Table 2.

Simulation Set A (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	2.32(0.78), 1.40(0.85)	2.95(0.26), 1.68(0.63)	2.95(0.22), 1.05(0.83)	2.75(0.54), 0.41(0.57)	2.52(0.56), 0.04(0.20)
	200	2.83(0.49), 1.69(0.61)	2.99(0.10), 1.63(0.58)	3.00(0.00), 1.32(0.76)	2.92(0.31), 0.58(0.67)	2.96(0.20), 0.11(0.31)
	400	2.96(0.24), 1.72(0.51)	3.00(0.00), 1.77(0.49)	3.00(0.00), 1.40(0.79)	2.96(0.20), 0.47(0.61)	3.00(0.00), 0.10(0.30)
Sc. 4	100	2.07(0.73), 1.26(0.85)	2.63(0.56), 1.49(0.70)	2.78(0.48), 1.00(0.85)	2.54(0.64), 0.60(0.70)	2.19(0.54), 0.08(0.27)
	200	2.33(0.74), 1.31(0.86)	2.89(0.31), 1.73(0.55)	2.98(0.14), 1.25(0.82)	2.86(0.38), 0.57(0.66)	2.71(0.46), 0.12(0.33)
	400	2.74(0.50), 1.61(0.67)	2.99(0.10), 1.72(0.55)	3.00(0.00), 1.17(0.87)	2.93(0.26), 0.47(0.59)	2.92(0.27), 0.15(0.39)
p = 100, q= 10: Best Case = 3 scalars, 2 functions; Worst Case = 0 scalars, 0 functions
Sc. 2	100	2.00(0.80), 0.96(0.78)	2.89(0.35), 1.09(0.79)	2.84(0.42), 0.44(0.64)	2.27(0.79), 0.27(0.57)	1.93(0.67), 0.01(0.10)
	200	2.54(0.74), 0.98(0.80)	3.00(0.00), 1.45(0.70)	2.98(0.20), 0.52(0.69)	2.64(0.64), 0.28(0.51)	2.75(0.48), 0.02(0.14)
	400	2.90(0.36), 0.95(0.80)	3.00(0.00), 1.75(0.50)	3.00(0.00), 0.77(0.80)	2.72(0.53), 0.26(0.52)	2.99(0.10), 0.02(0.14)
Sc. 4	100	1.55(0.69), 0.66(0.82)	2.39(0.71), 0.98(0.80)	2.55(0.58), 0.37(0.61)	2.28(0.67), 0.28(0.53)	1.75(0.56), 0.03(0.17)
	200	2.00(0.77), 0.92(0.90)	2.81(0.46), 1.44(0.72)	2.83(0.38), 0.50(0.70)	2.54(0.61), 0.37(0.60)	2.34(0.57), 0.02(0.14)
	400	2.14(0.75), 0.88(0.86)	2.98(0.14), 1.53(0.70)	2.99(0.10), 0.37(0.63)	2.68(0.57), 0.27(0.51)	2.83(0.38), 0.01(0.10)
Mean number of covariates that are incorrectly identified as moderators.
p = 5, q = 3: Best Case = 0 scalars, 0 functions; Worst Case = 3 scalars, 1 function
Sc. 2	100	1.06(1.03), 0.65(0.48)	0.96(1.02), 0.72(0.45)	1.51(1.18), 0.33(0.47)	0.64(0.76), 0.15(0.36)	0.08(0.27), 0.03(0.17)
	200	1.45(1.09), 0.73(0.45)	0.73(0.90), 0.55(0.50)	1.45(1.18), 0.31(0.46)	0.45(0.67), 0.08(0.27)	0.06(0.24), 0.03(0.17)
	400	1.21(0.97), 0.76(0.43)	0.63(0.82), 0.62(0.49)	1.13(1.06), 0.31(0.46)	0.23(0.45), 0.07(0.26)	0.02(0.14), 0.01(0.10)
Sc. 4	100	1.07(1.06), 0.62(0.49)	1.23(1.03), 0.72(0.45)	1.84(1.12), 0.37(0.49)	1.09(1.07), 0.22(0.42)	0.12(0.41), 0.04(0.20)
	200	1.11(0.99), 0.59(0.49)	1.16(1.04), 0.66(0.48)	1.78(1.12), 0.36(0.48)	0.92(0.88), 0.20(0.40)	0.32(0.51), 0.02(0.14)
	400	1.38(1.00), 0.73(0.45)	1.25(1.04), 0.67(0.47)	1.71(1.14), 0.32(0.47)	0.61(0.72), 0.09(0.29)	0.29(0.52), 0.05(0.22)
p = 100, q = 10: Best Case = 0 scalars, 0 functions; Worst Case = 98 scalars, 8 functions
Sc. 2	100	17.67(17.44), 3.42(2.59)	19.51(15.83), 2.83(2.24)	29.75(27.22), 0.81(1.19)	25.86(21.34), 1.44(1.67)	0.76(1.04), 0.06(0.24)
	200	16.64(16.15), 2.84(2.31)	15.73(15.51), 3.12(2.23)	19.43(21.97), 0.76(1.35)	21.61(20.19), 1.07(1.38)	0.40(0.71), 0.05(0.26)
	400	9.61(9.48), 2.55(1.65)	19.26(17.53), 3.23(2.26)	17.62(24.77), 0.79(1.63)	15.09(16.43), 0.97(1.27)	0.13(0.39), 0.03(0.17)
Sc. 4	100	14.64(20.33), 2.37(2.58)	21.06(18.23), 3.21(2.71)	27.43(26.40), 0.94(1.43)	26.40(24.59), 1.25(1.87)	1.01(1.34), 0.03(0.17)
	200	20.80(22.97), 3.26(2.96)	24.04(17.47), 4.07(2.34)	27.53(27.58), 1.02(1.93)	26.79(21.84), 1.33(1.61)	0.73(1.14), 0.05(0.22)
	400	13.22(17.07), 2.50(2.47)	18.60(16.42), 3.44(2.18)	16.70(23.30), 0.58(1.37)	23.44(22.54), 1.26(1.58)	0.57(1.07), 0.01(0.10)