Table A9.
Summary results under simulation scenarios where the hierarchy is violated for some interactions. In each cell, mean (sd) based on 200 replicates.
| M:TP | M:FP | I:TP | I:FP | RSSE | PMSE | |
|---|---|---|---|---|---|---|
| D1: N(0,1) | ||||||
| LTS-MCP-Hier | 7.8(0.4) | 4.0(4.4) | 10.5(2.0) | 2.5(1.7) | 3.46(0.35) | 3.90(0.95) |
| LS-MCP | 5.5(1.0) | 5.0(4.4) | 16.8(1.0) | 17.8(9.8) | 2.95(0.44) | 1.51(0.60) |
| LAD-Lasso | 7.9(0.4) | 15.0(7.4) | 17.9(2.9) | 36.0(12.1) | 2.23(0.59) | 2.25(1.17) |
| RLARS | 7.3(0.7) | 1.0(1.5) | 8.9(2.2) | 14.4(7.9) | 4.02(0.38) | 4.29(1.08) |
| LTS-MCP | 6.2(1.1) | 7.0(3.0) | 16.8(1.3) | 26.8(6.9) | 2.48(0.57) | 1.11(0.35) |
| LS-MCP-Hier | 7.8(0.4) | 6.0(5.9) | 11.3(1.9) | 2.9(1.6) | 3.40(0.45) | 3.78(1.28) |
| D2: 0.9N(0,1) + 0.1Cauchy(0,5) | ||||||
| LTS-MCP-Hier | 7.7(0.5) | 6.0(5.9) | 10.1(2.0) | 2.9(1.6) | 3.58(0.34) | 4.19(1.02) |
| LS-MCP | 2.2(1.8) | 17.0(7.4) | 3.5(3.2) | 71.4(10.6) | 38.37(84.37) | 2057.01(11618.56) |
| LAD-Lasso | 7.2(0.7) | 2.0(1.5) | 8.2(2.7) | 7.7(3.1) | 3.88(0.36) | 6.93(1.99) |
| RLARS | 7.0(0.9) | 1.0(1.5) | 7.1(2.3) | 12.4(7.2) | 4.44(0.43) | 5.43(1.59) |
| LTS-MCP | 6.1(1.0) | 8.0(3.0) | 16.2(1.6) | 33.2(6.8) | 2.78(0.53) | 1.39(0.48) |
| LS-MCP-Hier | 5.8(1.4) | 110.0(32.6) | 2.4(2.6) | 34.2(95.9) | 29.73(50.07) | 1510.65(6857.39) |
| D3: 0.9N(0,1) + 0.1N(20,1) | ||||||
| LTS-MCP-Hier | 7.6(0.6) | 5.0(4.4) | 10.2(2.2) | 2.8(1.6) | 3.60(0.47) | 4.32(1.49) |
| LS-MCP | 2.6(1.1) | 22.0(5.2) | 4.0(1.6) | 66.9(5.3) | 10.47(0.68) | 38.04(6.53) |
| LAD-Lasso | 6.9(0.9) | 2.5(2.2) | 6.4(2.2) | 8.7(3.1) | 4.13(0.34) | 8.07(2.19) |
| RLARS | 5.8(1.1) | 1.0(1.5) | 4.4(1.9) | 11.9(5.8) | 5.12(0.49) | 8.10(2.43) |
| LTS-MCP | 6.2(1.0) | 8.0(3.0) | 16.6(1.4) | 29.2(6.1) | 2.61(0.54) | 1.18(0.37) |
| LS-MCP-Hier | 6.2(1.0) | 96.5(8.2) | 2.7(1.6)) | 7.3(5.7) | 9.76(0.64) | 42.01(9.31) |
| D4: N(0,1) and with leverage points | ||||||
| LTS-MCP-Hier | 7.3(1.1) | 7.5(8.2) | 9.4(3.2) | 2.8(1.8) | 3.78(0.76) | 5.35(3.54) |
| LS-MCP | 1.1(0.9) | 21.0(4.4) | 4.9(2.5) | 67.0(6.2) | 7.90(0.91) | 22.21(7.30) |
| LAD-Lasso | 3.8(1.2) | 4.0(3.0) | 6.0(2.4) | 13.0(4.3) | 4.56(0.35) | 11.86(2.85) |
| RLARS | 6.8(1.0) | 0.0(0.0) | 8.1(1.9) | 12.8(6.6) | 4.27(0.42) | 4.78(1.44) |
| LTS-MCP | 6.2(1.1) | 9.0(3.0) | 16.5(1.5) | 32.4(6.6) | 2.64(0.57) | 1.24(0.43) |
| LS-MCP-Hier | 4.8(1.3) | 91.0(7.4) | 2.2(2.1) | 5.0(4.1) | 7.55(1.16) | 28.00(10.44) |
| D5: 0.9N(0,1) + 0.1Cauchy(0,5) and with leverage points | ||||||
| LTS-MCP-Hier | 7.5(0.9) | 8.0(4.4) | 9.5(2.5) | 3.0(2.0) | 3.77(0.71) | 5.32(3.72) |
| LS-MCP | 0.6(0.7) | 19.0(5.9) | 2.0(1.8) | 68.5(17.0) | 32.80(78.33) | 1370.28(8180.45) |
| LAD-Lasso | 3.9(1.3) | 4.0(1.5) | 5.5(2.1) | 12.2(3.5) | 4.57(0.33) | 12.16(3.24) |
| RLARS | 6.6(1.0) | 1.0(1.5) | 6.8(2.2) | 12.2(6.5) | 4.57(0.40) | 5.88(1.67) |
| LTS-MCP | 6.2(1.1) | 10.0(3.0) | 16.4(1.5) | 34.4(7.1) | 2.68(0.57) | 1.28(0.44) |
| LS-MCP-Hier | 4.4(1.6) | 113.0(25.2) | 1.4(2.1) | 31.8(88.0) | 28.25(46.51) | 1477.08(7265.55) |