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

From: Performance of penalized maximum likelihood in estimation of genetic covariances matrices

Cov.1

Strategy2

Penalty

  

P λ

P λ

P λ 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