Table 2.
Ratio of MSE (saturated model MSE / alternative method MSE) and Monte Carlo (MC) bias and standard errors for each scenario with sample size n = 500 over 1,000 MC datasets. Scenarios 1–9 have 10 covariates and Scenario 10 has varying covariate set sizes (p). In the simulations with correlated covariates, ρ(Vi, Vj) = 0.6 for i ≠ j ≤ 5 and ρ(Vi, Vj) = 0 for i ≠ j > 5.
| GLiDeR | Backward selection | MADR | Adaptive lasso | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Scenario | MSE Ratio |
MC Bias |
MC SD |
MSE Ratio |
MC Bias |
MC SD |
MSE Ratio |
MC Bias |
MC SD |
MSE Ratio |
MC Bias |
MC SD |
| Independent covariates | ||||||||||||
|
| ||||||||||||
| 1 | 1.10 | 0.00 | 0.09 | 1.02 | 0.00 | 0.09 | 1.11 | 0.00 | 0.09 | 1.12 | 0.00 | 0.09 |
| 2 | 1.09 | 0.00 | 0.09 | 1.02 | 0.00 | 0.10 | 1.12 | 0.00 | 0.09 | 1.13 | 0.00 | 0.09 |
| 3 | 2.91 | 0.00 | 0.09 | 1.04 | 0.00 | 0.15 | 3.06 | 0.00 | 0.09 | 3.20 | 0.00 | 0.09 |
| 4 | 1.01 | 0.00 | 0.10 | 1.01 | 0.00 | 0.10 | 1.02 | 0.00 | 0.10 | 0.79 | 0.05 | 0.10 |
| 5 | 1.67 | −0.04 | 0.63 | 1.05 | −0.04 | 0.80 | 1.65 | −0.03 | 0.64 | 1.64 | −0.04 | 0.64 |
| 6 | 18.35 | 0.00 | 0.31 | 0.95 | −0.03 | 1.36 | 18.53 | 0.00 | 0.31 | 16.30 | 0.00 | 0.33 |
| 7 | 1.14 | −0.05 | 0.84 | 1.04 | −0.06 | 0.88 | 1.12 | −0.05 | 0.85 | 1.16 | −0.05 | 0.83 |
| 8 | 1.26 | 0.01 | 0.12 | 1.04 | 0.01 | 0.13 | 1.25 | 0.02 | 0.12 | 1.35 | 0.01 | 0.11 |
| 9 | 1.05 | 0.00 | 0.11 | 1.04 | 0.00 | 0.11 | 1.06 | 0.00 | 0.11 | 1.06 | 0.00 | 0.11 |
|
| ||||||||||||
| Correlated covariates | ||||||||||||
|
| ||||||||||||
| 1 | 1.16 | 0.00 | 0.09 | 1.01 | 0.00 | 0.10 | 1.20 | 0.00 | 0.09 | 1.20 | 0.00 | 0.09 |
| 2 | 1.09 | 0.00 | 0.10 | 1.02 | 0.00 | 0.10 | 1.09 | 0.00 | 0.10 | 1.14 | 0.02 | 0.10 |
| 3 | 5.55 | 0.00 | 0.13 | 0.94 | −0.02 | 0.32 | 5.29 | −0.01 | 0.14 | 7.49 | 0.02 | 0.11 |
| 4 | 1.05 | 0.01 | 0.11 | 1.04 | 0.01 | 0.11 | 1.08 | 0.01 | 0.11 | 0.25 | 0.20 | 0.11 |
| 5 | 3.30 | 0.39 | 1.99 | 1.02 | 0.05 | 3.64 | 2.68 | 0.45 | 2.20 | 2.14 | 0.99 | 2.15 |
| 6 | 305.39 | −0.02 | 0.92 | 1.61 | −0.10 | 12.69 | 74.41 | 0.02 | 1.86 | 199.97 | 0.05 | 1.14 |
| 7 | 1.27 | 0.06 | 0.86 | 1.09 | 0.05 | 0.93 | 1.15 | 0.07 | 0.91 | 1.96 | 0.05 | 0.69 |
| 8 | 1.28 | 0.01 | 0.15 | 1.12 | 0.01 | 0.16 | 1.29 | 0.02 | 0.15 | 1.29 | 0.02 | 0.15 |
| 9 | 1.05 | 0.00 | 0.11 | 1.06 | 0.00 | 0.11 | 1.06 | 0.00 | 0.11 | 1.06 | 0.00 | 0.11 |
|
| ||||||||||||
| Scenario 10 | ||||||||||||
|
| ||||||||||||
| p = 100 | 1.60 | 0.00 | 0.26 | * | * | * | * | * | * | 0.51 | −0.42 | 0.20 |
| p = 500 | 13.65 | −0.06 | 0.32 | * | * | * | * | * | * | 6.22 | −0.42 | 0.20 |
| p = 1000 | 13.76 | −0.14 | 0.29 | * | * | * | * | * | * | 7.43 | −0.39 | 0.20 |
Bold indicates significant difference (5% significance level) between MSEs (testing equality) from the saturated method (full model) vs. the alternative method using the paired t-test.