Page 307 - Linear Models for the Prediction of Animal Breeding Values

SOLVING FOR PERMANENT ENVIRONMENTAL (pe) EFFECTS. Only the data file sorted by dams
is required to obtain solutions for pe effects.
The records for the tth dam are read from file C while ARHS and DIAG are
accumulated as:
ˆ
ˆ
−1
ˆ
ˆ
ARHS = ARHS + r (y − hd − b − u − m )
t t pa ijklt i j k l
for parent records and:
ˆ
ˆ
ˆ
ARHS = ARHS + r −1 (y − hd − b − 0.5(u + u ) − m )
ˆ
ˆ
t t np ijklt i j s d l
for non-parent records.
DIAG = DIAG + r −1
t t n
At the end of records for the tth dam, solutions are computed as:
2
p ˆ e = ARHS /(DIAG + 1/s )
t t t p
The solution for permanent environmental effect for animal 5 in the first round of
iteration is:
ˆ
ˆ
ARHS = r (y − hd − b − uˆ − mˆ )
−1
5 pa 8 1 1 8 5
= r (40 − 3.679 − 30.0 − 1.4822 − (−0.2246))
−1
pa
= 0.01459
DIAG = r + 0.025 = 0.02786
−1
5 pa
and:
p ˆ e = 0.01459/0.02786 = 0.524
5
Further iterations are carried out until convergence is achieved. The convergence
criteria defined in Section 17.3.1 could also be used. The solutions for the first round
of iteration and at convergence are shown below.
Solutions
Effects At round 1 At convergence
Herd
1 30.000 30.563
2 33.600 33.950
3 31.333 31.997
Sex of calf
Male 3.679 3.977
Female −2.657 −2.872
Animal
1 0.000 0.564
2 −1.729 −1.246
3 0.896 1.166
4 0.000 −0.484
5 −0.583 0.630
6 −0.554 −0.859
Continued

Solving Linear Equations 291