Table 5:
Comparison of eight methods
| Possible directions | Our approach | LvLiNGAM | SLIM | ||||
|---|---|---|---|---|---|---|---|
| t-dist. | Gaussian | Num. | lat. conf. | Num. | lat. conf. | ||
| 1 | 4 | 1 | 4 | 10 | |||
| x1(FO) ← x3(FE) | ✓ | ✓ | ✓ | ✓ | |||
| x2(SI) ← x1(FO) | ✓ | ✓ | ✓ | ✓ | |||
| x2(SI) ← x3(FE) | ✓ | ✓ | ✓ | ✓ | ✓ | ||
| x2(SI) ← x4(SO) | ✓ | ✓ | ✓ | ✓ | |||
| x2(SI) ← x5(SE) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| x2(SI) ← x6(NS) | ✓ | ✓ | ✓ | ✓ | |||
| x4(SO) ← x1 (FO) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| x4(SO) ← x3(FE) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| x4(SO) ← x5(SE) | ✓ | ✓ | ✓ | ✓ | |||
| x4(SO) ← x6(NS) | ✓ | ✓ | ✓ | ✓ | ✓ | ||
| x5(SE) ← x1(FO) | ✓ | ||||||
| x5(SE) ← x3(FE) | ✓ | ✓ | ✓ | ✓ | ✓ | ||
| x5(SE) ← x6(NS) | ✓ | ✓ | ✓ | ✓ | ✓ | ||
| x6(NS) ← x1(FO) | ✓ | ✓ | |||||
| x6(NS) ← x3(FE) | ✓ | ✓ | ✓ | ✓ | |||
| Num. of successes | 12 | 11 | 10 | 9 | 9 | 7 | 8 |
| Standard errors | 1.55 | 1.71 | 1.83 | 1.90 | 1.90 | 1.93 | 1.93 |
| Precisions | 0.80 | 0.73 | 0.67 | 0.60 | 0.60 | 0.47 | 0.53 |
| Possible directions | LiNGAM-GC-UK | ICA | Direct | Pairwise | PNL | ||
| x1(FO) ← x3(FE) | ✓ | ✓ | |||||
| x2(SI) ← x1(FO) | ✓ | ✓ | ✓ | ||||
| x2(SI) ← x3(FE) | ✓ | ✓ | |||||
| x2(SI) ← x4(SO) | ✓ | ✓ | ✓ | ||||
| x2(SI) ← x5(SE) | ✓ | ✓ | |||||
| x2(SI) ← x6(NS) | ✓ | ✓ | |||||
| x4(SO) ← x1(FO) | ✓ | ✓ | |||||
| x4(SO) ← x3(FE) | ✓ | ✓ | |||||
| x4(SO) ← x5(SE) | ✓ | ✓ | |||||
| x4(SO) ← x6(NS) | ✓ | ||||||
| x5(SE) ← x1(FO) | ✓ | ✓ | ✓ | ||||
| x5(SE) ← x3(FE) | ✓ | ✓ | |||||
| x5(SE) ← x6(NS) | |||||||
| x6(NS) ← x1(FO) | ✓ | ✓ | |||||
| x6(NS) ← x3(FE) | ✓ | ✓ | ✓ | ||||
| Num. of successes | 3 | 8 | 9 | 2 | 9 | ||
| Standard errors | 1.55 | 1.93 | 1.90 | 1.32 | 1.90 | ||
| Precisions | 0.20 | 0.53 | 0.60 | 0.13 | 0.60 | ||
FO: Father’s Occupation
FE: Father’s Education
SI: Son’s Income
SO: Son’s Occupation
SE: Son’s Education
NS: Number of Siblings
ICA: ICA-LiNGAM (Shimizu et al., 2006)
Direct: DirectLiNGAM (Shimizu et al., 2011)
Pairwise: Pairwise LiNGAM (Hyvärinen and Smith, 2013)
PNL: Post-nonlinear causal model (Zhang and Hyvärinen, 2009)