Table 2 Performances of RF, BRT, LASSO and UFMLR in the 500 simulated datasets
| Â | n | RF | BRT | LASSO-max | LASSO-se | UFMLR05 | UFMLR05 backward | UFMLR20 | UFMLR20 backward |
|---|---|---|---|---|---|---|---|---|---|
Type I error 5% | Â | Â | Â | Â | Â | Â | Â | Â | Â |
True Positive Rates (TPR) | 8 | 85% (55% - 100%) | 80% (51% - 100%) | 78% (52% - 100%) | 71% (41% - 100%) | 28% (3% - 54%) | 45% (20% - 70%) | 26% (0% - 65%) | 49% (15% - 84%) |
Covariates with pairwise interaction | 4 | 86% (49% - 100%) | 80% (41% - 100%) | 77% (40% - 100%) | 69% (26% - 100%) | 24% (0% - 63%) | 41% (0% - 83%) | 24% (0% - 72%) | 46% (0% - 96%) |
Covariates without pairwise interaction | 4 | 84% (46% - 100%) | 79% (41% - 100%) | 79% (41% - 100%) | 73% (32% - 100%) | 32% (0% - 74%) | 50% (6% - 93%) | 28% (0% - 76%) | 53% (5% - 100%) |
Continuous covariates | 4 | 90% (55% - 100%) | 82% (47% - 100%) | 82% (49% - 100%) | 77% (41% - 100%) | 35% (0% - 74%) | 49% (15% - 84%) | 29% (0% - 76%) | 55% (14% - 95%) |
Binary covariates | 4 | 80% (34% - 100%) | 78% (35% - 100%) | 74% (34% - 100%) | 64% (20% - 100%) | 22% (0% - 57%) | 41% (8% - 74%) | 23% (0% - 69%) | 44% (0% - 90%) |
False Positive Rates (FPR) | 292 | 4% (1% - 6%) | 4% (2% - 6%) | 9% (0% - 17%) | 4% (0% - 9%) | 2% (1% - 4%) | 3% (1% - 5%) | 4% (0% - 12%) | 9% (0% - 18%) |
Covariates correlated with associated covariates | 12 | 46% (7% - 85%) | 33% (3% - 63%) | 23% (0% - 48%) | 18% (0% - 41%) | 4% (0% - 15%) | 7% (0% - 22%) | 9% (0% - 39%) | 19% (0% - 60%) |
Covariates uncorrelated with associated covariates | 280 | 2% (0% - 4%) | 3% (1% - 5%) | 8% (0% - 17%) | 3% (0% - 8%) | 2% (1% - 4%) | 3% (1% - 4%) | 4% (0% - 11%) | 8% (0% - 16%) |
Continuous covariates | 146 | 3% (0% - 6%) | 3% (1% - 6%) | 9% (0% - 18%) | 4% (0% - 9%) | 2% (0% - 5%) | 3% (0% - 6%) | 5% (0% - 13%) | 9% (0% - 18%) |
Binary covariates | 146 | 4% (0% - 8%) | 5% (2% - 9%) | 9% (0% - 18%) | 3% (0% - 9%) | 2% (0% - 5%) | 3% (0% - 5%) | 4% (0% - 12%) | 9% (0% - 18%) |