# Table 1 Mean percentage reduction in average loss in estimates of covariance matrices (Σ G : genetic, Σ E : residual and Σ p : phenotypic).

Cov.1 Strategy2 Penalty
$P λ$ $P λ ℓ$ $P λ ℓ 2$ $P β a$ $P β b$ $P β c$ $P Σ$ $P Σ 2$ $P ρ$ $P ρ 2$
5 traits
Σ G V∞ 35.8 71.3 72.9 66.7 71.4 67.9 70.6 70.0 72.0 72.2
CV3 23.1 55.9 60.7 59.2 58.1 61.1 54.9 52.9 54.4 56.9
L5% 41.3 68.3 70.2 67.6 69.5 69.3 64.1 66.7 70.5 71.5
Σ E V∞ 57.9 43.4 61.6 59.3 60.9 59.7 13.3 54.2 37.3 60.0
CV3 14.1 26.7 44.3 38.7 36.0 39.6 10.7 43.0 22.8 40.9
L5% 43.6 35.0 55.9 54.2 54.1 54.0 7.2 51.4 33.2 55.7
Σ P V∞ 1.1 1.2 1.3 1.3 1.2 1.2 1.2 1.7 2.2 2.4
CV3 -0.4 0.4 0.5 0.3 0.1 0.3 0.2 0.1 0.4 0.8
L5% -0.7 0.7 0.8 0.5 0.5 0.5 0.3 1.0 1.0 1.2
9 traits
Σ G V∞ 48.4 64.8 68.4 65.3 68.9 66.7 64.0 62.8 71.3 73.3
L5% 24.1 67.5 67.7 65.4 66.5 66.4 68.0 67.7 69.5 69.4
Σ E V∞ 62.9 60.5 68.8 67.8 67.3 68.3 10.4 61.1 57.9 70.2
L5% 63.0 16.4 59.3 60.9 62.6 61.7 9.9 47.4 17.2 56.3
Σ P V∞ 1.3 1.9 1.9 2.0 1.8 2.0 1.2 1.7 2.5 3.0
L5% 1.2 0.5 1.1 1.2 1.3 1.2 0.6 0.7 1.1 1.2
1. Data for s = 100 sire families; using different penalties and up to three strategies to determine the tuning factor (V∞: using population values, CV3: using 3-fold cross-validation, and L5%: limiting the change in log likelihood)
2. 1Covariance matrix
3. 2Method to determine the tuning factors