Weighted two-stage analyses

# packages
pacman::p_load(dplyr, purrr, tibble, tidyr, stringr, # data handling
               nlme, lme4, glmmTMB, sommer, # mixed modelling
               AICcmodavg, mixedup)         # mixed model extractions

# data
dat <- readr::read_csv("data/Winter Wheat 2016.csv") %>% 
  dplyr::select(Year, everything()) %>% 
  mutate_at(vars(Year:Cultivar), as.factor)

Year	Zone	Location	Rep	Alpha	Cultivar	Yield
2016	South	07BM20	1	2	22455	727.3249
2016	South	07BM20	2	3	22455	721.4117
2016	South	07BM20	1	7	23286	830.3894
2016	South	07BM20	2	4	23286	806.8322
2016	South	07BM20	1	7	23524	810.4373
2016	South	07BM20	2	8	23524	833.9282
2016	South	07BM20	1	4	24054	898.0152
2016	South	07BM20	2	1	24054	874.5377
2016	South	07BM20	1	1	24521	852.6834
2016	South	07BM20	2	2	24521	846.8028
2016	South	07BM20	1	3	24984	768.3876
2016	South	07BM20	2	3	24984	837.1984
2016	South	07BM20	1	1	25512	829.0663
2016	South	07BM20	2	1	25512	811.6733
2016	South	07BM20	1	6	25965	872.8433
2016	South	07BM20	2	8	25965	849.0925
2016	South	07BM20	1	1	26362	877.3207
2016	South	07BM20	2	7	26362	929.6114
2016	South	07BM20	1	7	26742	866.9745
2016	South	07BM20	2	3	26742	837.4855
2016	South	07BM20	1	6	26777	842.2327
2016	South	07BM20	2	6	26777	871.8888
2016	South	07BM20	1	3	27110	834.4164
2016	South	07BM20	2	1	27110	816.7878
2016	South	07BM20	1	1	27125	878.4325
2016	South	07BM20	2	5	27125	925.2823
2016	South	07BM20	1	4	27130	816.6504
2016	South	07BM20	2	8	27130	881.2774
2016	South	07BM20	1	3	27543	899.4013
2016	South	07BM20	2	6	27543	852.6791
2016	South	07BM20	1	4	27546	821.6075
2016	South	07BM20	2	2	27546	804.0016
2016	South	07BM20	1	2	27548	804.0778
2016	South	07BM20	2	1	27548	833.2110
2016	South	07BM20	1	4	27590	834.0864
2016	South	07BM20	2	5	27590	886.9510
2016	South	07BM20	1	2	27592	845.6966
2016	South	07BM20	2	7	27592	893.0083
2016	South	07BM20	1	8	27593	884.8773
2016	South	07BM20	2	7	27593	896.5976
2016	South	07BM20	1	4	27599	873.1738
2016	South	07BM20	2	7	27599	861.3742
2016	South	07BM20	1	5	27600	866.8977
2016	South	07BM20	2	8	27600	890.3273
2016	South	07BM20	1	2	27605	842.8482
2016	South	07BM20	2	2	27605	801.5899
2016	South	07BM20	1	2	27609	761.3134
2016	South	07BM20	2	5	27609	772.7617
2016	South	07BM20	1	3	27669	814.8698
2016	South	07BM20	2	8	27669	838.4892
2016	South	07BM20	1	2	28128	907.3745
2016	South	07BM20	2	4	28128	930.9426
2016	South	07BM20	1	3	28209	811.3320
2016	South	07BM20	2	5	28209	899.5202
2016	South	07BM20	1	2	28949	912.7323
2016	South	07BM20	2	8	28949	977.9274
2016	South	07BM20	1	1	28950	756.7839
2016	South	07BM20	2	8	28950	797.2228
2016	South	07BM20	1	8	28954	866.5706
2016	South	07BM20	2	2	28954	831.2004
2016	South	07BM21	1	7	22455	1029.3683
2016	South	07BM21	2	8	22455	1011.1896
2016	South	07BM21	1	6	23286	1160.4312
2016	South	07BM21	2	3	23286	1054.6327
2016	South	07BM21	1	5	23524	1075.0613
2016	South	07BM21	2	5	23524	1051.2687
2016	South	07BM21	1	4	24054	1111.2612
2016	South	07BM21	2	5	24054	1155.3462
2016	South	07BM21	1	5	24521	1103.2905
2016	South	07BM21	2	8	24521	1164.5686
2016	South	07BM21	1	4	24984	1065.1897
2016	South	07BM21	2	3	24984	1086.7991
2016	South	07BM21	1	8	25512	1079.0086
2016	South	07BM21	2	8	25512	1124.1063
2016	South	07BM21	1	6	25965	1158.2143
2016	South	07BM21	2	2	25965	1002.2965
2016	South	07BM21	1	1	26362	1127.6725
2016	South	07BM21	2	2	26362	1196.1547
2016	South	07BM21	1	2	26742	1095.8919
2016	South	07BM21	2	5	26742	1106.0422
2016	South	07BM21	1	3	26777	1115.2381
2016	South	07BM21	2	5	26777	1080.2225
2016	South	07BM21	1	3	27110	1141.4525
2016	South	07BM21	2	2	27110	1145.8539
2016	South	07BM21	1	7	27125	1061.0872
2016	South	07BM21	2	1	27125	1033.9701
2016	South	07BM21	1	1	27130	1046.1721
2016	South	07BM21	2	7	27130	1165.8961
2016	South	07BM21	1	7	27543	1120.5770
2016	South	07BM21	2	2	27543	1088.0005
2016	South	07BM21	1	4	27546	970.9841
2016	South	07BM21	2	2	27546	1068.7553
2016	South	07BM21	1	5	27548	1060.0229
2016	South	07BM21	2	1	27548	1000.6153
2016	South	07BM21	1	1	27590	1029.4978
2016	South	07BM21	2	1	27590	1061.1799
2016	South	07BM21	1	8	27592	1095.1628
2016	South	07BM21	2	5	27592	1063.1793
2016	South	07BM21	1	7	27593	1089.7632
2016	South	07BM21	2	7	27593	1100.2537
2016	South	07BM21	1	1	27599	1099.3357
2016	South	07BM21	2	3	27599	1080.8060
2016	South	07BM21	1	3	27600	1129.4645
2016	South	07BM21	2	8	27600	1139.8748
2016	South	07BM21	1	7	27605	1083.8253
2016	South	07BM21	2	3	27605	1020.8942
2016	South	07BM21	1	4	27609	1140.6148
2016	South	07BM21	2	1	27609	1177.4254
2016	South	07BM21	1	6	27669	1087.7269
2016	South	07BM21	2	5	27669	1091.7166
2016	South	07BM21	1	7	28128	1158.6847
2016	South	07BM21	2	4	28128	1043.2536
2016	South	07BM21	1	3	28209	1129.7566
2016	South	07BM21	2	4	28209	1108.7524
2016	South	07BM21	1	4	28949	1052.2477
2016	South	07BM21	2	8	28949	1192.2971
2016	South	07BM21	1	5	28950	1206.2481
2016	South	07BM21	2	2	28950	1230.0106
2016	South	07BM21	1	5	28954	1114.6990
2016	South	07BM21	2	6	28954	1097.7253
2016	South	07BM22	1	7	22455	819.6187
2016	South	07BM22	2	6	22455	847.0165
2016	South	07BM22	1	2	23286	849.7257
2016	South	07BM22	2	6	23286	900.4337
2016	South	07BM22	1	7	23524	901.4886
2016	South	07BM22	2	4	23524	685.6775
2016	South	07BM22	1	1	24054	955.5500
2016	South	07BM22	2	6	24054	1001.8610
2016	South	07BM22	1	4	24521	926.2059
2016	South	07BM22	2	5	24521	922.3946
2016	South	07BM22	1	5	24984	1018.3700
2016	South	07BM22	2	7	24984	981.1299
2016	South	07BM22	1	2	25512	888.9895
2016	South	07BM22	2	5	25512	913.3269
2016	South	07BM22	1	8	25965	988.8755
2016	South	07BM22	2	5	25965	959.8080
2016	South	07BM22	1	6	26362	906.0697
2016	South	07BM22	2	6	26362	971.8693
2016	South	07BM22	1	7	26742	900.1115
2016	South	07BM22	2	5	26742	946.4055
2016	South	07BM22	1	7	26777	905.4283
2016	South	07BM22	2	7	26777	883.3969
2016	South	07BM22	1	5	27110	984.0181
2016	South	07BM22	2	2	27110	873.0590
2016	South	07BM22	1	2	27125	924.7595
2016	South	07BM22	2	7	27125	1011.4416
2016	South	07BM22	1	2	27130	921.2537
2016	South	07BM22	2	8	27130	947.6934
2016	South	07BM22	1	5	27543	933.4796
2016	South	07BM22	2	1	27543	870.3746
2016	South	07BM22	1	4	27546	894.5526
2016	South	07BM22	2	7	27546	868.8225
2016	South	07BM22	1	3	27548	914.0728
2016	South	07BM22	2	6	27548	918.5665
2016	South	07BM22	1	5	27590	985.5936
2016	South	07BM22	2	8	27590	999.6490
2016	South	07BM22	1	1	27592	791.5379
2016	South	07BM22	2	5	27592	911.2438
2016	South	07BM22	1	3	27593	890.3123
2016	South	07BM22	2	2	27593	856.1849
2016	South	07BM22	1	6	27599	903.1960
2016	South	07BM22	2	2	27599	764.0221
2016	South	07BM22	1	1	27600	901.5087
2016	South	07BM22	2	1	27600	779.2659
2016	South	07BM22	1	8	27605	858.5939
2016	South	07BM22	2	3	27605	836.7718
2016	South	07BM22	1	2	27609	913.3892
2016	South	07BM22	2	1	27609	882.2267
2016	South	07BM22	1	1	27669	846.3420
2016	South	07BM22	2	2	27669	850.3326
2016	South	07BM22	1	6	28128	942.1420
2016	South	07BM22	2	7	28128	903.4617
2016	South	07BM22	1	7	28209	935.9827
2016	South	07BM22	2	8	28209	862.1291
2016	South	07BM22	1	8	28949	913.8614
2016	South	07BM22	2	8	28949	1072.1976
2016	South	07BM22	1	7	28950	942.7756
2016	South	07BM22	2	1	28950	861.7975
2016	South	07BM22	1	2	28954	904.0544
2016	South	07BM22	2	3	28954	847.4830
2016	South	07BM23	1	8	22455	821.2007
2016	South	07BM23	2	8	22455	876.7706
2016	South	07BM23	1	2	23286	885.4570
2016	South	07BM23	2	5	23286	928.5000
2016	South	07BM23	1	3	23524	877.6036
2016	South	07BM23	2	1	23524	908.2890
2016	South	07BM23	1	2	24054	876.4197
2016	South	07BM23	2	2	24054	907.2795
2016	South	07BM23	1	6	24521	929.6578
2016	South	07BM23	2	7	24521	954.4487
2016	South	07BM23	1	2	24984	918.2887
2016	South	07BM23	2	7	24984	943.1073
2016	South	07BM23	1	1	25512	910.6488
2016	South	07BM23	2	8	25512	929.1079
2016	South	07BM23	1	5	25965	900.5850
2016	South	07BM23	2	7	25965	833.1943
2016	South	07BM23	1	3	26362	902.7840
2016	South	07BM23	2	5	26362	914.9838
2016	South	07BM23	1	7	26742	908.9759
2016	South	07BM23	2	4	26742	946.0770
2016	South	07BM23	1	4	26777	960.6798
2016	South	07BM23	2	3	26777	954.5216
2016	South	07BM23	1	1	27110	954.0211
2016	South	07BM23	2	4	27110	929.4012
2016	South	07BM23	1	8	27125	967.6723
2016	South	07BM23	2	4	27125	955.3453
2016	South	07BM23	1	1	27130	966.5780
2016	South	07BM23	2	2	27130	978.8132
2016	South	07BM23	1	2	27543	881.6546
2016	South	07BM23	2	1	27543	918.3902
2016	South	07BM23	1	4	27546	882.7495
2016	South	07BM23	2	6	27546	895.0956
2016	South	07BM23	1	5	27548	887.3005
2016	South	07BM23	2	6	27548	917.8971
2016	South	07BM23	1	5	27590	927.7278
2016	South	07BM23	2	2	27590	921.5839
2016	South	07BM23	1	7	27592	905.9635
2016	South	07BM23	2	8	27592	936.7785
2016	South	07BM23	1	5	27593	951.9990
2016	South	07BM23	2	8	27593	964.3626
2016	South	07BM23	1	6	27599	961.5740
2016	South	07BM23	2	5	27599	955.4101
2016	South	07BM23	1	5	27600	936.1003
2016	South	07BM23	2	5	27600	948.3369
2016	South	07BM23	1	1	27605	898.9544
2016	South	07BM23	2	5	27605	905.1116
2016	South	07BM23	1	6	27609	952.4557
2016	South	07BM23	2	1	27609	946.3108
2016	South	07BM23	1	5	27669	893.4807
2016	South	07BM23	2	4	27669	893.4807
2016	South	07BM23	1	2	28128	942.3204
2016	South	07BM23	2	6	28128	948.4793
2016	South	07BM23	1	2	28209	892.5463
2016	South	07BM23	2	8	28209	941.4529
2016	South	07BM23	1	1	28949	1008.5137
2016	South	07BM23	2	6	28949	1026.9621
2016	South	07BM23	1	6	28950	946.2584
2016	South	07BM23	2	4	28950	940.0737
2016	South	07BM23	1	7	28954	931.4198
2016	South	07BM23	2	6	28954	931.4198
2016	North	07BM25	1	6	22455	641.5342
2016	North	07BM25	2	8	22455	510.4177
2016	North	07BM25	1	2	23286	560.4516
2016	North	07BM25	2	6	23286	592.4774
2016	North	07BM25	1	7	23524	558.9090
2016	North	07BM25	2	6	23524	568.1091
2016	North	07BM25	1	4	24054	680.3784
2016	North	07BM25	2	5	24054	682.7085
2016	North	07BM25	1	7	24521	590.9922
2016	North	07BM25	2	1	24521	534.9297
2016	North	07BM25	1	3	24984	713.0400
2016	North	07BM25	2	3	24984	647.5806
2016	North	07BM25	1	5	25512	694.7617
2016	North	07BM25	2	2	25512	634.1449
2016	North	07BM25	1	7	25965	617.9795
2016	North	07BM25	2	7	25965	472.1641
2016	North	07BM25	1	5	26362	690.1017
2016	North	07BM25	2	1	26362	592.8390
2016	North	07BM25	1	8	26742	615.5849
2016	North	07BM25	2	7	26742	606.1506
2016	North	07BM25	1	8	26777	609.7213
2016	North	07BM25	2	8	26777	549.2146
2016	North	07BM25	1	3	27110	656.9303
2016	North	07BM25	2	5	27110	633.5520
2016	North	07BM25	1	5	27125	675.9000
2016	North	07BM25	2	3	27125	627.1237
2016	North	07BM25	1	6	27130	662.7143
2016	North	07BM25	2	5	27130	643.9139
2016	North	07BM25	1	4	27543	643.0899
2016	North	07BM25	2	1	27543	562.1254
2016	North	07BM25	1	8	27546	611.7152
2016	North	07BM25	2	1	27546	595.4954
2016	North	07BM25	1	7	27548	608.5076
2016	North	07BM25	2	2	27548	592.4338
2016	North	07BM25	1	2	27590	697.7318
2016	North	07BM25	2	7	27590	580.6627
2016	North	07BM25	1	1	27592	587.5538
2016	North	07BM25	2	7	27592	550.6877
2016	North	07BM25	1	7	27593	635.0088
2016	North	07BM25	2	3	27593	639.6952
2016	North	07BM25	1	7	27599	620.2589
2016	North	07BM25	2	5	27599	673.8903
2016	North	07BM25	1	3	27600	656.5544
2016	North	07BM25	2	4	27600	640.5965
2016	North	07BM25	1	7	27605	651.4319
2016	North	07BM25	2	4	27605	679.1524
2016	North	07BM25	1	8	27609	612.0220
2016	North	07BM25	2	2	27609	563.7045
2016	North	07BM25	1	3	27669	670.0269
2016	North	07BM25	2	8	27669	604.6584
2016	North	07BM25	1	4	28128	686.8429
2016	North	07BM25	2	6	28128	605.6283
2016	North	07BM25	1	6	28209	668.1495
2016	North	07BM25	2	7	28209	603.1905
2016	North	07BM25	1	3	28949	677.7977
2016	North	07BM25	2	1	28949	619.7671
2016	North	07BM25	1	4	28950	730.1157
2016	North	07BM25	2	2	28950	692.6739
2016	North	07BM25	1	5	28954	682.5977
2016	North	07BM25	2	5	28954	677.9856
2016	North	07BM26	1	1	22455	963.4176
2016	North	07BM26	2	8	22455	932.2623
2016	North	07BM26	1	3	23286	973.3814
2016	North	07BM26	2	8	23286	992.7041
2016	North	07BM26	1	1	23524	1059.5370
2016	North	07BM26	2	6	23524	991.9583
2016	North	07BM26	1	2	24054	1032.0960
2016	North	07BM26	2	1	24054	1118.7055
2016	North	07BM26	1	4	24521	1019.1231
2016	North	07BM26	2	1	24521	1069.9582
2016	North	07BM26	1	4	24984	1015.2886
2016	North	07BM26	2	4	24984	1039.5778
2016	North	07BM26	1	4	25512	966.3794
2016	North	07BM26	2	2	25512	1007.0439
2016	North	07BM26	1	2	25965	1005.0179
2016	North	07BM26	2	4	25965	973.5354
2016	North	07BM26	1	6	26362
2016	North	07BM26	2	2	26362
2016	North	07BM26	1	7	26742	1029.2631
2016	North	07BM26	2	6	26742	1048.4568
2016	North	07BM26	1	1	26777	1009.5497
2016	North	07BM26	2	5	26777	915.5820
2016	North	07BM26	1	1	27110	1057.8665
2016	North	07BM26	2	2	27110	1016.8078
2016	North	07BM26	1	8	27125	1047.9795
2016	North	07BM26	2	3	27125	1069.6619
2016	North	07BM26	1	3	27130	983.5572
2016	North	07BM26	2	4	27130	1031.8892
2016	North	07BM26	1	7	27543	1008.9643
2016	North	07BM26	2	2	27543	1023.3098
2016	North	07BM26	1	6	27546	1010.0613
2016	North	07BM26	2	1	27546	1048.5398
2016	North	07BM26	1	7	27548	995.6066
2016	North	07BM26	2	3	27548	938.0293
2016	North	07BM26	1	2	27590	1023.5543
2016	North	07BM26	2	3	27590	1038.0045
2016	North	07BM26	1	4	27592	976.2280
2016	North	07BM26	2	7	27592	1007.6413
2016	North	07BM26	1	4	27593	984.4078
2016	North	07BM26	2	3	27593	989.2691
2016	North	07BM26	1	5	27599	1056.2099
2016	North	07BM26	2	1	27599	1061.0108
2016	North	07BM26	1	8	27600	1062.7582
2016	North	07BM26	2	2	27600	1060.3646
2016	North	07BM26	1	6	27605	1020.2266
2016	North	07BM26	2	8	27605	1008.1672
2016	North	07BM26	1	2	27609	997.4454
2016	North	07BM26	2	8	27609	1054.4423
2016	North	07BM26	1	6	27669	1007.1895
2016	North	07BM26	2	5	27669	982.9782
2016	North	07BM26	1	5	28128	1060.0104
2016	North	07BM26	2	3	28128	1055.1702
2016	North	07BM26	1	3	28209	1057.0328
2016	North	07BM26	2	7	28209	1066.5772
2016	North	07BM26	1	1	28949	1025.1414
2016	North	07BM26	2	1	28949	1080.4894
2016	North	07BM26	1	7	28950	1073.6885
2016	North	07BM26	2	4	28950	1066.4501
2016	North	07BM26	1	8	28954	1019.5060
2016	North	07BM26	2	7	28954	949.9397
2016	Middle	07BM27	1	2	22455	1054.5036
2016	Middle	07BM27	2	1	22455	1053.2697
2016	Middle	07BM27	1	3	23286	1040.6251
2016	Middle	07BM27	2	2	23286	1013.6993
2016	Middle	07BM27	1	5	23524	1035.6504
2016	Middle	07BM27	2	2	23524	983.1932
2016	Middle	07BM27	1	1	24054	1095.7399
2016	Middle	07BM27	2	6	24054	1082.8047
2016	Middle	07BM27	1	8	24521	1057.0129
2016	Middle	07BM27	2	4	24521	1124.0479
2016	Middle	07BM27	1	6	24984	1168.3378
2016	Middle	07BM27	2	7	24984	1133.0462
2016	Middle	07BM27	1	4	25512	1097.3273
2016	Middle	07BM27	2	6	25512	1097.3829
2016	Middle	07BM27	1	6	25965	1158.1901
2016	Middle	07BM27	2	4	25965	1047.9719
2016	Middle	07BM27	1	7	26362	969.7034
2016	Middle	07BM27	2	7	26362	875.4764
2016	Middle	07BM27	1	4	26742	1040.3197
2016	Middle	07BM27	2	5	26742	1068.3131
2016	Middle	07BM27	1	7	26777	1003.2354
2016	Middle	07BM27	2	4	26777	994.9841
2016	Middle	07BM27	1	7	27110	1077.8938
2016	Middle	07BM27	2	5	27110	969.8409
2016	Middle	07BM27	1	2	27125	1099.6123
2016	Middle	07BM27	2	8	27125	1045.0624
2016	Middle	07BM27	1	2	27130	1101.5175
2016	Middle	07BM27	2	7	27130	1045.4730
2016	Middle	07BM27	1	5	27543	1225.2806
2016	Middle	07BM27	2	1	27543	1003.4312
2016	Middle	07BM27	1	8	27546	1042.2069
2016	Middle	07BM27	2	8	27546	1045.4587
2016	Middle	07BM27	1	6	27548	1095.5401
2016	Middle	07BM27	2	3	27548	1204.8185
2016	Middle	07BM27	1	2	27590	1101.7863
2016	Middle	07BM27	2	2	27590	1139.1811
2016	Middle	07BM27	1	8	27592	1080.7114
2016	Middle	07BM27	2	6	27592	1003.5497
2016	Middle	07BM27	1	3	27593	1148.0897
2016	Middle	07BM27	2	1	27593	992.9424
2016	Middle	07BM27	1	4	27599	1088.0450
2016	Middle	07BM27	2	2	27599	1059.5665
2016	Middle	07BM27	1	4	27600	1124.2272
2016	Middle	07BM27	2	8	27600	1147.4009
2016	Middle	07BM27	1	1	27605	975.4345
2016	Middle	07BM27	2	2	27605	969.7965
2016	Middle	07BM27	1	8	27609	1056.2865
2016	Middle	07BM27	2	3	27609	1017.4773
2016	Middle	07BM27	1	6	27669	1273.3470
2016	Middle	07BM27	2	2	27669	1042.6682
2016	Middle	07BM27	1	7	28128	1193.2099
2016	Middle	07BM27	2	6	28128	1199.4138
2016	Middle	07BM27	1	7	28209	1126.6890
2016	Middle	07BM27	2	8	28209	1117.2443
2016	Middle	07BM27	1	5	28949	1212.1974
2016	Middle	07BM27	2	3	28949	1113.2585
2016	Middle	07BM27	1	5	28950	1108.5987
2016	Middle	07BM27	2	8	28950	1345.2563
2016	Middle	07BM27	1	3	28954	1036.4071
2016	Middle	07BM27	2	8	28954	1033.3338
2016	Middle	07BM28	1	4	22455	697.7372
2016	Middle	07BM28	2	4	22455	641.2831
2016	Middle	07BM28	1	1	23286	747.6588
2016	Middle	07BM28	2	1	23286	711.0694
2016	Middle	07BM28	1	4	23524	636.0388
2016	Middle	07BM28	2	8	23524	629.4500
2016	Middle	07BM28	1	4	24054	690.8875
2016	Middle	07BM28	2	1	24054	727.3657
2016	Middle	07BM28	1	5	24521	734.5041
2016	Middle	07BM28	2	6	24521	741.1612
2016	Middle	07BM28	1	8	24984	672.7286
2016	Middle	07BM28	2	3	24984	670.5083
2016	Middle	07BM28	1	3	25512	674.6083
2016	Middle	07BM28	2	7	25512	652.3540
2016	Middle	07BM28	1	6	25965	707.3774
2016	Middle	07BM28	2	4	25965	709.5907
2016	Middle	07BM28	1	5	26362	707.3940
2016	Middle	07BM28	2	5	26362	696.4301
2016	Middle	07BM28	1	8	26742	786.8927
2016	Middle	07BM28	2	5	26742	736.6092
2016	Middle	07BM28	1	7	26777	761.0415
2016	Middle	07BM28	2	3	26777	708.6014
2016	Middle	07BM28	1	2	27110	692.6981
2016	Middle	07BM28	2	4	27110	704.2283
2016	Middle	07BM28	1	2	27125	670.5592
2016	Middle	07BM28	2	7	27125	686.9359
2016	Middle	07BM28	1	1	27130	689.2224
2016	Middle	07BM28	2	3	27130	698.4003
2016	Middle	07BM28	1	8	27543	788.4098
2016	Middle	07BM28	2	7	27543	725.8238
2016	Middle	07BM28	1	7	27546	795.2822
2016	Middle	07BM28	2	7	27546	738.4133
2016	Middle	07BM28	1	1	27548	666.7590
2016	Middle	07BM28	2	6	27548	653.0706
2016	Middle	07BM28	1	7	27590	737.1625
2016	Middle	07BM28	2	2	27590	701.0746
2016	Middle	07BM28	1	8	27592	760.2206
2016	Middle	07BM28	2	8	27592	698.4141
2016	Middle	07BM28	1	3	27593	738.8303
2016	Middle	07BM28	2	3	27593	745.8668
2016	Middle	07BM28	1	6	27599	783.8106
2016	Middle	07BM28	2	5	27599	759.1236
2016	Middle	07BM28	1	7	27600	790.9763
2016	Middle	07BM28	2	4	27600	718.6309
2016	Middle	07BM28	1	1	27605	665.9293
2016	Middle	07BM28	2	5	27605	659.3141
2016	Middle	07BM28	1	2	27609	540.6745
2016	Middle	07BM28	2	5	27609	540.6745
2016	Middle	07BM28	1	2	27669	687.6542
2016	Middle	07BM28	2	8	27669	730.7976
2016	Middle	07BM28	1	4	28128	736.2982
2016	Middle	07BM28	2	5	28128	722.6712
2016	Middle	07BM28	1	6	28209	721.2472
2016	Middle	07BM28	2	8	28209	710.3126
2016	Middle	07BM28	1	8	28949	797.5202
2016	Middle	07BM28	2	1	28949	788.6785
2016	Middle	07BM28	1	3	28950	723.7861
2016	Middle	07BM28	2	5	28950	703.5342
2016	Middle	07BM28	1	4	28954	672.5353
2016	Middle	07BM28	2	7	28954	635.9557
2016	Middle	07BM29	1	7	22455	348.4080
2016	Middle	07BM29	2	5	22455	424.5501
2016	Middle	07BM29	1	8	23286	519.7308
2016	Middle	07BM29	2	4	23286	500.1183
2016	Middle	07BM29	1	8	23524	330.8944
2016	Middle	07BM29	2	6	23524	345.1776
2016	Middle	07BM29	1	3	24054	357.3722
2016	Middle	07BM29	2	7	24054	236.6704
2016	Middle	07BM29	1	5	24521
2016	Middle	07BM29	2	4	24521	603.5316
2016	Middle	07BM29	1	1	24984
2016	Middle	07BM29	2	3	24984	458.1359
2016	Middle	07BM29	1	5	25512	599.3387
2016	Middle	07BM29	2	3	25512	574.9753
2016	Middle	07BM29	1	3	25965
2016	Middle	07BM29	2	1	25965	469.1078
2016	Middle	07BM29	1	6	26362	360.5430
2016	Middle	07BM29	2	4	26362	416.1973
2016	Middle	07BM29	1	6	26742	454.3487
2016	Middle	07BM29	2	8	26742	502.9422
2016	Middle	07BM29	1	6	26777	398.1568
2016	Middle	07BM29	2	2	26777	472.0661
2016	Middle	07BM29	1	1	27110	397.6717
2016	Middle	07BM29	2	6	27110	524.7384
2016	Middle	07BM29	1	4	27125	487.0809
2016	Middle	07BM29	2	5	27125	468.0729
2016	Middle	07BM29	1	4	27130	404.6341
2016	Middle	07BM29	2	8	27130	400.0359
2016	Middle	07BM29	1	5	27543	508.0339
2016	Middle	07BM29	2	7	27543	434.7598
2016	Middle	07BM29	1	1	27546	559.9167
2016	Middle	07BM29	2	7	27546	542.8013
2016	Middle	07BM29	1	3	27548	460.1600
2016	Middle	07BM29	2	4	27548	518.2855
2016	Middle	07BM29	1	2	27590
2016	Middle	07BM29	2	3	27590	505.5382
2016	Middle	07BM29	1	5	27592	514.0704
2016	Middle	07BM29	2	3	27592	531.2880
2016	Middle	07BM29	1	1	27593	415.5349
2016	Middle	07BM29	2	4	27593	558.8228
2016	Middle	07BM29	1	7	27599	626.0585
2016	Middle	07BM29	2	4	27599	571.8329
2016	Middle	07BM29	1	4	27600	558.6964
2016	Middle	07BM29	2	2	27600	491.2675
2016	Middle	07BM29	1	2	27605
2016	Middle	07BM29	2	7	27605	363.4018
2016	Middle	07BM29	1	7	27609	83.1913
2016	Middle	07BM29	2	6	27609	149.2549
2016	Middle	07BM29	1	1	27669
2016	Middle	07BM29	2	8	27669	431.0937
2016	Middle	07BM29	1	6	28128	523.1656
2016	Middle	07BM29	2	6	28128	462.0482
2016	Middle	07BM29	1	7	28209	359.1714
2016	Middle	07BM29	2	8	28209	368.2643
2016	Middle	07BM29	1	7	28949	537.6864
2016	Middle	07BM29	2	1	28949	630.1392
2016	Middle	07BM29	1	7	28950	326.8803
2016	Middle	07BM29	2	3	28950	427.7963
2016	Middle	07BM29	1	8	28954
2016	Middle	07BM29	2	8	28954	536.4864
2016	South	07BM30	1	5	22455	697.1874
2016	South	07BM30	2	3	22455	645.9877
2016	South	07BM30	1	6	23286	759.0762
2016	South	07BM30	2	3	23286	512.1869
2016	South	07BM30	1	6	23524	644.8328
2016	South	07BM30	2	6	23524	623.2122
2016	South	07BM30	1	2	24054	593.0267
2016	South	07BM30	2	2	24054	430.9506
2016	South	07BM30	1	1	24521	790.2458
2016	South	07BM30	2	5	24521	750.6786
2016	South	07BM30	1	3	24984	588.7325
2016	South	07BM30	2	4	24984	625.4255
2016	South	07BM30	1	5	25512	700.2470
2016	South	07BM30	2	1	25512	538.6927
2016	South	07BM30	1	1	25965	637.5069
2016	South	07BM30	2	3	25965	413.5608
2016	South	07BM30	1	3	26362	568.1390
2016	South	07BM30	2	3	26362	445.4423
2016	South	07BM30	1	2	26742	717.0305
2016	South	07BM30	2	4	26742	688.4373
2016	South	07BM30	1	3	26777	294.0247
2016	South	07BM30	2	2	26777	529.5605
2016	South	07BM30	1	5	27110	763.8197
2016	South	07BM30	2	2	27110	640.5346
2016	South	07BM30	1	4	27125	671.3193
2016	South	07BM30	2	4	27125	630.6826
2016	South	07BM30	1	5	27130	611.4437
2016	South	07BM30	2	6	27130	707.6136
2016	South	07BM30	1	2	27543	839.6179
2016	South	07BM30	2	1	27543	726.3318
2016	South	07BM30	1	1	27546	802.0397
2016	South	07BM30	2	6	27546	770.4161
2016	South	07BM30	1	6	27548	803.3323
2016	South	07BM30	2	4	27548	700.1870
2016	South	07BM30	1	2	27590	719.3896
2016	South	07BM30	2	1	27590	624.3759
2016	South	07BM30	1	4	27592	650.1453
2016	South	07BM30	2	3	27592	551.8987
2016	South	07BM30	1	4	27593	780.1462
2016	South	07BM30	2	6	27593	824.3363
2016	South	07BM30	1	2	27599	761.2306
2016	South	07BM30	2	3	27599	622.0809
2016	South	07BM30	1	6	27600	889.3269
2016	South	07BM30	2	5	27600	716.3420
2016	South	07BM30	1	3	27605	611.1059
2016	South	07BM30	2	5	27605	602.3914
2016	South	07BM30	1	3	27609	309.0891
2016	South	07BM30	2	5	27609	395.5727
2016	South	07BM30	1	1	27669	583.3843
2016	South	07BM30	2	4	27669	505.2380
2016	South	07BM30	1	3	28128	815.9065
2016	South	07BM30	2	1	28128	661.0907
2016	South	07BM30	1	4	28209	655.4579
2016	South	07BM30	2	3	28209	532.4584
2016	South	07BM30	1	4	28949	717.5473
2016	South	07BM30	2	1	28949	620.5667
2016	South	07BM30	1	6	28950	551.0540
2016	South	07BM30	2	2	28950	366.6649
2016	South	07BM30	1	6	28954	726.9928
2016	South	07BM30	2	6	28954	745.4527
2016	Middle	07BM32	1	3	22455	1000.1913
2016	Middle	07BM32	2	1	22455	1006.5580
2016	Middle	07BM32	1	1	23286	1006.3037
2016	Middle	07BM32	2	3	23286	1030.8380
2016	Middle	07BM32	1	2	23524	978.1325
2016	Middle	07BM32	2	2	23524	1055.5864
2016	Middle	07BM32	1	2	24054	1031.0790
2016	Middle	07BM32	2	1	24054	1133.1633
2016	Middle	07BM32	1	4	24521	1095.8539
2016	Middle	07BM32	2	2	24521	1132.4509
2016	Middle	07BM32	1	5	24984	1058.2291
2016	Middle	07BM32	2	1	24984	1064.7115
2016	Middle	07BM32	1	4	25512	1050.5852
2016	Middle	07BM32	2	6	25512	1013.0481
2016	Middle	07BM32	1	6	25965	1065.1875
2016	Middle	07BM32	2	6	25965	1001.6155
2016	Middle	07BM32	1	2	26362	1042.5822
2016	Middle	07BM32	2	4	26362	1030.6888
2016	Middle	07BM32	1	3	26742	1095.8544
2016	Middle	07BM32	2	6	26742	1029.1096
2016	Middle	07BM32	1	5	26777	1067.8518
2016	Middle	07BM32	2	5	26777	1002.8536
2016	Middle	07BM32	1	6	27110	1098.6540
2016	Middle	07BM32	2	2	27110	1143.5935
2016	Middle	07BM32	1	2	27125	989.7357
2016	Middle	07BM32	2	3	27125	1036.4698
2016	Middle	07BM32	1	1	27130	1051.0775
2016	Middle	07BM32	2	5	27130	1030.1766
2016	Middle	07BM32	1	3	27543	1069.2424
2016	Middle	07BM32	2	2	27543	1084.8826
2016	Middle	07BM32	1	4	27546	1068.1483
2016	Middle	07BM32	2	5	27546	1015.6649
2016	Middle	07BM32	1	6	27548	1093.9976
2016	Middle	07BM32	2	3	27548	1020.9295
2016	Middle	07BM32	1	1	27590	1075.7332
2016	Middle	07BM32	2	1	27590	1042.3819
2016	Middle	07BM32	1	5	27592	1042.4085
2016	Middle	07BM32	2	2	27592	1037.4682
2016	Middle	07BM32	1	6	27593	1030.0792
2016	Middle	07BM32	2	3	27593	990.1929
2016	Middle	07BM32	1	4	27599	1131.1246
2016	Middle	07BM32	2	5	27599	1009.6398
2016	Middle	07BM32	1	5	27600	1104.6586
2016	Middle	07BM32	2	1	27600	1069.8956
2016	Middle	07BM32	1	2	27605	1061.1950
2016	Middle	07BM32	2	4	27605	1057.9018
2016	Middle	07BM32	1	3	27609	1005.3361
2016	Middle	07BM32	2	6	27609	1027.6870
2016	Middle	07BM32	1	6	27669	1042.0638
2016	Middle	07BM32	2	4	27669	1044.4943
2016	Middle	07BM32	1	4	28128	1146.2375
2016	Middle	07BM32	2	4	28128	1091.4462
2016	Middle	07BM32	1	3	28209	1145.4220
2016	Middle	07BM32	2	5	28209	1094.0796
2016	Middle	07BM32	1	1	28949	1063.7108
2016	Middle	07BM32	2	4	28949	1102.9247
2016	Middle	07BM32	1	2	28950	1070.4734
2016	Middle	07BM32	2	5	28950	1023.2614
2016	Middle	07BM32	1	1	28954	993.0285
2016	Middle	07BM32	2	2	28954	1021.8775
2016	South	07BM35	1	1	22455	805.7658
2016	South	07BM35	2	1	22455	804.4704
2016	South	07BM35	1	1	23286	942.9373
2016	South	07BM35	2	2	23286	519.1671
2016	South	07BM35	1	2	23524	862.7177
2016	South	07BM35	2	4	23524	796.9559
2016	South	07BM35	1	5	24054	646.6505
2016	South	07BM35	2	5	24054	767.7773
2016	South	07BM35	1	1	24521	904.8520
2016	South	07BM35	2	6	24521	884.6863
2016	South	07BM35	1	6	24984	762.7390
2016	South	07BM35	2	4	24984	776.3246
2016	South	07BM35	1	5	25512	720.3415
2016	South	07BM35	2	3	25512	876.2652
2016	South	07BM35	1	6	25965	705.8098
2016	South	07BM35	2	6	25965	864.7468
2016	South	07BM35	1	1	26362	825.5382
2016	South	07BM35	2	3	26362	893.5237
2016	South	07BM35	1	4	26742	866.3506
2016	South	07BM35	2	2	26742	814.2393
2016	South	07BM35	1	2	26777	860.7396
2016	South	07BM35	2	3	26777	906.0417
2016	South	07BM35	1	5	27110	781.9599
2016	South	07BM35	2	4	27110	956.3070
2016	South	07BM35	1	5	27125	818.9734
2016	South	07BM35	2	6	27125	880.7214
2016	South	07BM35	1	6	27130	775.6578
2016	South	07BM35	2	1	27130	892.6528
2016	South	07BM35	1	6	27543	854.4061
2016	South	07BM35	2	2	27543	893.2428
2016	South	07BM35	1	2	27546	842.3095
2016	South	07BM35	2	6	27546	907.1026
2016	South	07BM35	1	3	27548	908.1135
2016	South	07BM35	2	4	27548	908.1135
2016	South	07BM35	1	4	27590	865.5855
2016	South	07BM35	2	3	27590	925.1026
2016	South	07BM35	1	3	27592	823.8256
2016	South	07BM35	2	1	27592	782.3100
2016	South	07BM35	1	3	27593	916.7386
2016	South	07BM35	2	6	27593	860.4533
2016	South	07BM35	1	2	27599	916.5340
2016	South	07BM35	2	5	27599	956.0733
2016	South	07BM35	1	1	27600	901.7224
2016	South	07BM35	2	5	27600	901.7224
2016	South	07BM35	1	3	27605	843.7386
2016	South	07BM35	2	2	27605	856.7192
2016	South	07BM35	1	4	27609	256.9020
2016	South	07BM35	2	5	27609	345.2121
2016	South	07BM35	1	6	27669	687.8432
2016	South	07BM35	2	3	27669	933.3164
2016	South	07BM35	1	3	28128	936.1370
2016	South	07BM35	2	3	28128	994.6456
2016	South	07BM35	1	6	28209	1018.5923
2016	South	07BM35	2	5	28209	892.4809
2016	South	07BM35	1	4	28949	912.4263
2016	South	07BM35	2	4	28949	1035.3774
2016	South	07BM35	1	2	28950	568.7687
2016	South	07BM35	2	1	28950	676.2028
2016	South	07BM35	1	5	28954	681.5439
2016	South	07BM35	2	2	28954	850.7993
2016	Middle	07BM36	1	1	22455	553.0173
2016	Middle	07BM36	2	2	22455	610.7952
2016	Middle	07BM36	1	2	23286	597.8606
2016	Middle	07BM36	2	2	23286	643.3725
2016	Middle	07BM36	1	1	23524	501.4287
2016	Middle	07BM36	2	5	23524	563.8472
2016	Middle	07BM36	1	2	24054	623.8858
2016	Middle	07BM36	2	6	24054	671.5581
2016	Middle	07BM36	1	6	24521	678.6435
2016	Middle	07BM36	2	6	24521	709.9655
2016	Middle	07BM36	1	4	24984	626.2297
2016	Middle	07BM36	2	1	24984	630.4326
2016	Middle	07BM36	1	4	25512	644.6927
2016	Middle	07BM36	2	5	25512	665.2243
2016	Middle	07BM36	1	5	25965	566.5412
2016	Middle	07BM36	2	3	25965	618.8051
2016	Middle	07BM36	1	6	26362	591.9179
2016	Middle	07BM36	2	3	26362	551.0959
2016	Middle	07BM36	1	3	26742	607.9852
2016	Middle	07BM36	2	2	26742	639.0048
2016	Middle	07BM36	1	1	26777	607.8192
2016	Middle	07BM36	2	1	26777	620.2660
2016	Middle	07BM36	1	1	27110	628.6755
2016	Middle	07BM36	2	4	27110	716.1072
2016	Middle	07BM36	1	1	27125	670.3496
2016	Middle	07BM36	2	4	27125	722.2342
2016	Middle	07BM36	1	2	27130	616.0721
2016	Middle	07BM36	2	1	27130	676.2273
2016	Middle	07BM36	1	6	27543	642.3044
2016	Middle	07BM36	2	6	27543	681.2941
2016	Middle	07BM36	1	4	27546	640.3022
2016	Middle	07BM36	2	6	27546	667.4159
2016	Middle	07BM36	1	5	27548	574.9997
2016	Middle	07BM36	2	4	27548	604.0610
2016	Middle	07BM36	1	5	27590	620.4089
2016	Middle	07BM36	2	2	27590	587.4304
2016	Middle	07BM36	1	2	27592	648.2647
2016	Middle	07BM36	2	3	27592	675.2757
2016	Middle	07BM36	1	2	27593	573.2357
2016	Middle	07BM36	2	5	27593	641.2816
2016	Middle	07BM36	1	4	27599	663.6467
2016	Middle	07BM36	2	6	27599	673.8253
2016	Middle	07BM36	1	5	27600	685.7915
2016	Middle	07BM36	2	5	27600	687.8760
2016	Middle	07BM36	1	5	27605	624.9268
2016	Middle	07BM36	2	1	27605	577.1749
2016	Middle	07BM36	1	4	27609	592.0860
2016	Middle	07BM36	2	2	27609	548.6664
2016	Middle	07BM36	1	6	27669	683.3175
2016	Middle	07BM36	2	5	27669	683.3175
2016	Middle	07BM36	1	6	28128	653.1375
2016	Middle	07BM36	2	3	28128	657.3243
2016	Middle	07BM36	1	3	28209	656.8176
2016	Middle	07BM36	2	6	28209	677.3431
2016	Middle	07BM36	1	3	28949	708.7781
2016	Middle	07BM36	2	3	28949	630.7098
2016	Middle	07BM36	1	3	28950	663.7619
2016	Middle	07BM36	2	4	28950	712.8503
2016	Middle	07BM36	1	3	28954	621.4478
2016	Middle	07BM36	2	4	28954	627.6417
2016	Middle	07BM37	1	1	22455	471.4556
2016	Middle	07BM37	2	3	22455	524.3741
2016	Middle	07BM37	1	5	23286	514.7541
2016	Middle	07BM37	2	4	23286	528.7293
2016	Middle	07BM37	1	4	23524	421.7598
2016	Middle	07BM37	2	1	23524	531.2776
2016	Middle	07BM37	1	6	24054	550.8417
2016	Middle	07BM37	2	4	24054	627.4161
2016	Middle	07BM37	1	5	24521	533.4869
2016	Middle	07BM37	2	2	24521	595.5738
2016	Middle	07BM37	1	1	24984	458.7864
2016	Middle	07BM37	2	5	24984	533.6903
2016	Middle	07BM37	1	3	25512	533.6554
2016	Middle	07BM37	2	2	25512	568.9190
2016	Middle	07BM37	1	1	25965	442.0190
2016	Middle	07BM37	2	6	25965	593.2982
2016	Middle	07BM37	1	2	26362	436.9607
2016	Middle	07BM37	2	1	26362	575.6783
2016	Middle	07BM37	1	2	26742	615.1059
2016	Middle	07BM37	2	3	26742	499.3213
2016	Middle	07BM37	1	6	26777	533.7167
2016	Middle	07BM37	2	2	26777	579.3951
2016	Middle	07BM37	1	4	27110	649.9618
2016	Middle	07BM37	2	1	27110	667.4608
2016	Middle	07BM37	1	2	27125	627.9608
2016	Middle	07BM37	2	6	27125	645.1317
2016	Middle	07BM37	1	4	27130	544.2721
2016	Middle	07BM37	2	6	27130	530.2565
2016	Middle	07BM37	1	2	27543	560.9686
2016	Middle	07BM37	2	5	27543	584.5387
2016	Middle	07BM37	1	4	27546	505.6812
2016	Middle	07BM37	2	6	27546	615.9245
2016	Middle	07BM37	1	4	27548	453.0373
2016	Middle	07BM37	2	2	27548	492.3314
2016	Middle	07BM37	1	6	27590	456.6899
2016	Middle	07BM37	2	1	27590	565.6464
2016	Middle	07BM37	1	6	27592	526.1718
2016	Middle	07BM37	2	6	27592	580.6851
2016	Middle	07BM37	1	1	27593	572.7811
2016	Middle	07BM37	2	2	27593	649.7937
2016	Middle	07BM37	1	3	27599	607.1315
2016	Middle	07BM37	2	1	27599	646.7809
2016	Middle	07BM37	1	3	27600	679.5012
2016	Middle	07BM37	2	3	27600	707.2875
2016	Middle	07BM37	1	3	27605	463.8363
2016	Middle	07BM37	2	6	27605	548.3779
2016	Middle	07BM37	1	1	27609	326.7883
2016	Middle	07BM37	2	4	27609	336.6313
2016	Middle	07BM37	1	5	27669	684.0086
2016	Middle	07BM37	2	5	27669	644.7823
2016	Middle	07BM37	1	5	28128	539.2194
2016	Middle	07BM37	2	5	28128	532.0931
2016	Middle	07BM37	1	2	28209	636.1497
2016	Middle	07BM37	2	4	28209	664.5281
2016	Middle	07BM37	1	3	28949	509.2980
2016	Middle	07BM37	2	5	28949	553.2829
2016	Middle	07BM37	1	5	28950	485.6039
2016	Middle	07BM37	2	3	28950	508.7279
2016	Middle	07BM37	1	4	28954	523.0682
2016	Middle	07BM37	2	4	28954	608.6612
2016	North	07BM38	1	2	22455	960.3697
2016	North	07BM38	2	6	22455	886.4951
2016	North	07BM38	1	3	23286	990.4329
2016	North	07BM38	2	2	23286	995.3604
2016	North	07BM38	1	1	23524	866.0634
2016	North	07BM38	2	5	23524	811.9344
2016	North	07BM38	1	4	24054	1060.8452
2016	North	07BM38	2	1	24054	1065.7793
2016	North	07BM38	1	5	24521	1029.4521
2016	North	07BM38	2	3	24521	930.4664
2016	North	07BM38	1	2	24984	955.3176
2016	North	07BM38	2	2	24984	1004.5608
2016	North	07BM38	1	6	25512	956.6452
2016	North	07BM38	2	4	25512	883.0572
2016	North	07BM38	1	4	25965	1015.1403
2016	North	07BM38	2	4	25965	901.7994
2016	North	07BM38	1	6	26362	987.6855
2016	North	07BM38	2	6	26362	879.0401
2016	North	07BM38	1	6	26742	1026.2411
2016	North	07BM38	2	1	26742	991.5373
2016	North	07BM38	1	1	26777	917.2480
2016	North	07BM38	2	4	26777	838.3449
2016	North	07BM38	1	1	27110	953.8194
2016	North	07BM38	2	2	27110	1003.2401
2016	North	07BM38	1	3	27125	1065.0926
2016	North	07BM38	2	4	27125	931.9560
2016	North	07BM38	1	1	27130	957.0164
2016	North	07BM38	2	3	27130	952.0833
2016	North	07BM38	1	4	27543	1020.1931
2016	North	07BM38	2	2	27543	966.2406
2016	North	07BM38	1	3	27546	983.8944
2016	North	07BM38	2	6	27546	900.2634
2016	North	07BM38	1	2	27548	952.9790
2016	North	07BM38	2	4	27548	830.1724
2016	North	07BM38	1	5	27590	936.0363
2016	North	07BM38	2	4	27590	891.9299
2016	North	07BM38	1	6	27592	1007.7440
2016	North	07BM38	2	5	27592	929.0908
2016	North	07BM38	1	3	27593	1041.1583
2016	North	07BM38	2	3	27593	927.6671
2016	North	07BM38	1	3	27599	1033.3325
2016	North	07BM38	2	1	27599	1003.8087
2016	North	07BM38	1	1	27600	833.7998
2016	North	07BM38	2	1	27600	971.1316
2016	North	07BM38	1	4	27605	1024.2759
2016	North	07BM38	2	5	27605	872.3498
2016	North	07BM38	1	2	27609	984.5204
2016	North	07BM38	2	5	27609	886.0683
2016	North	07BM38	1	1	27669	1005.7263
2016	North	07BM38	2	6	27669	912.0557
2016	North	07BM38	1	4	28128	1061.1629
2016	North	07BM38	2	3	28128	967.3857
2016	North	07BM38	1	5	28209	990.6661
2016	North	07BM38	2	2	28209	1034.5872
2016	North	07BM38	1	5	28949	1077.4554
2016	North	07BM38	2	5	28949	993.8173
2016	North	07BM38	1	2	28950	995.1821
2016	North	07BM38	2	1	28950	1059.2284
2016	North	07BM38	1	6	28954	893.7093
2016	North	07BM38	2	3	28954	815.1414
2016	Middle	07BM39	1	1	22455	1145.7818
2016	Middle	07BM39	2	2	22455	1133.5492
2016	Middle	07BM39	4	1	22455
2016	Middle	07BM39	1	5	23286	1099.6956
2016	Middle	07BM39	2	3	23286	1117.8327
2016	Middle	07BM39	3	3	23286
2016	Middle	07BM39	4	2	23286
2016	Middle	07BM39	1	4	23524	1199.5640
2016	Middle	07BM39	2	1	23524	1191.6110
2016	Middle	07BM39	3	2	23524
2016	Middle	07BM39	4	8	23524
2016	Middle	07BM39	1	4	24054	1341.0520
2016	Middle	07BM39	2	4	24054	1267.3654
2016	Middle	07BM39	3	6	24054
2016	Middle	07BM39	4	3	24054
2016	Middle	07BM39	1	5	24521	1192.8820
2016	Middle	07BM39	2	1	24521	1178.9187
2016	Middle	07BM39	4	1	24521
2016	Middle	07BM39	1	6	24984	1211.0662
2016	Middle	07BM39	2	5	24984	1255.4843
2016	Middle	07BM39	4	6	24984
2016	Middle	07BM39	1	6	25512	1185.3151
2016	Middle	07BM39	2	4	25512	1167.5591
2016	Middle	07BM39	4	6	25512
2016	Middle	07BM39	1	3	25965	1225.8808
2016	Middle	07BM39	2	6	25965	1293.4922
2016	Middle	07BM39	4	1	25965
2016	Middle	07BM39	1	3	26362	1274.6901
2016	Middle	07BM39	2	2	26362	1168.3713
2016	Middle	07BM39	4	5	26362
2016	Middle	07BM39	1	1	26742	1136.4649
2016	Middle	07BM39	2	1	26742	1202.8711
2016	Middle	07BM39	4	3	26742
2016	Middle	07BM39	1	3	26777	1244.0348
2016	Middle	07BM39	2	5	26777	1205.9505
2016	Middle	07BM39	4	3	26777
2016	Middle	07BM39	1	2	27110	1248.8493
2016	Middle	07BM39	2	4	27110	1237.9888
2016	Middle	07BM39	4	2	27110
2016	Middle	07BM39	1	2	27125	1256.7511
2016	Middle	07BM39	2	6	27125	1207.9063
2016	Middle	07BM39	4	5	27125
2016	Middle	07BM39	1	3	27130	1248.8904
2016	Middle	07BM39	2	4	27130	1263.9516
2016	Middle	07BM39	4	2	27130
2016	Middle	07BM39	1	4	27543	1066.2678
2016	Middle	07BM39	2	3	27543	1105.6603
2016	Middle	07BM39	4	6	27543
2016	Middle	07BM39	1	6	27546	1187.6499
2016	Middle	07BM39	2	2	27546	1188.5481
2016	Middle	07BM39	4	4	27546
2016	Middle	07BM39	1	5	27548	1166.5517
2016	Middle	07BM39	2	5	27548	1169.4882
2016	Middle	07BM39	4	2	27548
2016	Middle	07BM39	1	1	27590	1180.8762
2016	Middle	07BM39	2	3	27590	1234.7731
2016	Middle	07BM39	4	3	27590
2016	Middle	07BM39	1	2	27592	1206.3984
2016	Middle	07BM39	2	5	27592	1178.5771
2016	Middle	07BM39	4	8	27592
2016	Middle	07BM39	1	1	27593	1187.0773
2016	Middle	07BM39	2	5	27593	1195.7752
2016	Middle	07BM39	4	8	27593
2016	Middle	07BM39	1	4	27599	1237.7353
2016	Middle	07BM39	2	5	27599	1223.8884
2016	Middle	07BM39	4	8	27599
2016	Middle	07BM39	1	2	27600	1183.4103
2016	Middle	07BM39	2	1	27600	1213.9695
2016	Middle	07BM39	4	5	27600
2016	Middle	07BM39	1	5	27605	1133.5459
2016	Middle	07BM39	2	6	27605	1147.4982
2016	Middle	07BM39	4	8	27605
2016	Middle	07BM39	1	3	27609	1256.0320
2016	Middle	07BM39	2	3	27609	1270.8387
2016	Middle	07BM39	4	5	27609
2016	Middle	07BM39	1	5	27669	1195.4497
2016	Middle	07BM39	2	4	27669	1187.9835
2016	Middle	07BM39	3	1	27669
2016	Middle	07BM39	1	4	28128	1228.4534
2016	Middle	07BM39	2	6	28128	1314.9562
2016	Middle	07BM39	4	4	28128
2016	Middle	07BM39	1	1	28209	1280.2065
2016	Middle	07BM39	2	6	28209	1206.5568
2016	Middle	07BM39	4	6	28209
2016	Middle	07BM39	1	6	28949	1286.3497
2016	Middle	07BM39	2	1	28949	1310.7443
2016	Middle	07BM39	4	6	28949
2016	Middle	07BM39	1	2	28950	1319.2708
2016	Middle	07BM39	2	2	28950	1287.1904
2016	Middle	07BM39	4	8	28950
2016	Middle	07BM39	1	6	28954	1213.3364
2016	Middle	07BM39	2	3	28954	1214.7907
2016	North	07BM40	1	2	22455	754.1164
2016	North	07BM40	2	3	22455	683.0615
2016	North	07BM40	1	4	23286	807.9155
2016	North	07BM40	2	5	23286	775.3043
2016	North	07BM40	1	6	23524	671.7081
2016	North	07BM40	2	4	23524	677.5214
2016	North	07BM40	1	1	24054	803.8051
2016	North	07BM40	2	6	24054	831.0883
2016	North	07BM40	1	3	24521	853.7184
2016	North	07BM40	2	4	24521	737.3262
2016	North	07BM40	1	4	24984	828.4827
2016	North	07BM40	2	1	24984	905.5264
2016	North	07BM40	1	3	25512	795.9042
2016	North	07BM40	2	6	25512	718.4452
2016	North	07BM40	1	6	25965	732.9555
2016	North	07BM40	2	1	25965	960.1505
2016	North	07BM40	1	3	26362	793.6519
2016	North	07BM40	2	1	26362	876.5708
2016	North	07BM40	1	1	26742	773.9077
2016	North	07BM40	2	4	26742	813.0203
2016	North	07BM40	1	1	26777	735.2090
2016	North	07BM40	2	3	26777	752.0861
2016	North	07BM40	1	5	27110	772.8934
2016	North	07BM40	2	6	27110	718.0669
2016	North	07BM40	1	2	27125	776.8068
2016	North	07BM40	2	6	27125	850.8634
2016	North	07BM40	1	5	27130	787.6371
2016	North	07BM40	2	5	27130	835.4523
2016	North	07BM40	1	1	27543	797.7993
2016	North	07BM40	2	2	27543	832.1349
2016	North	07BM40	1	3	27546	767.1929
2016	North	07BM40	2	5	27546	771.8773
2016	North	07BM40	1	1	27548	704.9474
2016	North	07BM40	2	1	27548	929.4862
2016	North	07BM40	1	2	27590	717.1058
2016	North	07BM40	2	2	27590	759.1968
2016	North	07BM40	1	5	27592	755.8966
2016	North	07BM40	2	4	27592	733.7728
2016	North	07BM40	1	6	27593	760.5080
2016	North	07BM40	2	3	27593	718.5778
2016	North	07BM40	1	6	27599	812.1260
2016	North	07BM40	2	5	27599	845.8134
2016	North	07BM40	1	5	27600	686.0075
2016	North	07BM40	2	2	27600	782.0071
2016	North	07BM40	1	1	27605	716.4749
2016	North	07BM40	2	5	27605	778.5483
2016	North	07BM40	1	4	27609	838.0706
2016	North	07BM40	2	6	27609	803.0651
2016	North	07BM40	1	2	27669	730.1855
2016	North	07BM40	2	1	27669	947.2392
2016	North	07BM40	1	2	28128	755.2169
2016	North	07BM40	2	4	28128	757.3147
2016	North	07BM40	1	4	28209	906.7811
2016	North	07BM40	2	2	28209	927.2271
2016	North	07BM40	1	6	28949	790.8603
2016	North	07BM40	2	2	28949	926.4066
2016	North	07BM40	1	3	28950	851.1403
2016	North	07BM40	2	3	28950	745.4742
2016	North	07BM40	1	5	28954	768.6542
2016	North	07BM40	2	3	28954	685.6983
2016	North	07BM41	1	6	22455	904.5432
2016	North	07BM41	2	2	22455	861.6964
2016	North	07BM41	1	5	23286	908.8877
2016	North	07BM41	2	3	23286	918.4049
2016	North	07BM41	1	2	23524	862.5361
2016	North	07BM41	2	4	23524	924.1458
2016	North	07BM41	1	3	24054	880.4003
2016	North	07BM41	2	6	24054	946.3126
2016	North	07BM41	1	4	24521	918.7473
2016	North	07BM41	2	3	24521	966.1054
2016	North	07BM41	1	5	24984	1010.3800
2016	North	07BM41	2	4	24984	1020.0027
2016	North	07BM41	1	4	25512	868.0104
2016	North	07BM41	2	4	25512	924.9291
2016	North	07BM41	1	1	25965	862.1046
2016	North	07BM41	2	4	25965	953.1046
2016	North	07BM41	1	5	26362	1030.1498
2016	North	07BM41	2	5	26362	1034.9190
2016	North	07BM41	1	2	26742	879.3119
2016	North	07BM41	2	3	26742	950.2242
2016	North	07BM41	1	6	26777	961.8560
2016	North	07BM41	2	1	26777	961.8560
2016	North	07BM41	1	3	27110	871.6056
2016	North	07BM41	2	2	27110	908.8935
2016	North	07BM41	1	3	27125	922.5012
2016	North	07BM41	2	1	27125	1013.3174
2016	North	07BM41	1	1	27130	779.3850
2016	North	07BM41	2	3	27130	926.7078
2016	North	07BM41	1	5	27543	904.9481
2016	North	07BM41	2	1	27543	923.8998
2016	North	07BM41	1	2	27546	892.7070
2016	North	07BM41	2	6	27546
2016	North	07BM41	1	6	27548	960.1654
2016	North	07BM41	2	6	27548	955.3885
2016	North	07BM41	1	6	27590	976.8157
2016	North	07BM41	2	3	27590	938.5092
2016	North	07BM41	1	4	27592	812.0844
2016	North	07BM41	2	1	27592	926.7316
2016	North	07BM41	1	4	27593	863.7743
2016	North	07BM41	2	5	27593	982.4246
2016	North	07BM41	1	2	27599	876.2602
2016	North	07BM41	2	2	27599	933.0987
2016	North	07BM41	1	5	27600	913.5100
2016	North	07BM41	2	2	27600	927.7836
2016	North	07BM41	1	2	27605	874.7533
2016	North	07BM41	2	5	27605	997.6915
2016	North	07BM41	1	1	27609	811.5975
2016	North	07BM41	2	5	27609	995.6225
2016	North	07BM41	1	3	27669	901.7775
2016	North	07BM41	2	4	27669	944.9477
2016	North	07BM41	1	3	28128	957.0184
2016	North	07BM41	2	5	28128	1028.7948
2016	North	07BM41	1	5	28209	901.6835
2016	North	07BM41	2	6	28209	1010.8346
2016	North	07BM41	1	4	28949	831.6461
2016	North	07BM41	2	6	28949
2016	North	07BM41	1	6	28950	1062.4921
2016	North	07BM41	2	4	28950	1086.4221
2016	North	07BM41	1	1	28954	803.3780
2016	North	07BM41	2	1	28954	874.2642

Motivation

This chapter deals with a topic that may not be familiar to many readers, but it was very important to us before and during our PhD, which was in the field of biostatistics/data science for plant breeding and other agricultural fields. Therefore, we here give a very brief summary:

A two-stage analysis is really just that: Trying to analyze a dataset not via a single model (in a single step), but in two separate stages/steps, where the output of the first stage/model is the input for the second stage/model. The motivation for doing a two-stage analysis for us was ever so often that data from a multi-environment-trial (MET) needed to be analyzed. An environment here refers to a year-location-combination, so that when multiple trials are set up at multiple locations and/or over multiple years we have a MET. Strictly speaking, data from a MET does not necessarily call for a two-stage analysis, but can indeed often just be analyzed in a single-stage analysis. However, there are arguments that speak for a two-stage analysis, such as the lower amount of required computational power and more dynamic/intuitive analyses of the single environments. For more info see SOURCES.

Example

The example in this chapter is taken from Buntaran et al. (2020). It considers data from a multi-environment trial with winter wheat varieties. The trial took place in 2016 across 18 locations in Sweden. Dry matter yield was analyzed. All trials were laid out as \(\alpha\)-designs with two replicates. Within each replicate, there were five to seven incomplete blocks. Sweden is divided into three different agricultural zones: South, Middle, and North. A zone is represented by a number of locations. The set of cultivars was the same across locations.

Modelling in two stages

In Stage I, the cultivar means per location are estimated via best linear unbiased estimation (BLUE). This is done via fitting a linear mixed model separately for each location and taking the cultivar effect as fixed. Thus, we obtain one adjusted mean yield value for each cultivar at each location.

In Stage II, the cultivar means obtained in Stage II serve as the response and

In such a two-stage approach, the cultivar main effect should be taken as fixed in Stage I in order to avoid double shrinkage (Damesa et al., 2017; Piepho et al., 2012).

Stage I

nlme

in progress, but probably not possible (?)

lme4

in progress, but probably not possible (?)

glmmTMB

in progress, but probably not possible (?)

sommer

in progress, but probably not possible (?)

SAS

In order to analyze each location separately in SAS, we can use the BY statement. However, the dataset must then also be sorted accordingly - in this case by Zone Location.

In order to obtain the adjusted cultivar means, we take Cultivar as a fixed effect in the model and add the LSMEANS Cultivar; statement. Furthermore, adding ODS OUTPUT LSMeans = stageIout_CultivarMeans; saves the means into an object called stageIout_CultivarMeans.

PROC SORT DATA=winterwheat; BY Zone Location Cultivar Rep Alpha; RUN; PROC MIXED DATA=winterwheat LOGNOTE; BY Zone Location; CLASS Cultivar Rep Alpha; MODEL Yield = Cultivar / DDFM=KR; RANDOM Rep Rep*Alpha; LSMEANS Cultivar / COV; ODS OUTPUT LSMeans = stageIout_CultivarMeans; RUN;

Notice that we also add /COV; to the LSMEANS statement. This is necessary for the Smith’s weights weighting approach, as it provides us with the estimated covariance matrix of the adjusted means and saves it, together with the means, into the stageIout_CultivarMeans object.

Stage II

Unweighted (not recommended)

nlme

in progress

lme4

in progress

glmmTMB

in progress

sommer

in progress

SAS

in progress

Smith’s Weights

nlme

in progress, but probably not possible (?)

lme4

in progress, but probably not possible (?)

glmmTMB

in progress, but probably not possible (?)

sommer

in progress, but probably not possible (?)

SAS

At this point we can conveniently make use of a SAS-macro that is described in more detail in Damesa et al., 2017 and can be found in their supplemental material. Note that a copy of it can also be found on github which makes its use in SAS via URL very convenient:

FILENAME smith URL "https://raw.githubusercontent.com/SchmidtPaul/utilities/master/SAS%20macros/get_Smith_weights.sas"; %INCLUDE smith; %get_smith_weights(data=stageIout_CultivarMeans, entry=Cultivar, by=Zone, by2=Location, outL=stageIIin_CultivarMeans);

As can be seen, the macro %get_smith_weights basically needs the stageIout_CultivarMeans object as input, the name of the (main) effect for which means were calculated (i.e. Cultivar), as well as the variables that were used in the BY statement in Stage I. It then produces a stageIIin_CultivarMeans object that serves as the dataset in Stage II with an additional column weight_Smith with the desired weights.

There are three things to consider when modelling the Smith’s weights approach in SAS:

1. The WEIGHT weight_Smith; statement, which provides the name of the column that holds the weights

2. The REPEATED; statement must be provided, as it directly changes how the WEIGHT statement operates

3. The PARMS ...(1) /HOLD=n statement makes sure that the error variance is forced to be equal to 1. Notice that the number of parameters (and thus the number of (1) that are required in the statement) differ between models. However, there must always at least be one, i.e. the error variance, and it will always be the last one in the PARMS statement. In this case the model has 5 parameters, i.e. variance components for the random effects Cultivar, Zone:Cultivar, Zone:Location:Cultivar and Zone:Location and for the error term.

PROC MIXED DATA=stageIIin_CultivarMeans; CLASS Cultivar Zone Location; MODEL Estimate = Zone; WEIGHT weight_Smith; RANDOM Int Zone Zone*Location / SUB=Cultivar; RANDOM Zone*Location; REPEATED; PARMS (1)(1)(1)(1)(1) / HOLD=5; RUN;

This model then provides us with the Cultivar-BLUPs across all environments obtained in a two-stage analyses using Smith’s weights.

Fully Efficient Weighting

nlme

in progress, but probably not possible (?)

lme4

in progress, but probably not possible (?)

glmmTMB

in progress, but probably not possible (?)

sommer

in progress, but probably not possible (?)

SAS

At this point we can conveniently make use of a SAS-macro that is described in more detail in Damesa et al., 2017 and can be found in their supplemental material. Note that a copy of it can also be found on github which makes its use in SAS via URL very convenient:

FILENAME fullyeff URL "https://raw.githubusercontent.com/SchmidtPaul/utilities/master/SAS%20macros/get_one_big_omega.sas"; %INCLUDE fullyeff; %get_one_big_omega(data=stageIout_CultivarMeans, entry=Cultivar, by=Zone, by2=Location, outL=stageIIin_CultivarMeans);

As can be seen, the macro %get_one_big_omega basically needs the stageIout_CultivarMeans object as input, the name of the (main) effect for which means were calculated (i.e. Cultivar), as well as the variables that were used in the BY statement in Stage I. It then produces a stageIIin_CultivarMeans object that serves as the dataset in Stage II ….

There are two things to consider when modelling the fully efficient weighting approach in SAS:

1. The REPEATED; statement …

2. The PARMS ...(1) /HOLD=n statement makes sure that the error variance is forced to be equal to 1. Notice that the number of parameters (and thus the number of (1) that are required in the statement) differ between models. However, there must always at least be one, i.e. the error variance, and it will always be the last one in the PARMS statement. In this case the model has 5 parameters, i.e. variance components for the random effects Cultivar, Zone:Cultivar, Zone:Location:Cultivar and Zone:Location and for the error term.

PROC MIXED DATA=stageIIin_CultivarMeans; CLASS Cultivar Zone Location row; MODEL Estimate = Zone /NOTEST; RANDOM Int Zone Zone*Location / SUB=Cultivar; RANDOM Zone*Location; REPEATED row / SUB=Zone*Location TYPE=lin(1) LDATA=stageIIin_CultivarMeans; PARMS (1)(1)(1)(1)(1) / HOLD=5; RUN;

 

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schmidtpaul1989@outlook.com