scenario 3: Group size


4/4

4/20

4/50

Average Number

MAE

Average Number

MAE

Average Number

MAE

gsslasso

9.09

0.58 (0.22)

9.26

0.64 (0.29)

9.27

0.69 (0.54)

lasso

53.75

3.90 (0.41)

54.58

3.94 (0.43)

53.96

3.93 (0.44)

grlasso

270.78

2.78 (1.22)

455.15

7.06 (1.69)

509.75

10.58 (1.71)

grMCP

13.40

0.57 (0.18)

40.00

3.50 (0.54)

84.50

10.09 (2.52)

grSCAD

56.16

0.85 (0.78)

53.85

3.62 (0.74)

100.00

7.86 (1.77)

cMCP

9.42

0.64 (0.29)

14.64

0.98 (0.33)

16.85

1.05 (0.38)

scenario 4: Number of nonnull groups


8/20

3/20

1/20

gsslasso

8.85

0.54 (0.19)

9.12

0.56 (0.19)

9.27

0.68 (0.26)

lasso

52.87

3.58 (0.44)

53.51

3.89 (0.43)

52.49

3.90 (0.41)

grlasso

757.1

19.84 (2.51)

610.25

13.91 (2.08)

461.25

7.64 (1.71)

grMCP

83.95

7.68 (0.60)

46.00

7.49 (1.51)

50.00

4.52 (0.67)

grSCAD

410.3

10.80 (0.82)

142.30

8.04 (0.74)

55.85

4.57 (0.74)

cMCP

13.22

0.83 (0.38)

15.74

0.96 (0.35)

14.81

1.03 (0.31)

scenario 5: Correlation coefficients within group


r = 0

r = 0.5

r = 0.7

gsslasso

9.18

0.85 (0.72)

8.90

1.07 (0.99)

8.11

3.54 (0.54)

lasso

59.10

3.42 (0.35)

52.63

4.04 (0.49)

48.82

5.25 (0.50)

grlasso

557.00

10.27 (1.25)

490.50

11.88 (1.75)

465.90

13.61 (2.45)

grMCP

61.71

7.38 (0.89)

57.40

8.14 (1.29)

53.54

9.59 (0.83)

grSCAD

148.68

7.42 (0.67)

170.61

8.78 (1.16)

194.58

11.28 (1.28)

cMCP

16.72

0.98 (0.47)

14.32

0.98 (0.37)

21.51

3.53 (0.40)

 Notes: in scenario 3, group size “4/50” denotes that there are four nonezero coefficients embedded in a group with 50 predictors. The group size is 50. This is true for “4/20” and “4/4”. The optimal s_{0} = 0.02 for different group size settings. The slab scales, s_{1}, are 1 in this scenario. In scenario 4 “8/20” denotes that there are 8 nonnull groups among 20 groups. Each nonnull group includs at least one nonzero coefficients. The optimal s_{0} = 0.02 for the three settings. In scenario 5, the optimal s_{0} are 0.02, 0.03, and 0.04 for different correlation coefficients, 0.0, 0.5, and 0.7 within group, respectively. The slab scales, s_{1}, are 1 in this scenario 3, 4 and 5. Values in the parentheses are standard errors. “gsslasso” represents the proposed group spikeandslab lasso cox