Dtype | Potential outcomes of D
|
---|
D
T( ω) |
D
ce
( ω) |
---|
|
D
11( ω) |
D
01( ω) |
D
10( ω) |
D
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., D
ce
(ω) ≥ D
c ' e '(ω) for ∀ω whenever c ≥ c ' and e ≥ e '), these response types are excluded.
-
b Given no interaction at the individual level on the additive scale between C and E in the counterfactual framework (i.e., D
11(ω) − D
01(ω) − D
10(ω) + D
00(ω) = 0 for ∀ω), these response types are excluded.
-
c Given no interaction at the individual level on the multiplicative scale between C and E in the counterfactual framework (i.e., D
11(ω)D
00(ω) = D
01(ω)D
10(ω) for ∀ω), these response types are excluded.