24 12 12 32.68323
#> 427.7 2.5358269 16 9 7 36.19020
#> 450.3 3.4327401 20 14 6 36.19602
#> 506.2 2.2644412 15 4 11 33.26623
#> Canchan 3.6100050 36 16 20 27.00126
#> Desiree 5.8538044 54 26 28 16.15569
#> Unica 5.7091275 26 24 2 39.10400
# With default n (N') and ssi.method = "rao"
SIPC.AMMI(model, ssi.method = "rao")
#> SIPC SSI rSIPC rY means
#> 102.18 2.9592568 1.5124653 16 23 26.31947
#> 104.22 2.2591593 1.8772594 9 13 31.28887
#> 121.31 3.3872806 1.5531093 18 15 30.10174
#> 141.28 4.3846248 1.7378762 22 1 39.75624
#> 157.26 5.4846596 1.5578664 26 5 36.95181
#> 163.9 2.6263670 1.4355650 11 27 21.41747
#> 221.19 2.0218098 1.7071153 6 26 22.98480
#> 233.11 2.1624442 1.8300896 7 17 28.66655
#> 235.6 4.8273551 1.6608098 24 4 38.63477
#> 241.2 2.0056410 1.8242469 5 22 26.34039
#> 255.7 3.6075128 1.5341245 20 14 30.58975
#> 314.12 2.4584089 1.7062126 10 18 28.17335
#> 317.6 1.8698826 2.1873134 3 9 35.32583
#> 319.20 5.9590451 1.5886436 28 3 38.75767
#> 320.16 2.7040109 1.5751613 12 21 26.34808
#> 342.15 2.9755899 1.4988930 17 24 26.01336
#> 346.2 3.9525017 1.2672546 21 25 23.84175
#> 351.26 4.5622439 1.6019853 23 8 36.11581
#> 364.21 0.7526264 3.6831976 2 10 34.05974
#> 402.7 0.2284995 9.3696848 1 19 27.47748
#> 405.2 2.7952381 1.6378227 13 16 28.98663
#> 406.12 2.8834753 1.7371554 15 12 32.68323
#> 427.7 2.0049278 2.1457493 4 7 36.19020
#> 450.3 2.8200387 1.8667975 14 6 36.19602
#> 506.2 2.2178470 1.9576974 8 11 33.26623
#> Canchan 3.5328212 1.4284673 19 20 27.00126
#> Desiree 5.8073242 0.8601813 27 28 16.15569
#> Unica 5.0654615 1.6572552 25 2 39.10400
# Changing the ratio of weights for Rao's SSI
SIPC.AMMI(model, ssi.method = "rao", a = 0.43)
#> SIPC SSI rSIPC rY means
#> 102.18 2.9592568 1.1395125 16 23 26.31947
#> 104.22 2.2591593 1.3887312 9 13 31.28887
#> 121.31 3.3872806 1.2272836 18 15 30.10174
#> 141.28 4.3846248 1.4861641 22 1 39.75624
#> 157.26 5.4846596 1.3566391 26 5 36.95181
#> 163.9 2.6263670 1.0153407 11 27 21.41747
#> 221.19 2.0218098 1.1612364 6 26 22.98480
#> 233.11 2.1624442 1.3197119 7 17 28.66655
#> 235.6 4.8273551 1.4321829 24 4 38.63477
#> 241.2 2.0056410 1.2739673 5 22 26.34039
#> 255.7 3.6075128 1.2281898 20 14 30.58975
#> 314.12 2.4584089 1.2572786 10 18 28.17335
#> 317.6 1.8698826 1.5970821 3 9 35.32583
#> 319.20 5.9590451 1.4034355 28 3 38.75767
#> 320.16 2.7040109 1.1670035 12 21 26.34808
#> 342.15 2.9755899 1.1279873 17 24 26.01336
#> 346.2 3.9525017 0.9880230 21 25 23.84175
#> 351.26 4.5622439 1.3600729 23 8 36.11581
#> 364.21 0.7526264 2.2167818 2 10 34.05974
#> 402.7 0.2284995 4.5396387 1 19 27.47748
#> 405.2 2.7952381 1.2429858 13 16 28.98663
#> 406.12 2.8834753 1.3544008 15 12 32.68323
#> 427.7 2.0049278 1.5952740 4 7 36.19020
#> 450.3 2.8200387 1.4754330 14 6 36.19602
#> 506.2 2.2178470 1.4600692 8 11 33.26623
#> Canchan 3.5328212 1.1160645 19 20 27.00126
#> Desiree 5.8073242 0.6701345 27 28 16.15569
#> Unica 5.0654615 1.4393751 25 2 39.10400