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ANSC*6370 - QG and Animal Breeding
Fall 2003 - Assignment 12

The data below are exactly as given in the notes, plus one additional cow (9 with parents 7 and 2), and shown below.

Cow	Visit	Age	Age Group	Obs.
1	1	22	1	224
2	1	30	2	244
3	1	28	1	224
1	2	34	2	236
2	2	42	3	247
3	2	40	3	242
4	2	20	1	220
1	3	47	3	239
2	3	55	4	241
4	3	33	2	234
2	4	66	4	244
4	4	44	3	228
9	4	25	1	217

Let the model be

$$\begin{eqnarray*}y_{ijkm:t} & = & V_{i} + AG_{j} \\ & & + (a_{k0}z_{0} + a_{k1... ...0}z_{0} + p_{k1} z_{1} + p_{k2} z_{2}) \\ & & + e_{ijkm:t} \\ \end{eqnarray*}$$

Thus, the model uses age groups (4 of them) in place of the fixed regressions to account for the shape of the phenotypic relationship between the observations and age.

Use the same parameters as given in the notes for ${\bf G}$and ${\bf P}$. The residual variance, however, will be different for each age group, as follows: 0.8 for age group 1, 0.92 for age group 2, 1.05 for age group 3, and 1.15 for age group 4. Thus, ${\bf R}$ is diagonal, but the diagonals differ depending on the age group to which the cow's observation belongs.

Construct the MME and solve. Calculate EBVs for age 24 months and rank the animals. Compare the age group solutions to the fixed regressions in the notes.

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