Page 239 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

13.2.3 Numerical example

Example 13.1
The analysis of categorical traits is illustrated below, using the calving ease data
described by Gianola and Foulley (1983) but with a relationship matrix included for
the sires and the age of dam effect omitted from the model. The data consisted of
calving ease scores from 28 male and female calves born in two herd–years from cows
mated to four sires. Cows were scored for calving ease using three ordered categories:
1 = normal birth, 2 = slight difficulty and 3 = extreme difficulty. The data set is pre-
sented in Table 13.2.
The following pedigree was assumed for the four sires:

Animal Sire Dam

1 0 0
2 0 0
3 1 0
4 3 0

1
The sire variance used in the analysis was assumed to be 19 . In the underlying
2
2
2
2
2
scale, residual variance equals one; therefore, s /s = 4 − h /h = 19. Thus the s assumed
e s s
corresponded to a heritability of 0.20 on the underlying scale.
Table 13.2. Distribution of calving ease score by herd–year and sex of calf subclasses.
Category of response a
Sex of Sire of
Herd calf calf 1 2 3 Total
1 Male 1 1 0 0 1
1 Female 1 1 0 0 1
1 Male 1 1 0 0 1
1 Female 2 0 1 0 1
1 Male 2 1 0 1 2
1 Female 2 3 0 0 3
1 Male 3 1 1 0 2
1 Female 3 0 1 0 1
1 Male 3 1 0 0 1
2 Female 1 2 0 0 2
2 Male 1 1 0 0 1
2 Male 1 0 0 1 1
2 Female 2 1 0 1 2
2 Male 2 1 0 0 1
2 Female 3 0 1 0 1
2 Male 3 0 0 1 1
2 Male 4 0 1 0 1
2 Female 4 1 0 0 1
2 Female 4 2 0 0 2
2 Male 4 2 0 0 2
a 1, normal birth; 2, slight difficulty; 3, extreme difficulty.

Analysis of Ordered Categorical Traits 223