TABLE 1.
Simulation results for p = 100, q = 100, n = 600
| Method | numSNP | Estimation loss | Model error | True positive | False positive | MCC |
|---|---|---|---|---|---|---|
| IVGC | βk = 0.5, k = 1,…,10 | |||||
| 3 | 0.65 (0.31) | 0.33 (0.12) | 10 (0) | 4.67 (3.72) | 0.82 (0.11) | |
| 4 | 0.65 (0.30) | 0.35 (0.12) | 9.99 (0.07) | 4.05 (3.51) | 0.84 (0.11) | |
| 5 | 1.19 (1.22) | 0.55 (0.41) | 9.72 (0.96) | 3.35 (3.22) | 0.85 (0.11) | |
| βk ~ U (0.5, 1), k = 1,…,10 | ||||||
| 3 | 1.24 (0.35) | 0.57 (0.13) | 9.99 (0.07) | 4.5 (3.49) | 0.83 (0.11) | |
| 4 | 1.48 (0.40) | 0.69 (0.15) | 9.99 (0.07) | 4.00 (3.70) | 0.84 (0.11) | |
| 5 | 1.98 (1.64) | 0.90 (0.53) | 9.76 (0.87) | 2.96 (3.05) | 0.86 (0.12) | |
| IV | βk = 0.5, k = 1,…,10 | |||||
| 3 | 1.51 (0.4) | 0.64 (0.13) | 10 (0) | 5.09 (3.75) | 0.81 (0.11) | |
| 4 | 1.86 (0.47) | 0.77 (0.16) | 9.96 (0.18) | 4.26 (3.57) | 0.83 (0.11) | |
| 5 | 4.36 (0.78) | 1.59 (0.29) | 7.61 (1.01) | 3.68 (3.29) | 0.70 (0.13) | |
| βk ~ U (0.5, 1), k = 1,…,10 | ||||||
| 3 | 1.99 (0.60) | 0.85 (0.19) | 9.97 (0.16) | 5.30 (3.91) | 0.80 (0.11) | |
| 4 | 2.71 (0.71) | 1.12 (0.24) | 9.95 (0.23) | 4.75 (3.73) | 0.82 (0.11) | |
| 5 | 5.89 (1.29) | 2.22 (0.46) | 7.99 (1.01) | 2.92 (2.65) | 0.75 (0.12) | |
Abbreviation: IV, instrumental variable; IVGC, IV regression with graph-constrained regularization.
The numbers in the parentheses are the empirical SE.