Table 1.
Simulation results of linear mixed effects models comparing SCAD, LASSO, and ALASSO penalty functions with random effect and ICQ penalty estimates
| β Estimate (D Estimate) | ||||
|---|---|---|---|---|
| Model | Method | MRME | ZERO1 | ZERO2 |
| n = 50, σ = 3 | SCAD-RE | 0.576 (0.980) | 0.11 (0.94) | 0.00 (0.00) |
| SCAD-ICQ | 0.552 (0.259) | 0.01 (0.09) | 0.00 (0.01) | |
| LASSO-RE | 0.983 (0.988) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.605 (0.241) | 0.04 (0.10) | 0.00 (0.01) | |
| ALASSO-RE | 0.949 (0.983) | 0.80 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.597 (0.263) | 0.01 (0.13) | 0.00 (0.01) | |
| True | 0.559 (0.228) | 0.00 (0.00) | 0.00 (0.00) | |
| n = 50, σ = 1 | SCAD-RE | 0.906 (0.803) | 0.58 (1.00) | 0.00 (0.00) |
| SCAD-ICQ | 0.869 (0.461) | 0.03 (0.13) | 0.00 (0.00) | |
| LASSO-RE | 0.997 (0.996) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.884 (0.438) | 0.04 (0.08) | 0.00 (0.00) | |
| ALASSO-RE | 0.983 (0.989) | 0.81 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.858 (0.441) | 0.03 (0.10) | 0.00 (0.00) | |
| True | 0.846 (0.439) | 0.00 (0.00) | 0.00 (0.00) | |
| n = 100, σ = 3 | SCAD-RE | 0.571 (0.970) | 0.13 (0.93) | 0.00 (0.00) |
| SCAD-ICQ | 0.565 (0.219) | 0.01 (0.04) | 0.00 (0.00) | |
| LASSO-RE | 0.993 (0.994) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.584 (0.232) | 0.01 (0.04) | 0.00 (0.00) | |
| ALASSO-RE | 0.949 (0.987) | 0.81 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.574 (0.205) | 0.01 (0.04) | 0.00 (0.00) | |
| True | 0.513 (0.196) | 0.00 (0.00) | 0.00 (0.00) | |
| n = 100, σ = 1 | SCAD-RE | 0.895 (0.803) | 0.57 (1.00) | 0.00 (0.00) |
| SCAD-ICQ | 0.820 (0.452) | 0.01 (0.07) | 0.00 (0.00) | |
| LASSO-RE | 0.999 (0.997) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.835 (0.478) | 0.03 (0.08) | 0.00 (0.00) | |
| ALASSO-RE | 0.982 (0.989) | 0.82 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.839 (0.415) | 0.02 (0.06) | 0.00 (0.00) | |
| True | 0.832 (0.392) | 0.00 (0.00) | 0.00 (0.00) | |
| n = 200, σ = 3 | SCAD-RE | 0.553 (0.987) | 0.13 (0.94) | 0.00 (0.00) |
| SCAD-ICQ | 0.554 (0.245) | 0.01 (0.07) | 0.00 (0.00) | |
| LASSO-RE | 0.995 (0.996) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.617 (0.244) | 0.05 (0.09) | 0.00 (0.00) | |
| ALASSO-RE | 0.934 (0.992) | 0.78 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.603 (0.237) | 0.02 (0.11) | 0.00 (0.00) | |
| True | 0.546 (0.218) | 0.00 (0.00) | 0.00 (0.00) | |
| n = 200, σ = 1 | SCAD-RE | 0.902 (0.833) | 0.55 (1.00) | 0.00 (0.00) |
| SCAD-ICQ | 0.853 (0.487) | 0.01 (0.12) | 0.00 (0.00) | |
| LASSO-RE | 0.998 (0.998) | 0.99 (1.00) | 0.00 (0.00) | |
| LASSO-ICQ | 0.873 (0.554) | 0.07 (0.20) | 0.00 (0.00) | |
| ALASSO-RE | 0.982 (0.991) | 0.79 (1.00) | 0.00 (0.00) | |
| ALASSO-ICQ | 0.871 (0.468) | 0.02 (0.11) | 0.00 (0.00) | |
| True | 0.839 (0.408) | 0.00 (0.00) | 0.00 (0.00) | |