Table 3.
Simulation Set B (with error in functional predictors) Scenarios 2 and 4. Each set of values corresponds to the mean(sd) scalar covariates selected, mean(sd) functional covariates selected for each setting and method. Top: Mean(sd) number of correctly identified moderators. The best case is 3 true scalar and 2 true functional moderators selected. Bottom: Mean(sd) number of covariates that are incorrectly identified as moderators. The best case is 0 spurious scalar and 0 spurious functional covariates selected.
| n | MC | MC-A | MC-AL | OWL | MC-CART | |
|---|---|---|---|---|---|---|
| Mean number of correctly identified moderators. | ||||||
|
| ||||||
| p = 5, q = 3: Best Case = 3 scalars, 2 functions; Worst Case = 0 scalars, 0 functions | ||||||
|
| ||||||
| Sc. 2 | 100 | 2.00(0.85), 1.40(0.84) | 2.83(0.43), 1.79(0.54) | 2.87(0.39), 0.97(0.81) | 2.24(0.83), 0.16(0.37) | 2.22(0.70), 0.08(0.27) |
| 200 | 2.31(0.77), 1.45(0.85) | 2.98(0.14), 1.95(0.22) | 2.93(0.36), 0.95(0.78) | 2.61(0.69), 0.12(0.38) | 2.74(0.54), 0.03(0.17) | |
| 400 | 2.74(0.52), 1.78(0.56) | 3.00(0.00), 1.98(0.14) | 3.00(0.00), 1.05(0.87) | 2.96(0.20), 0.10(0.30) | 2.98(0.14), 0.06(0.24) | |
| Sc. 4 | 100 | 1.90(0.75), 1.22(0.89) | 2.59(0.65), 1.65(0.67) | 2.72(0.53), 0.89(0.87) | 2.33(0.71), 0.28(0.47) | 2.11(0.62), 0.10(0.30) |
| 200 | 2.04(0.83), 1.23(0.92) | 2.90(0.33), 1.80(0.47) | 2.92(0.31), 0.86(0.78) | 2.68(0.62), 0.21(0.46) | 2.60(0.53), 0.06(0.24) | |
| 400 | 2.35(0.77), 1.56(0.78) | 2.98(0.14), 1.92(0.31) | 3.00(0.00), 1.17(0.88) | 2.86(0.40), 0.12(0.33) | 2.90(0.30), 0.08(0.31) | |
|
| ||||||
| p = 100, q = 10: Best Case = 3 scalars, 2 functions; Worst Case = 0 scalars, 0 functions | ||||||
|
| ||||||
| Sc. 2 | 100 | 1.54(0.72), 0.83(0.85) | 2.43(0.73), 1.07(0.86) | 2.52(0.76), 0.41(0.70) | 1.61(0.71), 0.08(0.31) | 1.44(0.64), 0.02(0.14) |
| 200 | 1.85(0.82), 0.97(0.85) | 2.98(0.20), 1.58(0.64) | 2.86(0.43), 0.45(0.76) | 2.02(0.82), 0.11(0.31) | 2.32(0.62), 0.00(0.00) | |
| 400 | 2.13(0.85), 0.98(0.84) | 3.00(0.00), 1.94(0.28) | 3.00(0.00), 0.31(0.63) | 2.49(0.67), 0.07(0.26) | 2.93(0.26), 0.01(0.10) | |
| Sc. 4 | 100 | 1.35(0.61), 0.60(0.80) | 2.29(0.66), 0.97(0.87) | 2.42(0.64), 0.34(0.58) | 1.98(0.80), 0.20(0.49) | 1.46(0.52), 0.01(0.10) |
| 200 | 1.69(0.77), 0.86(0.86) | 2.72(0.53), 1.44(0.69) | 2.74(0.52), 0.27(0.60) | 2.12(0.78), 0.11(0.40) | 2.11(0.63), 0.00(0.00) | |
| 400 | 1.85(0.81), 0.84(0.86) | 2.98(0.14), 1.75(0.52) | 2.98(0.14), 0.38(0.65) | 2.58(0.62), 0.18(0.44) | 2.72(0.47), 0.00(0.00) | |
|
| ||||||
| Mean number of covariates that are incorrectly identi_ed as moderators. | ||||||
|
| ||||||
| p = 5, q = 3: Best Case = 0 scalars, 0 functions; Worst Case = 3 scalars, 1 function | ||||||
|
| ||||||
| Sc. 2 | 100 | 1.04(1.02), 0.63(0.49) | 1.24(1.11), 0.73(0.45) | 1.83(1.11), 0.31(0.46) | 0.40(0.64), 0.05(0.22) | 0.18(0.44), 0.01(0.10) |
| 200 | 1.20(1.07), 0.73(0.45) | 0.87(1.00), 0.68(0.47) | 1.61(1.13), 0.30(0.46) | 0.44(0.62), 0.11(0.31) | 0.16(0.39), 0.01(0.10) | |
| 400 | 1.38(1.05), 0.83(0.38) | 0.65(0.90), 0.63(0.49) | 1.70(1.22), 0.33(0.47) | 0.26(0.46), 0.03(0.17) | 0.10(0.30), 0.03(0.17) | |
| Sc. 4 | 100 | 1.10(1.11), 0.58(0.50) | 1.30(1.04), 0.70(0.46) | 1.68(1.04), 0.37(0.49) | 0.88(0.92), 0.13(0.34) | 0.33(0.55), 0.05(0.22) |
| 200 | 1.04(1.12), 0.56(0.50) | 1.31(0.94), 0.74(0.44) | 1.74(1.05), 0.33(0.47) | 0.70(0.69), 0.10(0.30) | 0.30(0.48), 0.02(0.14) | |
| 400 | 1.42(1.08), 0.72(0.45) | 1.34(1.00), 0.67(0.47) | 2.08(1.03), 0.44(0.50) | 0.66(0.68), 0.07(0.26) | 0.51(0.63), 0.01(0.10) | |
|
| ||||||
| p = 100, q = 10: Best Case = 0 scalars, 0 functions; Worst Case = 98 scalars, 8 functions | ||||||
|
| ||||||
| Sc. 2 | 100 | 18.48(20.12), 2.93(2.79) | 20.42(15.62), 3.24(2.46) | 33.73(28.17), 1.06(1.38) | 11.62(14.93), 0.59(1.14) | 1.24(1.28), 0.06(0.24) |
| 200 | 22.07(24.35), 3.29(2.86) | 17.36(16.71), 4.08(2.37) | 32.66(31.87), 1.53(2.48) | 12.05(13.27), 0.56(0.92) | 1.21(1.69), 0.07(0.26) | |
| 400 | 15.48(20.56), 3.11(2.60) | 19.59(16.76), 4.62(2.51) | 23.32(26.50), 0.96(1.74) | 11.37(12.84), 0.69(1.15) | 0.73(1.20), 0.06(0.28) | |
| Sc. 4 | 100 | 15.34(19.75), 2.13(2.57) | 21.89(17.78), 3.26(2.57) | 29.03(26.56), 0.91(1.37) | 19.01(21.68), 0.96(1.62) | 1.02(1.29), 0.04(0.20) |
| 200 | 23.14(25.35), 2.97(2.98) | 23.82(17.16), 4.26(2.42) | 28.49(28.27), 1.10(2.00) | 15.32(16.45), 0.49(0.85) | 1.08(1.40), 0.03(0.17) | |
| 400 | 17.89(23.22), 3.12(3.02) | 17.51(16.09), 4.40(2.34) | 25.30(26.51), 1.01(1.80) | 15.53(17.28), 0.81(1.07) | 0.97(1.36), 0.05(0.26) | |