Page 150 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

where q′ is a vector of ones with size equal to the number of TD records for the ith
i
cow. The matrices Q′Q and Z′Z are both diagonal and equal. Thus:
Q′Q = Z′Z = diag[10, 10, 5, 7, 10]
−1
The matrix A has been given in Example 4.1. The remaining matrices in the
MME could be obtained as outlined in earlier chapters. Solving the MME, with the
solution for the 10th level of HTD effects constrained to zero, give the following results:

Effects Solutions
HTD
1 10.9783
2 7.9951
3 8.7031
4 8.2806
5 6.3813
6 3.1893
7 3.3099
8 3.3897
9 0.6751
10 0.0000
Fixed regression coefficients
1 16.3082
2 −0.5227
3 −0.1245
4 0.5355
5 −0.4195
Animal effect
EBV for daily yield EBV for 305-day yield
1 −0.3300 −100.6476
2 −0.1604 −48.9242
3 0.4904 149.5718
4 0.0043 1.3203
5 −0.2449 −74.7065
6 −0.8367 −255.2063
7 1.1477 350.0481
8 0.3786 115.4757
Permanent environmental effects
Cow Solutions for daily yield Solutions for daily yield
4 −0.6156 −187.7634
5 −0.4151 −126.6150
6 −1.6853 −514.0274
7 2.8089 856.7092
8 −0.0928 −28.3035
EBV, estimated breeding value.
The solutions for the fixed regressions are regression coefficients from which
plots of lactation curves can be obtained. In practice, the fixed regressions are usually
fitted within group of cows calving in the same season in the same parity and of simi-
lar age. Thus the curves obtained for various groups of cows are useful for examining
the influence of different environmental factors on lactation curves. In Example 9.1,

134 Chapter 9