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Table 4 Vector autoregressive model.

From: The impact of measurement errors in the identification of regulatory networks

EM

n

β 0

β 1

β 2

β 3

β 4

β 5

β 6

β 7

  

0

0

-0.1

-0.2

-0.3

-0.4

0.5

0.6

0

50

6.48

5.66

10.47

23.78

44.69

66.62

83.62

93.13

 

100

5.86

5.44

16.09

49.39

81.50

96.45

99.37

99.97

 

200

5.72

5.07

30.90

81.55

98.90

100.00

100.00

100.00

 

400

5.19

5.21

54.80

98.49

100.00

100.00

100.00

100.00

0.2

50

5.39 (6.64)

5.08 (5.40)

8.13 (8.80)

20.17 (20.78)

37.99 (38.41)

59.73 (59.74)

78.68 (75.96)

89.67 (87.72)

 

100

5.26 (6.17)

5.20 (5.20)

13.41 (14.65)

41.15 (42.79)

74.12 (75.29)

93.39 (93.78)

98.84 (98.60)

99.91 (99.91)

 

200

4.84 (5.50)

5.22 (5.46)

24.19 (26.85)

73.89 (76.10)

97.15 (97.57)

99.91 (99.92)

100.0 (100.0)

100.0 (100.0)

 

400

5.72 (5.09)

5.53 (5.44)

44.73 (48.95)

96.59 (97.29)

99.97 (99.98)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

0.4

50

-

-

-

-

-

-

-

-

 

100

6.02 (6.48)

5.03 (5.15)

9.59 (11.39)

27.88 (31.93)

54.11 (57.93)

79.25 (81.32)

95.92 (93.17)

99.12 (98.03)

 

200

10.20 (5.79)

5.45 (4.97)

14.37 (19.86)

51.19 (58.67)

86.74 (90.40)

98.45 (98.90)

99.96 (99.88)

100.0 (100.0)

 

400

20.49 (5.52)

5.64 (5.06)

25.14 (36.21)

82.24 (88.42)

99.29 (99.66)

99.98 (100.0)

100.0 (100.0)

100.0 (100.0)

0.6

50

-

-

-

-

-

-

-

-

 

100

-

-

-

-

-

-

-

-

 

200

22.79 (5.39)

5.98 (5.14)

8.13 (13.65)

29.25 (39.74)

61.55 (70.80)

87.76 (91.46)

99.65 (98.34)

99.93 (99.68)

 

400

49.01 (5.36)

7.56 (4.97)

12.29 (24.33)

52.77 (69.83)

90.96 (95.68)

99.52 (99.83)

100.0 (100.0)

100.0 (100.0)

0.8

50

-

-

-

-

-

-

-

-

 

100

-

-

-

-

-

-

-

-

 

200

-

-

-

-

-

-

-

-

 

400

70.58 (5.49)

9.73 (5.29)

6.26 (15.25)

27.24 (46.89)

65.41 (81.53)

91.82 (96.48)

99.98 (99.45)

100.0 (99.45)

EM

n

β 8

β 9

      
  

0.7

0.8

      

0

50

97.52

99.20

      
 

100

100.00

100.00

      
 

200

100.00

100.00

      
 

400

100.00

100.00

      

0.2

50

96.11 (94.87)

98.44 (98.89)

      
 

100

100.0 (99.99)

100.0 (100.0)

      
 

200

100.0 (100.0)

100.0 (100.0)

      
 

400

100.0 (100.0)

100.0 (100.0)

      

0.4

50

-

-

      
 

100

99.89 (99.65)

99.99 (99.97)

      
 

200

100.0 (100.0)

100.0 (100.0)

      
 

400

100.0 (100.0)

100.0 (100.0)

      

0.6

50

-

-

      
 

100

-

-

      
 

200

100.0 (100.0)

100.0 (100.0)

      
 

400

100.0 (100.0)

100.0 (100.0)

      

0.8

50

-

-

      
 

100

-

-

      
 

200

-

-

      
 

400

100.0 (99.99)

100.0 (100.0)

      
  1. Percentage of the number of associations (rejected hypothesis) obtained using standard VAR and corrected VAR (between brackets) in 10,000 simulations. The first line contains the strength of association between predictors and response variables as described in simulation II. The rate of false-positives was controlled in 5%. In bold, are the rate of false-positives, i.e., the number of false-positives divided by the number of simulations. "-" means that it was not possible to calculate due to high measurement error when compared to sample's size. EM: Standard deviation of the Error of Measure. n: Number of samples. Notice that, in fact, the corrected VAR controls the rate of false positives in 5% in both cases, autoregressive (β0) and cross-autoregressive (β1) coefficients, while the usual VAR does not (values in bold).
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BMC Bioinformatics

ISSN: 1471-2105

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