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# Table 3 Estimates of variances (diagonals), co-variances (above the diagonal), and correlations (below the diagonal) between the random regression coefficients, along with the two eigenvalues (λ) and the relative proportions of variance that they explain (%)

Additive genetic Herd Permanent environment Average residual*
$${\alpha }_{0}$$ $${\alpha }_{1}$$ $${\alpha }_{0}$$ $${\alpha }_{1}$$ $${\alpha }_{0}$$ $${\alpha }_{1}$$
Model 3 using adjusted TD from Model 1
$${\alpha }_{0}$$ 1.097 (0.210) − 0.093 (0.062) 3.584 (0.171) − 0.349 (0.049) 2.908 (0.194) − 0.357 (0.064) 1.169
$${\alpha }_{1}$$ − 0.345 (0.211) 0.067 (0.036) − 0.355 (0.04) 0.270 (0.026) − 0.228 (0.038) 0.842 (0.043)
λ (%) 1.11 (94.98) 0.06 (5.02) 3.62 (93.93) 0.23 (6.07) 2.97 (79.15) 0.78 (20.85)
Model 3 using adjusted TD from Model 2-M1
$${\alpha }_{0}$$ 1.256 (0.227) − 0.105 (0.063) 4.063 (0.185) − 0.357 (0.048) 2.854 (0.204) − 0.331 (0.063) 1.072
$${\alpha }_{1}$$ − 0.357 (0.195) 0.069 (0.033) − 0.364 (0.043) 0.237 (0.023) − 0.229 (0.040) 0.734 (0.038)
λ (%) 1.27 (95.50) 0.06 (4.50) 4.10 (95.26) 0.20(4.74) 2.90 (80.95) 0.68 (19.05)
Model 4 using adjusted TD from Model 2-M2
$${\alpha }_{0}$$ 0.470 (0.105) − 0.094 (0.048) 2.321 (0.102) − 0.299 (0.048) 1.073
$${\alpha }_{1}$$ − 0.346 (0.158) 0.158 (0.042) − 0.210 (0.031) 0.867 (0.043)
λ (%) 0.50 (78.98) 0.13 (21.02) 2.38 (74.64) 0.81 (25.36)
Model 3: BC*ENV in the genetic analysis
$${\alpha }_{0}$$ 1.562 (0.233) − 0.149 (0.066) 2.875 (0.151) − 0.303 (0.043) 2.575 (0.200) − 0.289 (0.063) 1.072
$${\alpha }_{1}$$ − 0.459 (0.184) 0.068 (0.033) − 0.369 (0.046) 0.235 (0.023) − 0.211 (0.043) 0.734 (0.038)
λ (%) 1.58 (96.75) 0.05 (3.25) 2.91 (93.54) 0.20 (6.46) 2.62 (79.16) 0.69 (20.84)
Model 3: BC*ENV in the phenotype analysis
$${\alpha }_{0}$$ 0.642 (0.170) − 0.091 (0.057) 1.010 (0.081) − 0.088 (0.031) 3.034 (0.165) − 0.293 (0.058) 1.073
$${\alpha }_{1}$$ − 0.388 (0.214) 0.085 (0.034) − 0.182 (0.062) 0.228 (0.023) − 0.199 (0.037) 0.719 (0.038)
λ (%) 0.66 (90.30) 0.07 (9.70) 1.02 (82.33) 0.22 (17.67) 3.07 (81.83) 0.68 (18.17)
1. *Average of residual variance estimates for the eight lactation period classes: 8–49, 50–91, 92–133, 134–175, 176–217, 218–259, 260–301, and 302–340 days of lactation. The estimates of residual variances are for test-day milk yield in kg/dayay, whereas the genetic, PE, and herd variances are on the LP scale. The standard error of the estimates is given in brackets