Sample Output
Recall that the first step is AMMI analysis by MATMODEL to produce the
machine-readable file of AMMI parameters that comprises the input file for
AMMIWINS analysis. As in the article by Gauch and Zobel (1997),
the yield trial example used here is a Louisiana corn trial. These data
were analyzed in Kang (1993),
and M.S. Kang kindly supplied the original data and granted permission for
them to be reproduced in this documentation. This dataset has 16 genotypes
and 16 environments (that are combinations of 4 locations over 4 years)
with 4 replications (except that 32 of the 256 genotype-environment combinations
or treatments had only 3 replicates and 1 treatment had only 2 replicates,
so there are a total of 990 yield observations). This data file follows,
using a format suitable for MATMODEL, with a yield entry of 0 indicating
a missing datum.
Corn data, Kang 1993 (Agron. J. 85:754-757). LACA
Yield Mg/ha 0 16 GEN 16 ENV 4 REP RGE TRT RAN 0.0 F
(25X, 4F8.4)
AX85 1 M8172 1 6.1017 11.2690 8.0206 8.2840
AX85 1 PB3147 2 9.4818 10.7297 9.1807 8.9675
AX85 1 SB1860 3 11.6578 10.3346 10.4663 10.8363
AX85 1 PB3165 4 8.7669 10.7987 2.7592 9.4441
AX85 1 G4673A 5 8.8233 4.9666 10.3973 11.0495
AX85 1 COKER21 6 7.2869 13.4450 11.6014 8.3530
AX85 1 SB1827 7 8.6414 10.8237 5.7756 12.3539
AX85 1 M8150 8 5.8571 6.1456 7.2117 9.7138
AX85 1 G4765 9 8.5223 9.9521 9.3689 10.7548
AX85 1 G4733 10 9.4818 9.8643 9.5256 8.4784
AX85 1 PB3389 11 8.7794 8.2087 4.0511 10.9680
AX85 1 PB3320 12 10.9053 11.5261 8.4533 8.9424
AX85 1 SB1802 13 9.6134 11.6264 10.8300 8.5097
AX85 1 G4522 14 5.9449 10.4851 10.3973 8.2589
AX85 1 8951 15 5.8822 4.4022 5.7254 9.0553
AX85 1 8990 16 8.5035 6.3149 5.7442 9.0553
BR85 2 M8172 1 5.9575 8.0959 7.3998 8.0959
BR85 2 PB3147 2 6.1769 6.6974 4.8412 8.2526
BR85 2 SB1860 3 5.3178 7.3935 7.7321 7.8701
BR85 2 PB3165 4 3.4114 7.5377 6.7978 9.4629
BR85 2 G4673A 5 6.2459 8.9675 7.6757 4.9604
BR85 2 COKER21 6 8.0206 6.2835 5.5498 8.2903
BR85 2 SB1827 7 5.9386 8.5662 7.6067 6.1707
BR85 2 M8150 8 9.1368 8.5348 6.4278 9.2999
BR85 2 G4765 9 6.9295 6.1957 6.9608 7.9830
BR85 2 G4733 10 6.0013 6.1644 7.4876 8.1335
BR85 2 PB3389 11 4.7785 6.5469 8.8296 7.2367
BR85 2 PB3320 12 7.2869 8.7480 7.6130 7.9015
BR85 2 SB1802 13 7.6130 7.7384 8.5286 8.4408
BR85 2 G4522 14 7.6130 7.1427 8.2965 8.2087
BR85 2 8951 15 3.6246 6.5344 8.1084 7.4249
BR85 2 8990 16 2.1948 4.1451 5.3617 4.8224
BC85 3 M8172 1 6.9295 5.1673 6.8918 5.8258
BC85 3 PB3147 2 5.1610 6.1957 5.8508 6.9734
BC85 3 SB1860 3 4.2016 4.6280 7.0549 7.2305
BC85 3 PB3165 4 6.4591 5.9136 6.8918 6.9106
BC85 3 G4673A 5 3.3738 6.0515 6.9169 4.8914
BC85 3 COKER21 6 5.2112 6.9859 3.7940 5.3492
BC85 3 SB1827 7 4.4775 4.6531 7.0486 6.4090
BC85 3 M8150 8 3.8253 6.0202 6.0013 2.7467
BC85 3 G4765 9 3.7877 6.1769 6.4905 5.4370
BC85 3 G4733 10 3.1041 3.2797 5.7129 5.5185
BC85 3 PB3389 11 3.6435 5.2363 5.2865 3.5368
BC85 3 PB3320 12 5.5122 3.4491 4.9792 7.2117
BC85 3 SB1802 13 2.9348 4.5716 2.8972 6.5030
BC85 3 G4522 14 5.7380 4.1138 3.5996 4.0761
BC85 3 8951 15 3.2735 2.9599 4.8914 4.3521
BC85 3 8990 16 2.9097 2.8282 4.1138 5.3115
SJ85 4 M8172 1 9.0240 7.4374 8.2464 6.9608
SJ85 4 PB3147 2 8.1335 8.6101 7.0674 6.1393
SJ85 4 SB1860 3 8.1586 7.1866 7.0235 7.5189
SJ85 4 PB3165 4 7.4688 7.9830 8.3279 6.6786
SJ85 4 G4673A 5 6.6974 7.2305 8.0582 7.2618
SJ85 4 COKER21 6 8.6603 6.3212 8.2276 7.9140
SJ85 4 SB1827 7 6.9922 7.6882 10.3785 7.4562
SJ85 4 M8150 8 6.0452 8.1837 6.1895 4.8475
SJ85 4 G4765 9 7.6255 7.0423 7.6882 8.7480
SJ85 4 G4733 10 4.6468 7.2555 7.3308 4.5527
SJ85 4 PB3389 11 9.3751 7.1301 6.7978 .0000
SJ85 4 PB3320 12 4.3583 7.2618 4.3772 5.4495
SJ85 4 SB1802 13 6.5093 5.6376 8.0770 5.8320
SJ85 4 G4522 14 7.0486 5.5436 8.2338 2.7655
SJ85 4 8951 15 4.0573 6.1017 4.4211 5.4558
SJ85 4 8990 16 7.6067 5.3178 4.6907 4.0761
AX86 5 M8172 1 8.4408 10.0524 9.5006 10.2844
AX86 5 PB3147 2 9.1494 10.2844 8.2025 7.4123
AX86 5 SB1860 3 13.2694 9.7828 10.3660 7.8074
AX86 5 PB3165 4 6.1393 8.4847 10.6482 6.1581
AX86 5 G4673A 5 9.8204 9.1494 6.7037 9.5884
AX86 5 COKER21 6 6.2773 10.7798 7.9391 11.0809
AX86 5 SB1827 7 9.9458 9.2309 8.7480 9.7890
AX86 5 M8150 8 7.9203 8.4533 11.0934 9.7514
AX86 5 G4765 9 9.5507 8.4031 7.6443 7.7635
AX86 5 G4733 10 11.4947 11.0370 12.4166 7.4123
AX86 5 PB3389 11 8.6038 10.6921 9.8580 8.9048
AX86 5 PB3320 12 10.0085 9.9834 8.9675 7.4625
AX86 5 SB1802 13 7.9893 10.6105 11.3568 7.4688
AX86 5 G4522 14 11.0620 10.7610 8.3969 6.6096
AX86 5 8951 15 4.6531 9.7953 9.0365 11.8585
AX86 5 8990 16 4.6907 9.4567 9.8894 10.8551
BR86 6 M8172 1 7.5377 8.6665 12.7991 8.7731
BR86 6 PB3147 2 7.5127 8.1272 6.9295 9.2058
BR86 6 SB1860 3 8.5662 6.6974 6.8918 6.9922
BR86 6 PB3165 4 7.9767 6.5344 5.0356 6.5595
BR86 6 G4673A 5 7.4437 7.9077 7.6632 8.6603
BR86 6 COKER21 6 7.1866 6.8228 7.6506 5.8320
BR86 6 SB1827 7 9.3626 7.4437 8.0018 10.5165
BR86 6 M8150 8 9.4065 9.6511 6.9044 9.7702
BR86 6 G4765 9 6.8730 8.0394 7.0298 6.2020
BR86 6 G4733 10 9.0929 8.2526 7.0800 7.1678
BR86 6 PB3389 11 6.3525 6.5657 4.9102 7.0235
BR86 6 PB3320 12 7.8262 8.3592 8.1084 4.5716
BR86 6 SB1802 13 8.9424 5.7881 7.0110 7.1740
BR86 6 G4522 14 9.0240 7.9140 7.1364 6.5908
BR86 6 8951 15 7.2681 6.6347 6.7476 7.6067
BR86 6 8990 16 3.9507 4.2831 9.9772 7.1928
BC86 7 M8172 1 2.2952 3.7877 3.2797 5.1422
BC86 7 PB3147 2 4.9102 4.3583 7.3433 5.7380
BC86 7 SB1860 3 .5769 2.7091 7.0486 5.0043
BC86 7 PB3165 4 3.6246 .4139 4.4963 6.7727
BC86 7 G4673A 5 1.2166 1.8374 4.3144 6.4278
BC86 7 COKER21 6 1.9754 4.3583 6.6786 6.6096
BC86 7 SB1827 7 .3449 1.8562 3.7877 4.3395
BC86 7 M8150 8 1.2856 2.0882 1.1476 5.5059
BC86 7 G4765 9 .5769 1.3796 5.2802 4.8224
BC86 7 G4733 10 .5769 2.4081 2.1321 5.0482
BC86 7 PB3389 11 2.8031 2.1572 1.3796 5.6439
BC86 7 PB3320 12 1.7245 3.9946 3.9006 6.0829
BC86 7 SB1802 13 .5518 4.2455 1.1476 3.9006
BC86 7 G4522 14 .6396 1.8813 3.5557 3.8817
BC86 7 8951 15 1.3796 3.2797 3.6246 2.8909
BC86 7 8990 16 1.0786 1.5176 .6898 3.0289
SJ86 8 M8172 1 6.6284 7.1803 8.2464 8.6164
SJ86 8 PB3147 2 7.5315 7.3120 8.0770 7.6130
SJ86 8 SB1860 3 6.9734 6.3149 7.1364 7.1364
SJ86 8 PB3165 4 7.2179 7.7510 7.9893 8.3216
SJ86 8 G4673A 5 5.8320 7.0110 7.9830 11.5136
SJ86 8 COKER21 6 6.0452 6.5846 5.3993 7.7447
SJ86 8 SB1827 7 5.6439 6.4591 8.4282 9.7953
SJ86 8 M8150 8 6.4717 4.6907 7.1050 8.1523
SJ86 8 G4765 9 6.1268 8.8170 7.2367 7.7384
SJ86 8 G4733 10 6.9044 6.8918 7.8074 7.0235
SJ86 8 PB3389 11 6.7351 7.9579 6.4278 7.7510
SJ86 8 PB3320 12 7.6005 6.2835 7.4813 8.6979
SJ86 8 SB1802 13 5.1798 7.0925 7.2806 7.7321
SJ86 8 G4522 14 7.0674 6.3839 5.4871 6.5156
SJ86 8 8951 15 6.4968 7.2430 7.4311 7.7008
SJ86 8 8990 16 7.1615 6.4466 7.7447 7.6694
AX87 9 M8172 1 7.7259 6.3024 7.4750 6.2773
AX87 9 PB3147 2 6.6096 9.8392 10.5541 9.5382
AX87 9 SB1860 3 7.2744 8.1523 8.9048 8.7794
AX87 9 PB3165 4 10.5792 7.4938 9.9395 8.9487
AX87 9 G4673A 5 5.5185 9.1055 5.5937 6.9922
AX87 9 COKER21 6 8.0708 8.8484 7.7384 8.7731
AX87 9 SB1827 7 6.9420 3.6497 6.0139 4.2768
AX87 9 M8150 8 6.9232 9.2058 5.9763 5.4119
AX87 9 G4765 9 8.6853 7.6945 7.1364 9.4253
AX87 9 G4733 10 4.8788 6.0264 5.0732 8.3028
AX87 9 PB3389 11 8.0959 6.8918 8.3969 7.6443
AX87 9 PB3320 12 8.2401 4.9541 8.9236 8.6477
AX87 9 SB1802 13 6.1393 5.4119 7.2367 7.2367
AX87 9 G4522 14 5.6063 3.7689 8.5913 6.2835
AX87 9 8951 15 6.0390 4.6656 8.6289 7.8513
AX87 9 8990 16 8.4909 6.2773 5.7317 7.9454
BR87 10 M8172 1 11.7644 10.3973 11.8961 11.4195
BR87 10 PB3147 2 7.9767 9.4253 12.1532 .0000
BR87 10 SB1860 3 7.3183 9.2121 7.8325 .0000
BR87 10 PB3165 4 8.3906 9.7639 7.5064 .0000
BR87 10 G4673A 5 9.5758 9.4880 7.2994 .0000
BR87 10 COKER21 6 9.5445 9.1933 7.3935 .0000
BR87 10 SB1827 7 11.2125 11.1373 10.5165 11.2000
BR87 10 M8150 8 8.7041 7.4311 9.0741 6.0766
BR87 10 G4765 9 7.8889 7.7823 7.8513 .0000
BR87 10 G4733 10 8.6791 8.0394 6.9483 .0000
BR87 10 PB3389 11 7.7635 8.5474 8.7167 .0000
BR87 10 PB3320 12 9.7326 8.7480 6.9295 .0000
BR87 10 SB1802 13 9.6699 9.4880 9.5068 7.8889
BR87 10 G4522 14 8.8233 10.5102 8.7418 9.6260
BR87 10 8951 15 7.6945 8.0959 7.5754 .0000
BR87 10 8990 16 7.9955 6.7978 9.3501 .0000
BC87 11 M8172 1 7.6945 4.7848 7.1991 6.6786
BC87 11 PB3147 2 7.8388 7.8576 5.9073 5.4056
BC87 11 SB1860 3 7.6694 7.6318 6.4968 6.3400
BC87 11 PB3165 4 6.2271 3.3926 5.9198 5.3805
BC87 11 G4673A 5 5.7944 3.5996 7.0423 5.7944
BC87 11 COKER21 6 4.8475 7.4499 3.6246 5.6753
BC87 11 SB1827 7 6.2773 4.4461 7.4876 4.3019
BC87 11 M8150 8 6.7601 5.6063 4.8036 5.7630
BC87 11 G4765 9 3.5368 5.0858 5.0356 5.4119
BC87 11 G4733 10 5.0419 4.1451 4.0197 5.1297
BC87 11 PB3389 11 6.2585 5.0482 6.5093 3.6058
BC87 11 PB3320 12 6.8228 3.6246 4.1639 4.6531
BC87 11 SB1802 13 5.0858 5.0168 4.4524 3.4177
BC87 11 G4522 14 5.3931 5.6125 4.6719 5.1422
BC87 11 8951 15 6.5783 6.0891 6.0202 5.4432
BC87 11 8990 16 6.6535 6.6159 5.6564 3.6309
SJ87 12 M8172 1 7.9704 9.8267 7.4374 9.0365
SJ87 12 PB3147 2 9.2748 9.1557 10.3722 9.6950
SJ87 12 SB1860 3 8.4784 9.2811 8.2087 9.8580
SJ87 12 PB3165 4 8.5223 10.3283 9.7953 9.2685
SJ87 12 G4673A 5 8.0081 8.8233 9.4379 10.6419
SJ87 12 COKER21 6 7.8011 8.6101 7.6569 10.4914
SJ87 12 SB1827 7 8.1460 8.1586 9.5695 11.9776
SJ87 12 M8150 8 8.4220 9.6323 8.7480 8.6289
SJ87 12 G4765 9 7.9077 8.4345 9.2058 7.4750
SJ87 12 G4733 10 8.3404 8.0143 7.6506 8.2965
SJ87 12 PB3389 11 6.3901 8.6477 9.4692 8.7418
SJ87 12 PB3320 12 8.1398 7.7635 6.9922 7.7823
SJ87 12 SB1802 13 5.0356 7.6569 8.7355 5.0732
SJ87 12 G4522 14 6.7978 8.5348 7.9077 8.9299
SJ87 12 8951 15 8.5474 9.4128 10.0211 7.9077
SJ87 12 8990 16 8.0081 8.4157 8.9738 .0000
AX88 13 M8172 1 6.0013 6.0891 6.6598 .0000
AX88 13 PB3147 2 4.2455 5.5749 4.0636 .0000
AX88 13 SB1860 3 5.3241 5.4370 6.7978 6.2083
AX88 13 PB3165 4 5.2112 5.8320 5.9324 6.1707
AX88 13 G4673A 5 2.6903 3.8880 4.0072 1.5176
AX88 13 COKER21 6 2.5711 5.6753 5.5749 6.4403
AX88 13 SB1827 7 3.5243 1.4047 2.8533 3.1418
AX88 13 M8150 8 4.8977 5.8320 5.9888 2.7028
AX88 13 G4765 9 2.2387 5.0168 6.2459 4.7409
AX88 13 G4733 10 3.3424 4.4461 4.1828 1.7810
AX88 13 PB3389 11 2.9411 5.1422 3.2170 .0000
AX88 13 PB3320 12 3.6748 4.3521 3.2170 5.0043
AX88 13 SB1802 13 3.7689 2.5962 3.1606 3.7626
AX88 13 G4522 14 3.4365 2.8972 3.5807 2.5648
AX88 13 8951 15 4.1639 3.8504 3.9382 4.8224
AX88 13 8990 16 3.9758 4.1765 4.2141 1.9816
BR88 14 M8172 1 6.5908 5.2865 6.0264 .0000
BR88 14 PB3147 2 6.1268 8.3153 6.0703 4.1639
BR88 14 SB1860 3 6.5532 6.3024 7.6130 .0000
BR88 14 PB3165 4 6.2585 6.6159 6.3463 5.2614
BR88 14 G4673A 5 6.8040 10.4475 7.1050 5.9700
BR88 14 COKER21 6 6.5908 6.2835 6.2522 .0000
BR88 14 SB1827 7 4.6343 5.9888 7.9077 8.4784
BR88 14 M8150 8 6.7727 9.6762 8.0269 .0000
BR88 14 G4765 9 7.7259 5.6314 4.1702 3.6058
BR88 14 G4733 10 6.2146 7.6067 7.3308 .0000
BR88 14 PB3389 11 7.2430 6.2961 3.6936 5.3115
BR88 14 PB3320 12 7.5252 6.9357 6.1581 4.4712
BR88 14 SB1802 13 5.5875 7.2555 6.5281 6.6974
BR88 14 G4522 14 5.6439 6.3964 4.5214 7.2493
BR88 14 8951 15 4.6594 6.5093 8.6289 7.3057
BR88 14 8990 16 5.7630 5.4307 6.1707 .0000
BC88 15 M8172 1 6.4968 8.5913 7.7008 .0000
BC88 15 PB3147 2 7.2932 5.2614 7.4499 .0000
BC88 15 SB1860 3 6.8354 8.5223 7.9955 6.5657
BC88 15 PB3165 4 9.8016 4.8977 9.5256 9.4128
BC88 15 G4673A 5 8.1837 7.1803 5.9010 .0000
BC88 15 COKER21 6 5.0105 7.0862 4.1953 .0000
BC88 15 SB1827 7 2.3015 2.5774 6.1080 5.4683
BC88 15 M8150 8 2.8721 1.9628 3.7375 4.1012
BC88 15 G4765 9 6.8793 4.3082 3.5118 .0000
BC88 15 G4733 10 7.1301 6.1769 5.1924 5.6941
BC88 15 PB3389 11 4.7848 5.0356 5.5812 .0000
BC88 15 PB3320 12 4.5088 3.7626 5.7630 3.0540
BC88 15 SB1802 13 2.6652 1.5050 6.0390 7.1803
BC88 15 G4522 14 2.5837 1.8938 3.4177 5.8320
BC88 15 8951 15 5.7192 5.5373 5.4683 6.9295
BC88 15 8990 16 3.0101 3.3048 4.8977 5.3554
SJ88 16 M8172 1 7.9265 8.6665 6.3463 5.1046
SJ88 16 PB3147 2 6.4403 4.8224 4.8224 .0000
SJ88 16 SB1860 3 3.6685 7.2367 5.0732 3.5870
SJ88 16 PB3165 4 6.3463 8.3969 5.2614 7.5879
SJ88 16 G4673A 5 6.7915 8.8923 7.4374 4.2141
SJ88 16 COKER21 6 6.1330 3.7501 4.7032 3.2296
SJ88 16 SB1827 7 5.0795 6.4529 7.6694 3.9758
SJ88 16 M8150 8 6.7852 7.0549 .0000 .0000
SJ88 16 G4765 9 4.7283 8.8923 5.2488 4.2329
SJ88 16 G4733 10 6.9859 4.8349 5.8258 .0000
SJ88 16 PB3389 11 5.4683 6.6222 5.0732 .0000
SJ88 16 PB3320 12 4.0699 3.0164 4.5151 2.1196
SJ88 16 SB1802 13 6.7978 6.3964 5.9825 4.7848
SJ88 16 G4522 14 5.3366 6.3024 6.0139 7.7698
SJ88 16 8951 15 6.4215 5.6815 3.3675 3.8567
SJ88 16 8990 16 5.5686 1.9440 1.2354 .0000
8172 3147 1860 3165 4673 CK21 1827 8150 4765 4733 3389 3320 1802 4522 8951
8990
AX85 BR85 BC85 SJ85 AX86 BR86 BC86 SJ86 AX87 BR87 BC87 SJ87 AX88 BR88 BC88
SJ88
The above data file was analyzed by MATMODEL, requesting fitting mode,
machine-readable output, and 4 IPCA axes. The regular, extensive output
file is not reproduced here, but the brief machine-readable file follows.
This machine-readable output file from MATMODEL becomes the input file
for AMMIWINS analysis.
AMMI4 model for data with 16 GEN 16 ENV 4 REP and grand mean 6.69324.
1 8172 7.53321 .0033918 .8220707 .8905999 -.2365990
2 3147 7.35826 .7831559 -.2066205 .2666776 -.5524992
3 1860 7.31228 .7454234 -.5173331 -.3318093 -.0072376
4 3165 7.16570 1.2950096 .7704413 .4388174 .7539431
5 4673 6.97283 -.0928795 .6057231 .2839269 .1096351
6 CK21 6.87485 .5541510 -.8821288 .0524994 .0157770
7 1827 6.83676 -1.1352475 .0699490 .8365470 -.9458496
8 8150 6.64315 -.9872870 .5789365 -1.0044839 .6409547
9 4765 6.58784 .3224741 -.4515765 .3684762 .5573509
10 4733 6.49120 -.4748629 .0265244 -.2753153 .2586973
11 3389 6.43813 .1834179 .0372914 .1128048 .2233427
12 3320 6.43382 -.0206296 -1.1081402 -.4754639 -.0993735
13 1802 6.36085 -.7932791 -.6613697 .3079718 .5671935
14 4522 6.26179 -.9851075 -.0993046 .1468508 .1357470
15 8951 6.17400 .2308255 .9114446 -.9414958 -.2461961
16 8990 5.64716 .3714438 .1040922 -.6766037 -1.1748863
1 AX85 8.86994 -.1860068 -1.7044291 .3920800 .0373225
2 BR85 7.02048 -.8728857 -.3876220 -.2092572 .9685570
3 BC85 5.08559 .2967958 -.0775022 .4375629 .0017935
4 SJ85 6.85779 .1216018 -.1043597 .9369725 .0688908
5 AX86 9.17104 -.6215918 -.3008605 -.6179729 -.2190956
6 BR86 7.52696 -.9474823 .3699101 -.0488422 -.3245931
7 BC86 3.25748 .5930801 -.5355911 -.0032504 -.0622760
8 SJ86 7.23468 .0083917 .1917306 -.1273930 -.3218335
9 AX87 7.31806 1.1808709 -.4484661 -.4736400 .3493550
10 BR87 8.82340 -.6202854 .1037035 .9950322 -.9281897
11 BC87 5.55111 .1362898 .2710825 -.4982283 -.7311921
12 SJ87 8.57716 .1890083 .5304198 -.3482729 -.5660589
13 AX88 4.27088 .7227554 .1217071 -.4301329 .3438621
14 BR88 6.45155 -.6394526 .2299412 -.9776975 .0762362
15 BC88 5.50898 1.3381828 .7816441 .4394753 .1826084
16 SJ88 5.56672 -.6992719 .9586916 .5335645 1.1246134
The other input that AMMIWINS requires, besides the above file, is the specification of how many IPCA axes to use. Two lines of reasoning lead to the AMMI-1 model with 1 axis for this Louisiana corn trial. First, a quick and yet fairly reliable diagnostic estimates the amount of noise in the interaction as the error mean square times the interaction degrees of freedom, and then selects the AMMI model that leaves about this much sum of squares in the model's residual. Here the interaction noise is estimated as 2.03548 x 225 = 458. The interaction sum of squares is 738, comprised of 458 noise and 738 - 458 = 280 signal. IPCA 1 captures 230, which is most of this goal of 280, leaving behind 738 - 230 = 508 that is mostly noise, causing IPCA 2 and higher axes to capture mostly noise. Hence, AMMI-1 is indicated. Second, MATMODEL run in validation mode, using 3 replicates for modeling and the remaining 1 replicate for validating and averaging results over 1000 different randomizations, confirms that AMMI-1 is the most predictively accurate member of the AMMI family. AMMI-1 achieves a statistical efficiency of 1.7. Assuming that the statistical efficiency for the experiment's 4 replications is close to that for the validation's 3 modeling replications, this means that AMMI-1 estimates based on 4 replications are about as accurate as raw averages based on 4 x 1.7 = 6.8 replications. Given these 6.8 - 4 = 2.8 free replications for these 256 treatments, this equates to about 2.8 x 256 = 717 free yield observations. It pays to use the AMMI-1 model to gain accuracy without increasing experimental costs.
Given this diagnosis that AMMI-1 is the most predictively accurate member of the AMMI family for this particular corn trial, ordinarily AMMIWINS analysis would be requested for just this best model, AMMI-1. However, the present purpose is to illustrate AMMIWINS output for various models, so several models were requested.
The following sample output can be reproduced as follows. Start AMMIWINS, naming LACA.MR4 as the input file and LACA.WNS as the output file. After reading this input file, AMMIWINS will offer the four possible analyses. Reply "Y" for yes to AMMI-1, AMMI-2, and AMMI-4, but reply "N" for no to AMMI-3. Then AMMI-1 analysis begins. Regarding elimination of minor winners, reply -1 to eliminate genotype 3147 that defines a mega-environment with only one win. Then AMMI-2 analysis begins. Regarding the ranges of the IPCA 1 and IPCA 2 axes, reply "Y" for yes to accept the default ranges, which cover the parameter space occupied by actual environments; that is, from the LACA.MR4 input file, IPCA 1 environment scores run from -0.9474823 to 1.3381828, and IPCA 2 from -1.7044291 to 0.9586916. Then reply "12" and "0" to eliminate that minor genotype numbered 12 (namely genotype 3320), with the 0 signaling the end of the list. (The alternative response of "-1" would accomplish the same thing, but here an explicit list is given just to illustrate the other way to specify minor genotypes to be eliminated.) Finally, AMMI-4 analysis begins. Regarding minor winners, reply "-1" to eliminate small mega-environments containing only 1 environment. Again, normally interest would focus on AMMI-1 results for these data, but additional analyses were included here to illustrate the different kinds of output available for AMMI-1, AMMI-2, and higher AMMI models.
AMMIWINS Analysis
Input file: LACA.MR4
Output file: LACA.WNS
AMMI-1 Winners, Results for Genotypes
Win at score 1.3381830 is 4 3165 Nom. Yld. 8.89866
Win by main effect at score 0.0 is 1 8172 Nom. Yld. 7.53321
Win at score -.9474823 is 7 1827 Nom. Yld. 7.91239
Gen. Winners Env. IPCA 1 Switch Nominal Yield
4 3165 8.89866 at 1.3381830
.3762016 7.65288
2 3147
.2243623 7.53397
1 8172 7.53321 at 0.0
-.6116509 7.53114
7 1827 7.91239 at -.9474823
AMMI-1 Winners, Results for Mega-environments
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
4 3165 4 6.80286 | 5.93207 14.68
2 3147 1 5.98305 | 5.92657 .95
1 8172 5 8.25829 | 8.25829 .00
7 1827 6 8.40291 | 8.26417 1.68
Overall 16 7.80646 | 7.53321 3.63
AMMI-1 Winners, Genotypes Eliminated by User's Requests
1 winners were eliminated, as follows:
2 3147
AMMI-1 Winners, Results for Genotypes After Eliminations
Win at score 1.3381830 is 4 3165 Nom. Yld. 8.89866
Win by main effect at score 0.0 is 1 8172 Nom. Yld. 7.53321
Win at score -.9474823 is 7 1827 Nom. Yld. 7.91239
Gen. Winners Env. IPCA 1 Switch Nominal Yield
4 3165 8.89866 at 1.3381830
.2845345 7.53417
1 8172 7.53321 at 0.0
-.6116509 7.53114
7 1827 7.91239 at -.9474823
AMMI-1 Winners, Results for Mega-environments After Eliminations
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
4 3165 5 6.63077 | 5.93097 11.80
1 8172 5 8.25829 | 8.25829 .00
7 1827 6 8.40291 | 8.26417 1.68
Overall 16 7.80392 | 7.53321 3.59
AMMI-1 Winners, Results for Environments After Eliminations
Environments are grouped in 3 mega-environments.
Mega-environment 1 with 5 wins by 3165 gives boost of 11.80%
Environment IPCA 1 Score Exp. Yield Boost (%)
15 BC88 1.3381830 7.71440 21.42
9 AX87 1.1808710 9.31976 14.18
13 AX88 .7227554 5.67932 11.07
7 BC86 .5930801 4.49798 9.72
3 BC85 .2967958 5.94240 .27
Mega-environment 2 with 5 wins by 8172 gives boost of .00%
Environment IPCA 1 Score Exp. Yield Boost (%)
12 SJ87 .1890083 9.41777 .00
11 BC87 .1362898 6.39154 .00
4 SJ85 .1216018 7.69817 .00
8 SJ86 .0083917 8.07468 .00
1 AX85 -.1860068 9.70928 .00
Mega-environment 3 with 6 wins by 1827 gives boost of 1.68%
Environment IPCA 1 Score Exp. Yield Boost (%)
10 BR87 -.6202854 9.67110 .10
5 AX86 -.6215918 10.02022 .11
14 BR88 -.6394526 7.32101 .43
16 SJ88 -.6992719 6.50409 1.56
2 BR85 -.8728857 8.15494 3.79
6 BR86 -.9474823 8.74611 4.57
AMMI-2 Winners, Results for Genotypes
Calculated using a 70x70 grid over
IPCA 1 from -.9474823 to 1.3381830
IPCA 2 from -1.7044290 to .9586916
Key Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
1 3 1860 1625 8.16994 | 6.82255 19.75
2 1 8172 1022 7.89280 | 7.89280 .00
3 4 3165 988 8.56883 | 7.83587 9.35
4 7 1827 454 7.65285 | 7.21305 6.10
5 12 3320 377 7.98966 | 6.38554 25.12
6 6 CK21 307 8.28377 | 6.31394 31.20
7 2 3147 75 7.69061 | 7.43679 3.41
8 13 1802 52 7.82432 | 6.55504 19.36
Overall 4900 8.12691 | 7.22735 12.45
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AMMI-2 Winners, Results for Mega-environments
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
1 8172 6 8.18630 | 8.18630 .00
7 1827 3 8.96633 | 8.65607 3.58
2 3147 2 6.81933 | 6.73762 1.21
4 3165 2 7.04485 | 6.10470 15.40
3 1860 2 6.82253 | 5.72627 19.14
12 3320 1 10.50310 | 8.30812 26.42
Overall 16 7.99333 | 7.53321 6.11
AMMI-2 Winners, Genotypes Eliminated by User's Requests
1 winners were eliminated, as follows:
12 3320
AMMI-2 Winners, Results for Mega-environments After Eliminations
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
1 8172 6 8.18630 | 8.18630 .00
3 1860 3 7.95904 | 6.58688 20.83
7 1827 3 8.96633 | 8.65607 3.58
2 3147 2 6.81933 | 6.73762 1.21
4 3165 2 7.04485 | 6.10470 15.40
Overall 16 7.97639 | 7.53321 5.88
AMMI-2 Winners, Results for Environments After Eliminations
Environments are grouped in 5 mega-environments.
Mega-environment 1 with 6 wins by 8172 gives boost of .00%
Environment Exp. Yield Boost (%)
8 SJ86 8.23229 .00
10 BR87 9.74652 .00
11 BC87 6.61439 .00
12 SJ87 9.85381 .00
14 BR88 7.47838 .00
16 SJ88 7.19243 .00
Mega-environment 2 with 3 wins by 1860 gives boost of 20.83%
Environment Exp. Yield Boost (%)
1 AX85 10.23208 23.16
7 BC86 4.59569 25.59
9 AX87 9.04936 16.12
Mega-environment 3 with 3 wins by 1827 gives boost of 3.58%
Environment Exp. Yield Boost (%)
2 BR85 8.12783 7.81
5 AX86 9.99918 2.43
6 BR86 8.77198 1.20
Mega-environment 4 with 2 wins by 3147 gives boost of 1.21%
Environment Exp. Yield Boost (%)
3 BC85 5.99906 2.32
4 SJ85 7.63961 .36
Mega-environment 5 with 2 wins by 3165 gives boost of 15.40%
Environment Exp. Yield Boost (%)
13 AX88 5.77308 10.74
15 BC88 8.31661 18.88
AMMI-4 Winners, Results for Mega-environments
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
1 8172 5 7.99135 | 7.99135 .00
8 8150 3 8.89213 | 7.65865 16.11
4 3165 2 7.24536 | 6.04658 19.83
3 1860 2 6.90060 | 5.47995 25.92
7 1827 2 10.21340 | 9.77670 4.47
2 3147 1 6.53797 | 6.34367 3.06
6 CK21 1 10.47317 | 8.64847 21.10
AMMI-4 Winners, Genotypes Eliminated by User's Requests
2 winners were eliminated, as follows:
2 3147
6 CK21
AMMI-4 Winners, Results for Mega-environments After Eliminations
Genotype Wins Exp. Yield | 8172 Exp. Yield Boost (%)
1 8172 6 7.71674 | 7.71674 .00
8 8150 3 8.89213 | 7.65865 16.11
3 1860 3 7.96764 | 6.53612 21.90
4 3165 2 7.24536 | 6.04658 19.83
7 1827 2 10.21340 | 9.77670 4.47
AMMI-2 Winners, Results for Environments After Eliminations
Environments are grouped in 5 mega-environments.
Mega-environment 1 with 6 wins by 8172 gives boost of .00%
Environment Exp. Yield Boost (%)
3 BC85 6.25212 .00
4 SJ85 8.43055 .00
8 SJ86 8.19498 .00
11 BC87 6.34367 .00
12 SJ87 9.67757 .00
16 SJ88 7.40154 .00
Mega-environment 2 with 3 wins by 8150 gives boost of 16.11%
Environment Exp. Yield Boost (%)
2 BR85 8.43877 18.47
5 AX86 10.04077 8.40
14 BR88 8.19685 24.39
Mega-environment 3 with 3 wins by 1860 gives boost of 21.90%
Environment Exp. Yield Boost (%)
1 AX85 10.10172 16.80
7 BC86 4.59722 25.23
9 AX87 9.20398 26.27
Mega-environment 4 with 2 wins by 3165 gives boost of 19.83%
Environment Exp. Yield Boost (%)
13 AX88 5.84359 23.05
15 BC88 8.64714 17.74
Mega-environment 5 with 2 wins by 1827 gives boost of 4.47%
Environment Exp. Yield Boost (%)
6 BR86 9.03814 3.87
10 BR87 11.38867 4.94