SAS Output

Page 1 of PLOT for Protein for BY group Treatment=1.

Page 1 of PLOT for Protein for BY group Treatment=2.

Page 1 of PLOT for Protein for BY group Treatment=3.

Milk Protein Content Analysis

Multivariate Model

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structure	Unstructured
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	190
Columns in X	80
Columns in Z	0
Subjects	79
Max Obs Per Subject	19

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	2	586.83922651	13296908336
2	1	373.86373119	0.26179605
3	1	322.69564043	0.19479639
4	1	66.13778684	0.10685576
5	1	-95.35447301	0.06150382
6	1	-194.95930375	0.03633165
7	1	-256.07343179	0.02116720
8	1	-292.36148946	0.01174013
9	1	-312.59927455	0.00591523
10	1	-322.73177019	0.00252867
11	1	-326.99217575	0.00086760
12	1	-328.43239970	0.00026980
13	1	-328.87620749	0.00008268
14	1	-329.01165998	0.00001907
15	1	-329.04126971	0.00000181
16	1	-329.04387045	0.00000002
17	1	-329.04390316	0.00000000

Convergence criteria met.

Estimated R Matrix for Cow(Treatment) 1 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7	Col8	Col9	Col10	Col11	Col12	Col13	Col14	Col15	Col16	Col17	Col18	Col19
1	0.1621	0.04831	0.04907	0.03288	0.04387	0.03025	0.02582	0.02804	0.02501	0.01618	0.007152	0.02462	0.02937	0.01017	-0.00854	0.02225	0.01941	0.004659	0.03357
2	0.04831	0.07465	0.03439	0.03584	0.04287	0.02832	0.02743	0.02931	0.03227	0.01719	0.01892	0.006132	0.02545	0.01402	0.006996	0.03929	0.04579	0.01641	0.03299
3	0.04907	0.03439	0.06658	0.03940	0.04970	0.02999	0.02440	0.03529	0.03193	0.009953	0.01421	0.008366	0.01095	0.004287	-0.00073	0.01011	0.02502	0.01803	0.03140
4	0.03288	0.03584	0.03940	0.06456	0.05832	0.04250	0.03684	0.05008	0.03731	0.01721	0.01509	0.003488	0.01494	0.003158	-0.00439	0.01728	0.03614	0.03035	0.03464
5	0.04387	0.04287	0.04970	0.05832	0.1119	0.05234	0.05059	0.07140	0.05736	0.02208	0.01661	0.009470	0.006363	-0.01499	-0.03175	0.01239	0.02271	0.01168	0.05101
6	0.03025	0.02832	0.02999	0.04250	0.05234	0.08662	0.04228	0.05009	0.04255	0.02358	-0.00190	0.003111	0.02266	0.006507	-0.01875	-0.00424	0.02327	0.01066	0.01867
7	0.02582	0.02743	0.02440	0.03684	0.05059	0.04228	0.05822	0.05215	0.04345	0.03526	0.02160	0.01218	0.02216	0.007344	-0.01227	-0.00624	0.01050	0.01091	0.01577
8	0.02804	0.02931	0.03529	0.05008	0.07140	0.05009	0.05215	0.09524	0.06275	0.04658	0.03596	0.02167	0.02796	0.009012	-0.01574	-0.00676	0.02228	0.007974	0.02609
9	0.02501	0.03227	0.03193	0.03731	0.05736	0.04255	0.04345	0.06275	0.08838	0.04611	0.03667	0.02078	0.02528	0.01642	-0.01036	-0.00138	0.01601	0.000559	0.01322
10	0.01618	0.01719	0.009953	0.01721	0.02208	0.02358	0.03526	0.04658	0.04611	0.07787	0.05144	0.03774	0.04093	0.04236	0.01247	-0.00331	0.01717	0.008761	0.002616
11	0.007152	0.01892	0.01421	0.01509	0.01661	-0.00190	0.02160	0.03596	0.03667	0.05144	0.09411	0.05291	0.04938	0.05571	0.05258	0.01049	0.02462	0.02130	-0.00272
12	0.02462	0.006132	0.008366	0.003488	0.009470	0.003111	0.01218	0.02167	0.02078	0.03774	0.05291	0.08081	0.05921	0.06169	0.05370	0.02284	0.01049	0.01634	0.01788
13	0.02937	0.02545	0.01095	0.01494	0.006363	0.02266	0.02216	0.02796	0.02528	0.04093	0.04938	0.05921	0.08294	0.07614	0.06490	0.03117	0.02548	0.03425	0.01882
14	0.01017	0.01402	0.004287	0.003158	-0.01499	0.006507	0.007344	0.009012	0.01642	0.04236	0.05571	0.06169	0.07614	0.1025	0.09242	0.02816	0.02205	0.04239	0.004249
15	-0.00854	0.006996	-0.00073	-0.00439	-0.03175	-0.01875	-0.01227	-0.01574	-0.01036	0.01247	0.05258	0.05370	0.06490	0.09242	0.1348	0.04643	0.01937	0.05525	0.009739
16	0.02225	0.03929	0.01011	0.01728	0.01239	-0.00424	-0.00624	-0.00676	-0.00138	-0.00331	0.01049	0.02284	0.03117	0.02816	0.04643	0.09892	0.05845	0.05096	0.06479
17	0.01941	0.04579	0.02502	0.03614	0.02271	0.02327	0.01050	0.02228	0.01601	0.01717	0.02462	0.01049	0.02548	0.02205	0.01937	0.05845	0.08208	0.05165	0.05569
18	0.004659	0.01641	0.01803	0.03035	0.01168	0.01066	0.01091	0.007974	0.000559	0.008761	0.02130	0.01634	0.03425	0.04239	0.05525	0.05096	0.05165	0.08082	0.05632
19	0.03357	0.03299	0.03140	0.03464	0.05101	0.01867	0.01577	0.02609	0.01322	0.002616	-0.00272	0.01788	0.01882	0.004249	0.009739	0.06479	0.05569	0.05632	0.09921

Estimated R Correlation Matrix for Cow(Treatment) 1 1
Row	Col1	Col2	Col3	Col4	Col5	Col6	Col7	Col8	Col9	Col10	Col11	Col12	Col13	Col14	Col15	Col16	Col17	Col18	Col19
1	1.0000	0.4392	0.4724	0.3214	0.3257	0.2553	0.2658	0.2256	0.2090	0.1440	0.05790	0.2151	0.2533	0.07892	-0.05774	0.1757	0.1683	0.04071	0.2647
2	0.4392	1.0000	0.4878	0.5163	0.4691	0.3522	0.4161	0.3476	0.3973	0.2255	0.2257	0.07896	0.3235	0.1603	0.06973	0.4572	0.5850	0.2112	0.3833
3	0.4724	0.4878	1.0000	0.6010	0.5758	0.3949	0.3919	0.4432	0.4163	0.1382	0.1795	0.1141	0.1474	0.05189	-0.00774	0.1245	0.3384	0.2458	0.3864
4	0.3214	0.5163	0.6010	1.0000	0.6862	0.5683	0.6008	0.6386	0.4939	0.2427	0.1936	0.04829	0.2041	0.03882	-0.04706	0.2163	0.4965	0.4201	0.4328
5	0.3257	0.4691	0.5758	0.6862	1.0000	0.5316	0.6268	0.6916	0.5768	0.2365	0.1618	0.09959	0.06604	-0.1399	-0.2585	0.1177	0.2370	0.1228	0.4841
6	0.2553	0.3522	0.3949	0.5683	0.5316	1.0000	0.5953	0.5514	0.4863	0.2871	-0.02105	0.03718	0.2673	0.06905	-0.1735	-0.04585	0.2760	0.1274	0.2014
7	0.2658	0.4161	0.3919	0.6008	0.6268	0.5953	1.0000	0.7003	0.6057	0.5237	0.2918	0.1776	0.3190	0.09506	-0.1385	-0.08227	0.1519	0.1590	0.2075
8	0.2256	0.3476	0.4432	0.6386	0.6916	0.5514	0.7003	1.0000	0.6840	0.5409	0.3798	0.2470	0.3146	0.09121	-0.1389	-0.06960	0.2521	0.09089	0.2684
9	0.2090	0.3973	0.4163	0.4939	0.5768	0.4863	0.6057	0.6840	1.0000	0.5558	0.4021	0.2459	0.2953	0.1725	-0.09492	-0.01471	0.1880	0.006617	0.1411
10	0.1440	0.2255	0.1382	0.2427	0.2365	0.2871	0.5237	0.5409	0.5558	1.0000	0.6009	0.4757	0.5093	0.4742	0.1217	-0.03777	0.2148	0.1104	0.02976
11	0.05790	0.2257	0.1795	0.1936	0.1618	-0.02105	0.2918	0.3798	0.4021	0.6009	1.0000	0.6067	0.5589	0.5672	0.4667	0.1087	0.2801	0.2442	-0.02816
12	0.2151	0.07896	0.1141	0.04829	0.09959	0.03718	0.1776	0.2470	0.2459	0.4757	0.6067	1.0000	0.7233	0.6778	0.5144	0.2554	0.1288	0.2022	0.1997
13	0.2533	0.3235	0.1474	0.2041	0.06604	0.2673	0.3190	0.3146	0.2953	0.5093	0.5589	0.7233	1.0000	0.8257	0.6137	0.3441	0.3088	0.4183	0.2074
14	0.07892	0.1603	0.05189	0.03882	-0.1399	0.06905	0.09506	0.09121	0.1725	0.4742	0.5672	0.6778	0.8257	1.0000	0.7861	0.2797	0.2404	0.4657	0.04214
15	-0.05774	0.06973	-0.00774	-0.04706	-0.2585	-0.1735	-0.1385	-0.1389	-0.09492	0.1217	0.4667	0.5144	0.6137	0.7861	1.0000	0.4021	0.1841	0.5293	0.08420
16	0.1757	0.4572	0.1245	0.2163	0.1177	-0.04585	-0.08227	-0.06960	-0.01471	-0.03777	0.1087	0.2554	0.3441	0.2797	0.4021	1.0000	0.6487	0.5699	0.6540
17	0.1683	0.5850	0.3384	0.4965	0.2370	0.2760	0.1519	0.2521	0.1880	0.2148	0.2801	0.1288	0.3088	0.2404	0.1841	0.6487	1.0000	0.6341	0.6172
18	0.04071	0.2112	0.2458	0.4201	0.1228	0.1274	0.1590	0.09089	0.006617	0.1104	0.2442	0.2022	0.4183	0.4657	0.5293	0.5699	0.6341	1.0000	0.6290
19	0.2647	0.3833	0.3864	0.4328	0.4841	0.2014	0.2075	0.2684	0.1411	0.02976	-0.02816	0.1997	0.2074	0.04214	0.08420	0.6540	0.6172	0.6290	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
UN(1,1)	Cow(Treatment)	0.1621
UN(2,1)	Cow(Treatment)	0.04831
UN(2,2)	Cow(Treatment)	0.07465
UN(3,1)	Cow(Treatment)	0.04907
UN(3,2)	Cow(Treatment)	0.03439
UN(3,3)	Cow(Treatment)	0.06658
UN(4,1)	Cow(Treatment)	0.03288
UN(4,2)	Cow(Treatment)	0.03584
UN(4,3)	Cow(Treatment)	0.03940
UN(4,4)	Cow(Treatment)	0.06456
UN(5,1)	Cow(Treatment)	0.04387
UN(5,2)	Cow(Treatment)	0.04287
UN(5,3)	Cow(Treatment)	0.04970
UN(5,4)	Cow(Treatment)	0.05832
UN(5,5)	Cow(Treatment)	0.1119
UN(6,1)	Cow(Treatment)	0.03025
UN(6,2)	Cow(Treatment)	0.02832
UN(6,3)	Cow(Treatment)	0.02999
UN(6,4)	Cow(Treatment)	0.04250
UN(6,5)	Cow(Treatment)	0.05234
UN(6,6)	Cow(Treatment)	0.08662
UN(7,1)	Cow(Treatment)	0.02582
UN(7,2)	Cow(Treatment)	0.02743
UN(7,3)	Cow(Treatment)	0.02440
UN(7,4)	Cow(Treatment)	0.03684
UN(7,5)	Cow(Treatment)	0.05059
UN(7,6)	Cow(Treatment)	0.04228
UN(7,7)	Cow(Treatment)	0.05822
UN(8,1)	Cow(Treatment)	0.02804
UN(8,2)	Cow(Treatment)	0.02931
UN(8,3)	Cow(Treatment)	0.03529
UN(8,4)	Cow(Treatment)	0.05008
UN(8,5)	Cow(Treatment)	0.07140
UN(8,6)	Cow(Treatment)	0.05009
UN(8,7)	Cow(Treatment)	0.05215
UN(8,8)	Cow(Treatment)	0.09524
UN(9,1)	Cow(Treatment)	0.02501
UN(9,2)	Cow(Treatment)	0.03227
UN(9,3)	Cow(Treatment)	0.03193
UN(9,4)	Cow(Treatment)	0.03731
UN(9,5)	Cow(Treatment)	0.05736
UN(9,6)	Cow(Treatment)	0.04255
UN(9,7)	Cow(Treatment)	0.04345
UN(9,8)	Cow(Treatment)	0.06275
UN(9,9)	Cow(Treatment)	0.08838
UN(10,1)	Cow(Treatment)	0.01618
UN(10,2)	Cow(Treatment)	0.01719
UN(10,3)	Cow(Treatment)	0.009953
UN(10,4)	Cow(Treatment)	0.01721
UN(10,5)	Cow(Treatment)	0.02208
UN(10,6)	Cow(Treatment)	0.02358
UN(10,7)	Cow(Treatment)	0.03526
UN(10,8)	Cow(Treatment)	0.04658
UN(10,9)	Cow(Treatment)	0.04611
UN(10,10)	Cow(Treatment)	0.07787
UN(11,1)	Cow(Treatment)	0.007152
UN(11,2)	Cow(Treatment)	0.01892
UN(11,3)	Cow(Treatment)	0.01421
UN(11,4)	Cow(Treatment)	0.01509
UN(11,5)	Cow(Treatment)	0.01661
UN(11,6)	Cow(Treatment)	-0.00190
UN(11,7)	Cow(Treatment)	0.02160
UN(11,8)	Cow(Treatment)	0.03596
UN(11,9)	Cow(Treatment)	0.03667
UN(11,10)	Cow(Treatment)	0.05144
UN(11,11)	Cow(Treatment)	0.09411
UN(12,1)	Cow(Treatment)	0.02462
UN(12,2)	Cow(Treatment)	0.006132
UN(12,3)	Cow(Treatment)	0.008366
UN(12,4)	Cow(Treatment)	0.003488
UN(12,5)	Cow(Treatment)	0.009470
UN(12,6)	Cow(Treatment)	0.003111
UN(12,7)	Cow(Treatment)	0.01218
UN(12,8)	Cow(Treatment)	0.02167
UN(12,9)	Cow(Treatment)	0.02078
UN(12,10)	Cow(Treatment)	0.03774
UN(12,11)	Cow(Treatment)	0.05291
UN(12,12)	Cow(Treatment)	0.08081
UN(13,1)	Cow(Treatment)	0.02937
UN(13,2)	Cow(Treatment)	0.02545
UN(13,3)	Cow(Treatment)	0.01095
UN(13,4)	Cow(Treatment)	0.01494
UN(13,5)	Cow(Treatment)	0.006363
UN(13,6)	Cow(Treatment)	0.02266
UN(13,7)	Cow(Treatment)	0.02216
UN(13,8)	Cow(Treatment)	0.02796
UN(13,9)	Cow(Treatment)	0.02528
UN(13,10)	Cow(Treatment)	0.04093
UN(13,11)	Cow(Treatment)	0.04938
UN(13,12)	Cow(Treatment)	0.05921
UN(13,13)	Cow(Treatment)	0.08294
UN(14,1)	Cow(Treatment)	0.01017
UN(14,2)	Cow(Treatment)	0.01402
UN(14,3)	Cow(Treatment)	0.004287
UN(14,4)	Cow(Treatment)	0.003158
UN(14,5)	Cow(Treatment)	-0.01499
UN(14,6)	Cow(Treatment)	0.006507
UN(14,7)	Cow(Treatment)	0.007344
UN(14,8)	Cow(Treatment)	0.009012
UN(14,9)	Cow(Treatment)	0.01642
UN(14,10)	Cow(Treatment)	0.04236
UN(14,11)	Cow(Treatment)	0.05571
UN(14,12)	Cow(Treatment)	0.06169
UN(14,13)	Cow(Treatment)	0.07614
UN(14,14)	Cow(Treatment)	0.1025
UN(15,1)	Cow(Treatment)	-0.00854
UN(15,2)	Cow(Treatment)	0.006996
UN(15,3)	Cow(Treatment)	-0.00073
UN(15,4)	Cow(Treatment)	-0.00439
UN(15,5)	Cow(Treatment)	-0.03175
UN(15,6)	Cow(Treatment)	-0.01875
UN(15,7)	Cow(Treatment)	-0.01227
UN(15,8)	Cow(Treatment)	-0.01574
UN(15,9)	Cow(Treatment)	-0.01036
UN(15,10)	Cow(Treatment)	0.01247
UN(15,11)	Cow(Treatment)	0.05258
UN(15,12)	Cow(Treatment)	0.05370
UN(15,13)	Cow(Treatment)	0.06490
UN(15,14)	Cow(Treatment)	0.09242
UN(15,15)	Cow(Treatment)	0.1348
UN(16,1)	Cow(Treatment)	0.02225
UN(16,2)	Cow(Treatment)	0.03929
UN(16,3)	Cow(Treatment)	0.01011
UN(16,4)	Cow(Treatment)	0.01728
UN(16,5)	Cow(Treatment)	0.01239
UN(16,6)	Cow(Treatment)	-0.00424
UN(16,7)	Cow(Treatment)	-0.00624
UN(16,8)	Cow(Treatment)	-0.00676
UN(16,9)	Cow(Treatment)	-0.00138
UN(16,10)	Cow(Treatment)	-0.00331
UN(16,11)	Cow(Treatment)	0.01049
UN(16,12)	Cow(Treatment)	0.02284
UN(16,13)	Cow(Treatment)	0.03117
UN(16,14)	Cow(Treatment)	0.02816
UN(16,15)	Cow(Treatment)	0.04643
UN(16,16)	Cow(Treatment)	0.09892
UN(17,1)	Cow(Treatment)	0.01941
UN(17,2)	Cow(Treatment)	0.04579
UN(17,3)	Cow(Treatment)	0.02502
UN(17,4)	Cow(Treatment)	0.03614
UN(17,5)	Cow(Treatment)	0.02271
UN(17,6)	Cow(Treatment)	0.02327
UN(17,7)	Cow(Treatment)	0.01050
UN(17,8)	Cow(Treatment)	0.02228
UN(17,9)	Cow(Treatment)	0.01601
UN(17,10)	Cow(Treatment)	0.01717
UN(17,11)	Cow(Treatment)	0.02462
UN(17,12)	Cow(Treatment)	0.01049
UN(17,13)	Cow(Treatment)	0.02548
UN(17,14)	Cow(Treatment)	0.02205
UN(17,15)	Cow(Treatment)	0.01937
UN(17,16)	Cow(Treatment)	0.05845
UN(17,17)	Cow(Treatment)	0.08208
UN(18,1)	Cow(Treatment)	0.004659
UN(18,2)	Cow(Treatment)	0.01641
UN(18,3)	Cow(Treatment)	0.01803
UN(18,4)	Cow(Treatment)	0.03035
UN(18,5)	Cow(Treatment)	0.01168
UN(18,6)	Cow(Treatment)	0.01066
UN(18,7)	Cow(Treatment)	0.01091
UN(18,8)	Cow(Treatment)	0.007974
UN(18,9)	Cow(Treatment)	0.000559
UN(18,10)	Cow(Treatment)	0.008761
UN(18,11)	Cow(Treatment)	0.02130
UN(18,12)	Cow(Treatment)	0.01634
UN(18,13)	Cow(Treatment)	0.03425
UN(18,14)	Cow(Treatment)	0.04239
UN(18,15)	Cow(Treatment)	0.05525
UN(18,16)	Cow(Treatment)	0.05096
UN(18,17)	Cow(Treatment)	0.05165
UN(18,18)	Cow(Treatment)	0.08082
UN(19,1)	Cow(Treatment)	0.03357
UN(19,2)	Cow(Treatment)	0.03299
UN(19,3)	Cow(Treatment)	0.03140
UN(19,4)	Cow(Treatment)	0.03464
UN(19,5)	Cow(Treatment)	0.05101
UN(19,6)	Cow(Treatment)	0.01867
UN(19,7)	Cow(Treatment)	0.01577
UN(19,8)	Cow(Treatment)	0.02609
UN(19,9)	Cow(Treatment)	0.01322
UN(19,10)	Cow(Treatment)	0.002616
UN(19,11)	Cow(Treatment)	-0.00272
UN(19,12)	Cow(Treatment)	0.01788
UN(19,13)	Cow(Treatment)	0.01882
UN(19,14)	Cow(Treatment)	0.004249
UN(19,15)	Cow(Treatment)	0.009739
UN(19,16)	Cow(Treatment)	0.06479
UN(19,17)	Cow(Treatment)	0.05569
UN(19,18)	Cow(Treatment)	0.05632
UN(19,19)	Cow(Treatment)	0.09921

Fit Statistics
-2 Res Log Likelihood	-329.0
AIC (smaller is better)	51.0
AICC (smaller is better)	117.6
BIC (smaller is better)	501.2

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
189	1062.52	<.0001

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Treatment	2	70.7	10.22	0.0001
Week	18	35.7	8.66	<.0001
Treatment*Week	36	61.5	0.80	0.7594

Type 3 Hotelling-Lawley-McKeon Statistics
Effect	Num DF	Den DF	F Value	Pr > F
Week	18	59	10.81	<.0001
Treatment*Week	36	102	1.07	0.3819

Contrasts
Label	Num DF	Den DF	F Value	Pr > F
Barley vs Barley+Lupins	1	70.4	5.20	0.0257
Lupins vs Barley+Lupins	1	71	5.22	0.0253
Barley vs Lupins	1	70.7	20.43	<.0001

Milk Protein Content Analysis

Homogeneous Variance Compound Symmetry

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structure	Compound Symmetry
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	2
Columns in X	80
Columns in Z	0
Subjects	79
Max Obs Per Subject	19

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	2	427.52217160	0.00000104
2	1	427.52116565	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
CS	Cow(Treatment)	0.02833
Residual		0.06261

Fit Statistics
-2 Res Log Likelihood	427.5
AIC (smaller is better)	431.5
AICC (smaller is better)	431.5
BIC (smaller is better)	436.3

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	305.96	<.0001

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Treatment	2	76.7	9.19	0.0003
Week	18	1206	16.33	<.0001
Treatment*Week	36	1206	0.67	0.9360

Contrasts
Label	Num DF	Den DF	F Value	Pr > F
Barley vs Barley+Lupins	1	76.5	3.80	0.0548
Lupins vs Barley+Lupins	1	76.8	5.63	0.0201
Barley vs Lupins	1	76.7	18.29	<.0001

Milk Protein Content Analysis

Homogeneous Variance First-order Autoregressive

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structures	Variance Components, Autoregressive
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	3
Columns in X	80
Columns in Z	79
Subjects	1
Max Obs Per Subject	1501

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	3	126.92018363	0.00008740
2	1	126.83032515	0.00000099
3	1	126.82921389	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Cow(Treatment)		0.01838
AR(1)	Cow(Treatment)	0.5646
Residual		0.07662

Fit Statistics
-2 Res Log Likelihood	126.8
AIC (smaller is better)	132.8
AICC (smaller is better)	132.8
BIC (smaller is better)	139.9

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Treatment	2	77.4	9.12	0.0003
Week	18	1074	13.63	<.0001
Treatment*Week	36	1120	0.84	0.7340

Contrasts
Label	Num DF	Den DF	F Value	Pr > F
Barley vs Barley+Lupins	1	77	4.06	0.0475
Lupins vs Barley+Lupins	1	77.7	5.27	0.0244
Barley vs Lupins	1	77.4	18.19	<.0001

Milk Protein Content Analysis

Homogeneous Variance Toeplitz

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structure	Toeplitz
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	Profile
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	19
Columns in X	80
Columns in Z	0
Subjects	79
Max Obs Per Subject	19

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	2	47.11318133	0.01947966
2	1	20.44774678	0.00665614
3	1	11.44408368	0.00109281
4	1	10.01603821	0.00005429
5	1	9.95000492	0.00000020
6	1	9.94976484	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
TOEP(2)	Cow(Treatment)	0.06216
TOEP(3)	Cow(Treatment)	0.05374
TOEP(4)	Cow(Treatment)	0.04807
TOEP(5)	Cow(Treatment)	0.03981
TOEP(6)	Cow(Treatment)	0.02696
TOEP(7)	Cow(Treatment)	0.01984
TOEP(8)	Cow(Treatment)	0.01745
TOEP(9)	Cow(Treatment)	0.009548
TOEP(10)	Cow(Treatment)	0.005451
TOEP(11)	Cow(Treatment)	0.004145
TOEP(12)	Cow(Treatment)	0.01370
TOEP(13)	Cow(Treatment)	0.01331
TOEP(14)	Cow(Treatment)	0.01379
TOEP(15)	Cow(Treatment)	0.02167
TOEP(16)	Cow(Treatment)	0.01840
TOEP(17)	Cow(Treatment)	0.01488
TOEP(18)	Cow(Treatment)	0.01211
TOEP(19)	Cow(Treatment)	0.01391
Residual		0.09562

Fit Statistics
-2 Res Log Likelihood	9.9
AIC (smaller is better)	47.9
AICC (smaller is better)	48.6
BIC (smaller is better)	93.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
18	723.53	<.0001

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Treatment	2	76	9.10	0.0003
Week	18	484	18.08	<.0001
Treatment*Week	36	661	0.90	0.6400

Contrasts
Label	Num DF	Den DF	F Value	Pr > F
Barley vs Barley+Lupins	1	75.7	4.28	0.0419
Lupins vs Barley+Lupins	1	76.2	5.00	0.0282
Barley vs Lupins	1	76	18.17	<.0001

Milk Protein Content Analysis

Heterogeneous Variance Compound Symmetry

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structure	Heterogeneous Compound Symmetry
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	20
Columns in X	80
Columns in Z	0
Subjects	79
Max Obs Per Subject	19

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	2	366.76734970	0.00011759
2	1	366.64593128	0.00000052
3	1	366.64541370	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Var(1)	Cow(Treatment)	0.1793
Var(2)	Cow(Treatment)	0.07249
Var(3)	Cow(Treatment)	0.06636
Var(4)	Cow(Treatment)	0.05950
Var(5)	Cow(Treatment)	0.1076
Var(6)	Cow(Treatment)	0.09005
Var(7)	Cow(Treatment)	0.05398
Var(8)	Cow(Treatment)	0.08647
Var(9)	Cow(Treatment)	0.08501
Var(10)	Cow(Treatment)	0.07689
Var(11)	Cow(Treatment)	0.09706
Var(12)	Cow(Treatment)	0.08553
Var(13)	Cow(Treatment)	0.08036
Var(14)	Cow(Treatment)	0.1107
Var(15)	Cow(Treatment)	0.1152
Var(16)	Cow(Treatment)	0.1265
Var(17)	Cow(Treatment)	0.08503
Var(18)	Cow(Treatment)	0.09110
Var(19)	Cow(Treatment)	0.1044
CSH	Cow(Treatment)	0.3294

Fit Statistics
-2 Res Log Likelihood	366.6
AIC (smaller is better)	406.6
AICC (smaller is better)	407.3
BIC (smaller is better)	454.0

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
19	366.83	<.0001

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
Treatment	2	76	8.52	0.0005
Week	18	461	10.81	<.0001
Treatment*Week	36	630	0.72	0.8912

Contrasts
Label	Num DF	Den DF	F Value	Pr > F
Barley vs Barley+Lupins	1	75.9	3.51	0.0650
Lupins vs Barley+Lupins	1	76.2	5.24	0.0248
Barley vs Lupins	1	76.1	16.95	<.0001

Milk Protein Content Analysis

Heterogeneous Variance First-order Autoregressive

The Mixed Procedure

Model Information
Data Set	WORK.MILK
Dependent Variable	Protein
Covariance Structures	Variance Components, Heterogeneous Autoregressive
Subject Effect	Cow(Treatment)
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Prasad-Rao-Jeske-Kackar-Harville
Degrees of Freedom Method	Kenward-Roger

Class Level Information
Class	Levels	Values
Cow	79	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
Treatment	3	1 2 3
Week	19	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Dimensions
Covariance Parameters	21
Columns in X	80
Columns in Z	79
Subjects	1
Max Obs Per Subject	1501

Number of Observations
Number of Observations Read	1501
Number of Observations Used	1337
Number of Observations Not Used	164

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	733.47680176
1	2	51.32810427	0.00702647
2	1	41.73059104	0.00107803
3	1	40.33761697	0.00004744
4	1	40.28100325	0.00000012
5	1	40.28086190	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Cow(Treatment)		0.02192
Var(1)	Cow(Treatment)	0.1773
Var(2)	Cow(Treatment)	0.07272
Var(3)	Cow(Treatment)	0.07017
Var(4)	Cow(Treatment)	0.04628
Var(5)	Cow(Treatment)	0.09874
Var(6)	Cow(Treatment)	0.07963
Var(7)	Cow(Treatment)	0.04430
Var(8)	Cow(Treatment)	0.06999
Var(9)	Cow(Treatment)	0.07623
Var(10)	Cow(Treatment)	0.06865
Var(11)	Cow(Treatment)	0.08127
Var(12)	Cow(Treatment)	0.06403
Var(13)	Cow(Treatment)	0.04270
Var(14)	Cow(Treatment)	0.06181
Var(15)	Cow(Treatment)	0.08725
Var(16)	Cow(Treatment)	0.09719
Var(17)	Cow(Treatment)	0.05388
Var(18)	Cow(Treatment)	0.05086
Var(19)	Cow(Treatment)	0.06662
ARH(1)	Cow(Treatment)	0.5625

Fit Statistics
-2 Res Log Likelihood	40.3
AIC (smaller is better)	82.3
AICC (smaller is better)	83.0
BIC (smaller is better)