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Table 3 Mean relative bias (in %) in estimates of the i-th canonical eigenvalue and of the mean eigenvalue ( λ ¯ ) , and mean absolute bias in estimates of the i-th heritability (×100).

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

Penalty

q 1

i

None

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

Canonical eigenvalues

5

λ ̄

2.3

-5.4

6.6

2.1

3.4

-1.2

1.0

11.2

10.9

4.7

2.3

 

1

9.5

-12.9

-3.7

-9.6

-8.9

-12.9

-11.5

8.1

3.2

1.3

-3.0

 

2

26.5

16.1

16.3

16.1

24.7

19.5

19.5

24.9

26.3

16.2

15.5

 

4

-19.4

9.1

57.7

48.3

38.8

31.0

39.4

39.1

47.0

37.3

37.1

 

5

-78.8

-38.1

101.3

81.6

36.1

26.6

52.2

75.3

88.6

57.2

56.7

 

av.2

30.2

19.6

41.6

36.4

28.3

23.4

30.3

34.4

38.8

26.6

26.5

9

λ ̄

4.4

-9.9

9.5

3.2

11.8

0.8

7.2

19.7

18.2

6.3

2.5

 

1

22.4

-22.4

-3.8

-13.7

-6.9

-18.5

-12.7

21.6

8.8

2.9

-4.2

 

2

16.6

-17.5

-6.8

-10.0

0.5

-11.4

-6.2

16.1

11.0

-0.7

-3.1

 

8

-85.6

-16.4

139.4

111.7

80.8

77.8

104.4

87.5

110.1

86.5

82.2

 

9

-97.9

-35.0

270.1

217.5

133.2

134.0

190.5

184.1

217.0

133.4

131.7

 

av.

39.9

16.6

68.4

57.3

48.8

45.1

56.9

54.0

61.9

40.0

39.1

Heritabilities

5

1

-1.0

-9.1

-4.4

-7.8

-6.9

-8.3

-7.9

-0.7

-2.9

-1.9

-3.7

 

2

0.6

-3.4

0.0

-1.7

-1.1

-2.0

-1.7

2.2

1.4

-0.2

-1.4

 

4

0.9

0.2

3.2

2.2

2.5

2.0

2.1

4.1

4.3

1.0

0.5

 

5

1.1

1.2

4.6

3.6

3.7

3.2

3.4

5.1

5.4

1.6

1.3

 

av.

0.8

3.1

2.7

3.1

3.0

3.1

3.1

3.0

3.4

1.0

1.4

9

1

-0.5

-15.5

-6.8

-11.3

-7.6

-12.3

-10.0

0.9

-3.6

-2.0

-5.4

 

2

-0.1

-11.7

-4.8

-7.8

-4.5

-8.5

-6.6

1.9

-1.3

-1.8

-4.9

 

8

2.2

2.5

7.5

6.0

7.5

5.7

6.8

8.2

8.6

2.9

2.2

 

9

2.5

3.5

8.6

7.2

8.4

6.9

7.9

9.1

9.6

3.5

2.9

 

av.

1.3

5.4

4.8

4.8

4.9

5.0

4.9

5.4

5.1

1.9

2.5

  1. Data for s = 100 sire families; using different penalties (see text for notation) and population values to determine the tuning factor (strategy V∞)
  2. 1Number of traits
  3. 2Average of all q absolute values