| | |
Instrument strength
|
|---|
| | |
Weak
|
Mod
|
Strong
|
|---|
|
Level
|
Method
|
rB
|
sd
|
rMSE
|
pval
|
rB
|
sd
|
rMSE
|
pval
|
rB
|
sd
|
rMSE
|
pval
|
|---|
|
High
|
Tr
|
1.62
|
0.23
|
0.24
|
0.06
|
0.52
|
0.26
|
0.24
|
0.04
|
1.93
|
0.40
|
0.32
|
0.06
|
| |
Conv
|
46.14
|
0.23
|
1.40
|
1.00
|
42.40
|
0.26
|
1.29
|
1.00
|
39.62
|
0.39
|
1.23
|
1.00
|
| |
2SRI
|
14.98
|
0.66
|
0.85
|
0.13
|
9.41
|
0.47
|
0.53
|
0.09
|
8.49
|
0.44
|
0.53
|
0.10
|
| |
GMM
|
72.01
|
315.65
|
5.06
|
0.27
|
75.50
|
109.91
|
4.70
|
0.32
|
71.32
|
60.00
|
4.25
|
0.40
|
|
Med
|
Tr
|
0.58
|
0.25
|
0.23
|
0.05
|
1.25
|
0.31
|
0.30
|
0.07
|
1.61
|
0.48
|
0.32
|
0.04
|
| |
Conv
|
25.40
|
0.25
|
0.80
|
0.96
|
23.98
|
0.31
|
0.78
|
0.85
|
21.37
|
0.48
|
0.72
|
0.63
|
| |
2SRI
|
9.93
|
0.66
|
0.70
|
0.07
|
6.90
|
0.54
|
0.61
|
0.08
|
5.45
|
0.54
|
0.54
|
0.09
|
| |
GMM
|
36.76
|
47.90
|
43.89
|
0.40
|
32.85
|
32.04
|
2.17
|
0.51
|
44.82
|
41.87
|
3.36
|
0.35
|
|
Low
|
Tr
|
0.66
|
0.26
|
0.26
|
0.07
|
1.51
|
0.33
|
0.28
|
0.04
|
2.20
|
0.55
|
0.35
|
0.05
|
| |
Conv
|
7.86
|
0.26
|
0.35
|
0.15
|
7.96
|
0.33
|
0.37
|
0.11
|
7.72
|
0.55
|
0.41
|
0.10
|
| |
2SRI
|
6.43
|
0.71
|
0.74
|
0.07
|
5.76
|
0.64
|
0.62
|
0.06
|
5.91
|
0.66
|
0.67
|
0.10
|
| |
GMM
|
22.04
|
31.69
|
2.42
|
0.49
|
26.15
|
31.68
|
3.49
|
0.64
|
43.12
|
25.42
|
4.14
|
0.46
|
- Legend: Tr = True model, Conv = Conventional model, 2SRI = Two-Stage Residual Inclusion, GMM = Generalized Method of Moment. Low, Med (Medium), High denote the level of confounding whereas Weak, Mod (Moderate), Strong stand for instrument strength. For the criteria, rB= relative bias (%),sd= standard deviation, rMSE= root Mean Squares error and pval= non-coverage probabilities
