Page 250 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

13.3.2 Numerical application

Example 13.2
The bivariate analysis of a quantitative trait and a binary trait is illustrated using the
data presented by Foulley et al. (1983) but with a sire–maternal grandsire relationship
matrix included for the sires and pelvic opening omitted from the analysis. The data
consisted of birth weight (BW) and calving difficulty (CD) on 47 Blonde d’Aquitaine
heifers, with information on region of origin, sire of the heifer, calving season and sex
of the calf included. Calving difficulty was summarized into two categories: easy or
difficult calving. The data set is presented below:
Heifer Sex of Heifer Sex of
origin Sire Season calf BW CD a origin Sire Season calf BWT CD a
1 1 1 M 41.0 E 1 4 2 M 47.0 D
1 1 1 M 37.5 E 1 4 2 F 51.0 D
1 1 1 F 41.5 E 1 4 2 F 39.0 E
1 1 2 F 40.0 E 2 4 1 M 44.5 E
1 1 2 F 43.0 E 1 5 1 M 40.5 E
1 1 2 F 42.0 E 1 5 1 F 43.5 E
1 1 2 F 35.0 E 1 5 2 M 42.5 E
2 1 1 F 46.0 E 1 5 2 M 48.8 D
2 1 1 F 40.5 E 1 5 2 M 38.5 E
2 1 2 F 39.0 E 1 5 2 M 52.0 E
1 2 1 M 41.4 E 1 5 2 F 48.0 E
1 2 1 M 43.0 D 2 5 1 F 41.0 E
1 2 2 F 34.0 E 2 5 1 M 50.5 D
1 2 2 M 47.0 D 2 5 2 M 43.7 D
1 2 2 M 42.0 E 2 5 2 M 51.0 D
2 2 2 M 44.5 E 1 6 1 F 51.6 D
2 2 2 M 49.0 E 1 6 1 M 45.3 D
1 3 1 M 41.6 E 1 6 1 F 36.5 E
2 3 1 M 36.0 E 1 6 2 M 50.5 E
2 3 1 F 42.7 E 1 6 2 M 46.0 D
2 3 2 F 32.5 E 1 6 2 M 45.0 E
2 3 2 F 44.4 E 1 6 2 F 36.0 E
2 3 2 M 46.0 E 2 6 1 F 43.5 E
2 6 1 F 36.5 E
a CD, calving difficulty; D, difficulty, E, easy.

A summary of the data, in terms of marginal means of calving variables by level
of factors considered, is shown in the following table:

Factor Number Birth weight (kg) Frequency CD a
Heifer origin 1 30 43.02 0.267
2 17 43.02 0.176
Calving season 1 20 42.23 0.200
2 27 43.61 0.259
Continued

234 Chapter 13