Stype
|
Potential outcomes of S
|
---|
S
T( ω)
|
S
ed
( ω)
|
---|
|
S
11( ω)
|
S
01( ω)
|
S
10( ω)
|
S
00( ω)
|
---|
1
|
1
|
1
|
1
|
1
|
2 b, c
|
1
|
1
|
1
|
0
|
3 a, b, c
|
1
|
1
|
0
|
1
|
4
|
1
|
1
|
0
|
0
|
5 a, b, c
|
1
|
0
|
1
|
1
|
6
|
1
|
0
|
1
|
0
|
7 a, b, c
|
1
|
0
|
0
|
1
|
8 b
|
1
|
0
|
0
|
0
|
9 a, b, c
|
0
|
1
|
1
|
1
|
10 a, b, c
|
0
|
1
|
1
|
0
|
11 a
|
0
|
1
|
0
|
1
|
12 a, b
|
0
|
1
|
0
|
0
|
13 a
|
0
|
0
|
1
|
1
|
14 a, b
|
0
|
0
|
1
|
0
|
15 a, b
|
0
|
0
|
0
|
1
|
16
|
0
|
0
|
0
|
0
|
-
a Under the assumption of positive monotonicity (i.e., S
ed
(ω) ≥ S
e ' d '(ω) for ∀ω whenever e ≥ e ' and d ≥ d '), these response types are excluded.
-
b Given no interaction at the individual level on the additive scale between E and D in the counterfactual framework (i.e., S
11(ω) − S
01(ω) − S
10(ω) + S
00(ω) = 0 for ∀ω), these response types are excluded.
-
c Given no interaction at the individual level on the multiplicative scale between E and D in the counterfactual framework (i.e., S
11(ω)S
00(ω) = S
01(ω)S
10(ω) for ∀ω), these response types are excluded.