Table 3:
Number of successful discoveries (100 trials)
| Sample size | |||
|---|---|---|---|
| 50 | 100 | 200 | |
| Number of latent confounders Q = 0: | |||
| Our approach (t-distributed individual-specific effects) | 88 (3.25) | 91 (2.86) | 86 (3.47) |
| Our approach (Gaussian individual-specific effects) | 91 (2.86) | 87 (3.36) | 91 (2.86) |
| LvLiNGAM (1 latent confounder) | 73 (4.44) | 83 (3.76) | 83 (3.76) |
| LvLiNGAM (4 latent confounders) | 52 (5.00) | 68 (4.66) | 66 (4.74) |
| SLIM (1 latent confounder) | 29 (4.54) | 30 (4.58) | 25 (4.33) |
| SLIM (4 latent confounders) | 34 (4.74) | 31 (4.62) | 36 (4.80) |
| SLIM (10 latent confounders) | 30 (4.58) | 29 (4.54) | 30 (4.58) |
| LiNGAM-GC-UK | 33 (4.70) | 28 (4.49) | 35 (4.77) |
| ICA-LiNGAM | 93 (2.55) | 93 (2.55) | 96 (i.96) |
| DirectLiNGAM | 87 (3.36) | 95 (2.18) | 97 (1.71) |
| Pairwise LiNGAM | 89 (3.13) | 95 (2.18) | 95 (2.18) |
| Post-nonlinear causal model | 74 (4.39) | 71 (4.54) | 75 (4.33) |
| Number of latent confounders Q = 1: | |||
| Our approach t-distributed individual-specific effects) | 83 (3.76) | 80 (4.00) | 80 (4.00) |
| Our approach Gaussian individual-specific effects) | 79 (4.07) | 87 (3.36) | 69 (4.62) |
| LvLiNGAM (1 latent confounder) | 66 (4.74) | 71 (4.54) | 73 (4.44) |
| LvLiNGAM 4 latent confounders) | 63 (4.83) | 58 (4.94) | 67 (4.70) |
| SLIM (1 latent confounder) | 40 (4.90) | 47 (4.99) | 25 (4.33) |
| SLIM 4 latent confounders) | 40 (4.90) | 34 (4.74) | 44 (4.96) |
| SLIM (10 latent confounders) | 47 (4.99) | 39 (4.88) | 41 (4.92) |
| LiNGAM-GC-UK | 24 (4.27) | 32 (4.66) | 32 (4.66) |
| ICA-LiNGAM | 74 (4.39) | 71 (4.54) | 67 (4.70) |
| DirectLiNGAM | 48 (5.00) | 52 (5.00) | 54 (4.98) |
| Pairwise LiNGAM | 54 (4.98) | 58 (4.94) | 61 (4.88) |
| Post-nonlinear causal model | 55 (4.97) | 58 (4.94) | 57 (4.95) |
| Number of latent confounders Q = 6: | |||
| Our approach t-distributed individual-specific effects) | 88 (3.25) | 81 (3.92) | 87 (3.36) |
| Our approach Gaussian individual-specific effects) | 84 (3.67) | 85 (3.57) | 87 (3.36) |
| LvLiNGAM (1 latent confounder) | 58 (4.94) | 70 (4.58) | 70 (4.58) |
| LvLiNGAM 4 latent confounders) | 64 (4.80) | 61 (4.88) | 63 (4.83) |
| SLIM (1 latent confounder) | 50 (5.00) | 63 (4.83) | 47 (4.99) |
| SLIM 4 latent confounders) | 45 (4.97) | 47 (4.99) | 43 (4.95) |
| SLIM (10 latent confounders) | 58 (4.94) | 48 (5.00) | 58 (4.94) |
| LiNGAM-GC-UK | 29 (4.54) | 28 (4.49) | 21 (4.07) |
| ICA-LiNGAM | 74 (4.39) | 72 (4.49) | 47 (4.99) |
| DirectLiNGAM | 37 (4.83) | 48 (5.00) | 39 (4.88) |
| Pairwise LiNGAM | 48 (5.00) | 51 (5.00) | 37 (4.83) |
| Post-nonlinear causal model | 55 (4.97) | 42 (4.94) | 46 (4.98) |
| Number of latent confounders Q = 12: | |||
| Our approach t-distributed individual-specific effects) | 88 (3.25) | 86 (3.47) | 89 (3.13) |
| Our approach Gaussian individual-specific effects) | 91 (2.86) | 89 (3.13) | 91 (2.86) |
| LvLiNGAM (1 latent confounder) | 52 (5.00) | 55 (4.97) | 65 (4.77) |
| LvLiNGAM 4 latent confounders) | 65 (4.77) | 58 (4.94) | 64 (4.80) |
| SLIM (1 latent confounder) | 51 (5.00) | 55 (4.97) | 60 (4.90) |
| SLIM 4 latent confounders) | 45 (4.97) | 51 (5.00) | 63 (4.83) |
| SLIM 10 latent confounders) | 61 (4.88) | 54 (4.98) | 54 (4.98) |
| LiNGAM-GC-UK | 21 (4.07) | 25 (4.33) | 29 (4.54) |
| ICA-LiNGAM | 68 (4.66) | 72 (4.49) | 72 (4.49) |
| DirectLiNGAM | 37 (4.83) | 39 (4.88) | 38 (4.85) |
| Pairwise LiNGAM | 56 (4.96) | 42 (4.94) | 43 (4.95) |
| Post-nonlinear causal model | 51 (5.00) | 43 (4.95) | 46 (4.98) |
Largest numbers of successful discoveries were underlined.
Standard errors are shown in parentheses, which are computed assuming that the number of successes follow a binomial distribution.