Table 3 Simulation example 3: effect of multicollinearity among mandatory covariates
Method | rpe | g-measure | Sensitivity (\(\mathcal {M}\)) | Sensitivity (\(\mathcal {O}\)) | Specificity (\(\mathcal {O}\)) | |
|---|---|---|---|---|---|---|
ρ=0.75 | Ridge | 6.353 (0.022) | ||||
Lasso | 4.649 (0.167) | 0.802 (0.011) | 0.800 (0.000) | 0.700 (0.048) | 0.908 (0.004) | |
Elastic net | 4.410 (0.128) | 0.804 (0.005) | 1.000 (0.009) | 0.700 (0.006) | 0.858 (0.006) | |
\(\mathcal {M}\)-unpenalized lasso | 4.776 (0.260) | 0.829 (0.005) | 1.000 (0.000) | 0.700 (0.031) | 0.902 (0.007) | |
\(\mathcal {M}\)-unpenalized elastic net | 5.402 (0.190) | 0.823 (0.006) | 1.000 (0.000) | 0.700 (0.013) | 0.871 (0.009) | |
Ridle | 2.699 (0.152) | 0.893 (0.007) | 1.000 (0.000) | 0.900 (0.048) | 0.904 (0.004) | |
ρ=0.9 | Ridge | 6.270 (0.026) | ||||
Lasso | 4.914 (0.148) | 0.784 (0.010) | 0.600 (0.089) | 0.700 (0.036) | 0.908 (0.004) | |
Elastic net | 4.336 (0.135) | 0.816 (0.005) | 0.800 (0.092) | 0.700 (0.018) | 0.867 (0.008) | |
\(\mathcal {M}\)-unpenalized lasso | 6.992 (0.337) | 0.828 (0.008) | 1.000 (0.000) | 0.700 (0.031) | 0.902 (0.006) | |
\(\mathcal {M}\)-unpenalized elastic net | 7.245 (0.237) | 0.827 (0.005) | 1.000 (0.000) | 0.700 (0.045) | 0.860 (0.011) | |
Ridle | 3.000 (0.214) | 0.890 (0.006) | 1.000 (0.000) | 0.800 (0.045) | 0.900 (0.004) | |
ρ=0.99 | Ridge | 6.231 (0.031) | ||||
Lasso | 7.322 (0.200) | 0.745 (0.005) | 0.400 (0.000) | 0.700 (0.000) | 0.913 (0.003) | |
Elastic net | 5.003 (0.155) | 0.804 (0.006) | 0.800 (0.049) | 0.700 (0.019) | 0.883 (0.006) | |
\(\mathcal {M}\)-unpenalized lasso | 36.214 (2.064) | 0.824 (0.006) | 1.000 (0.000) | 0.700 (0.046) | 0.904 (0.005) | |
\(\mathcal {M}\)-unpenalized elastic net | 33.583 (2.197) | 0.830 (0.004) | 1.000 (0.010) | 0.700 (0.045) | 0.867 (0.010) | |
Ridle | 4.193 (0.343) | 0.890 (0.005) | 1.000 (0.000) | 0.800 (0.029) | 0.904 (0.004) |