Table 5.
Simulation results for Experiment 3: 15% non-zero coefficients, ρ = 0.4, n = 600.
|
The Poisson Component | ||||||||
|---|---|---|---|---|---|---|---|---|
| Method | MRMSEa | Specificityb | Sensitivityc | Under fitd | Exact fite | Over fitf | ||
| 1 | 2 | ≥3 | ||||||
| 30% zeros
| ||||||||
| PR-LASSO | 1.344 | 0.655 | 1.000 | 0.000 | 0.000 | 0.001 | 0.026 | 0.973 |
| PR-SCAD | 1.439 | 0.723 | 1.000 | 0.000 | 0.014 | 0.043 | 0.088 | 0.855 |
| ZIP-LASSO | 0.391 | 0.961 | 1.000 | 0.000 | 0.538 | 0.290 | 0.121 | 0.051 |
| ZIP-SCAD | 0.080 | 0.948 | 1.000 | 0.000 | 0.652 | 0.092 | 0.084 | 0.172 |
|
| ||||||||
| 45% zeros
| ||||||||
| PR-LASSO | 2.864 | 0.568 | 1.000 | 0.000 | 0.000 | 0.000 | 0.001 | 0.999 |
| PR-SCAD | 3.647 | 0.652 | 1.000 | 0.000 | 0.000 | 0.001 | 0.015 | 0.984 |
| ZIP-LASSO | 0.372 | 0.953 | 1.000 | 0.000 | 0.479 | 0.316 | 0.126 | 0.079 |
| ZIP-SCAD | 0.147 | 0.876 | 1.000 | 0.000 | 0.202 | 0.183 | 0.209 | 0.406 |
|
| ||||||||
|
The Zero Component
| ||||||||
| 30% zeros
| ||||||||
| ZIP-LASSO | 1.832 | 1.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| ZIP-SCAD | 1.508 | 1.000 | 0.192 | 0.950 | 0.049 | 0.001 | 0.000 | 0.000 |
|
| ||||||||
| 45% zeros
| ||||||||
| ZIP-LASSO | 2.640 | 1.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| ZIP-SCAD | 0.794 | 0.998 | 0.655 | 0.680 | 0.309 | 0.009 | 0.002 | 0.000 |
a
MRMSE = Median of the ratio of the reduced model MSE to the full model MSE.
b
Specificity = Mean of the proportion of zero coefficients that were correctly identified.
c
Sensitivity = Mean of the proportion of nonzero coefficients that were correctly identified.
d
Under fit = Probability of excluding any significant coefficients.
e
Exact fit = Probability of selecting the exact sub-model.
f
Over fit = Probabilities of including all significant variables and some noise variables (1, 2, ≥ 3).