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6 W A W C 12
7 U A 7 8
8 U A U Y U A U Y
9 16
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11 1 i p a=1 i 2 Y i = Yi a=1 p a=1 i 3 p a=1 i p U L L L A L U A L L A
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15 ˆθ 0 θ 1 W ˆθ 0 ˆθ 1 W i [Y i θ 0 + θ 1 A i ] 2. [Y A = a] = θ 0 a A = a i i=1 Y iw i i=1 W i 95 θ 1 = 3.4 W A = 1/f(A L) SW A = f(a)/f(a L) 95
16 a E[Y a ] = β 0 + β 1 a. V E[Y a A, V ] = β 0 + β 1 a + β 2 V a + β 3 V. β 3 V A V L A B A B A B
17 W A,C = W A W C A, C L Y a=1,c=0 Π(A, C) L L SW A,C = SW A SW C SW C = P r[c = 0 A]/P r[c = 0 L, A] L C L L(and ) W A,C = 1/f(A, C = 0 L) A C f(a, C = 0 L) = f(a L) P r[c = 0 L, A] L f(a L) P r[c = 0 L, A] L L C A L E[Y a=1,c=0 ]
18 E[Y a=1,c=0 ] A = 1 A = 0 a E[Y A = a, C = 0, L = l] P r[l = l]. l L P r[l = l] P DF f L (l) Y E[Y A = a, C = 0, L = l]df L (l). A 9 L L l E[Y A = a, C = 0, L = l] A
19 l E[Y A = a, L = l] P r[l = l] A = 1 A = 0 A Y L L
20 l L L L A SW A (L) 1 L P r[a = 1 Y a=0, L] = P r[a = 1 L]
21 A logitp r[a = 1 Y a=0, L] = α 0 + α 1 Y a=0 + α 2 L α 2 L L p L 1,..., L p α 2 L = p j=1 α 2jL j α 1 Y a=0 A L E[Y a Y a=0 A = a, L] = β 1 a + β 2 al L β 0 β 3 L Y a=1 Y a=0
22 A Y A Y L Y a i Y a=0 i = ϕ 1 a + ϕ 2 al i ϕ 1 + ϕ 2 l L = l Y a=0 Y a=1 L E[Y a Y a=0 A = a, L] = β 1 a Yi a Yi a=0 = ϕ 1 a i ϕ 1 β i Y a Y a=0 = ϕ 1 a Y a=0 = Y a ϕ 1 a Y a=0 = Y ϕ 1 a ϕ 1 Y a=0 ϕ 1
23 ϕ 1 H(β 1 ) = Y a=1 H(β 1 ) Y a=0 L V V V E[Y a Y a=0 A = a, L] = β 1 a + β 2 av Y a i Y a=0 i = ϕ 1 a + ϕ 2 av logitp r[a = 1 H(ϕ ), L] = α 0 + α 1 H(ϕ ) + α 2 H(ϕ )V + α 3 L. A
24 L Y A E[Y a,c=0 L] = β 0 + β 1 a + β 2 al + β 3 L E[Y a,c=0 L = l] E[Y A = 1, C = 0, L = l] E[Y A = 1, C = 0, L = l] = α 0 + α 1 a + α 2 al + α 3 L L L p(l) Y a A L Y a A p(l) p(l) 1 0 L p(l) p(l)
25 E[Y A, C = 0, p(l)] s E[Y a=1,c=0 p(l) = s] E[Y a=0,c=0 p(l) = s] E[Y a=1,c=0 ] E[Y a=0,c=0 ] E[Y A, C = 0, p(l)] 13 L p(l) p(l) s p(l) s ± 0.05 A L L A L A A Y a L a
26 Z A Z Y A Z Y E[Y a=1 ] E[Y a=0 ] E[Y Z = 1] E[Y Z = 0] E[A Z = 1] E[A Z = 0] Z Cov(Y,Z) Cov(A,Z) Z Y Z A
27 E[A Z] = α 0 + α 1 Z Ê[A Z] E[Y Z] = β 0 + β 1 Ê[A Z] ˆβ 1 10 A Y Z E[Y a=1 Y a=0 Z = 1, A = a] = E[Y a=1 Y a=0 Z = 0, A = a] a = 0, 1 A z=1 = 1 A z=0 = 1 A z=1 = 0 A z=0 = 0 A z=1 = 1 A z=0 = 0 A z=1 = 0 A z=0 = 1
28 A z=1 A z=0 E[Y a=1 Y a=0 A z=1 = 1, A z=0 = 0]. Z Y Z Z Y Z A A Z Y Z U z U z A uz u z U z
29 Z A Z A A U A U Z A Z 95 A A Z Y Z Y V
30 Z Z Y
31 k P r[t > k] k k 1 P r[t > k] = P r[t k] t k t P r[t = k T > k 1] k k k k t k
32 D k k P r[d k = 0] = P r[t > k] k P r[d k = 1] = P r[t k] k P r[d k = 1 D k 1 = 0] k = 1 k = 0 k 0 k P r[d k = 0] = k P r[d m = 0 D m 1 = 0] m=1 k k P r[d k = 1 D k 1 = 0] k k 1 P r[d k = 0] k
33 k P r[d k+1 = 1 D k = 0] logitp r[d k+1 = 1 D k = 1, A] = θ 0,k + θ 1 A + θ 2 A k + θ 3 A k 2 θ 0,k = θ 0 + θ 4 k + θ 3 A k 2 P r[d k+1 = 0 A = a] P r[d k+1 = 0 D k = 0, A = a]
34
35 A = 1 E = 1 A = 1 E = A Y U A A U Y Y
36 n 95 n
37 $
38 P r[a = a L = l] = 0 P r[l = l] 0 E[Y A = a, L = l] E[Y A, L] α 1 = 0 L
39 α E[Y a,c=0 L] = β 0 + β 1 a + β 2 al + β 3 L, β 1 β 2 β 0 β Z A Y A
40 Z A Y Z A Y
41 P r[y = 0 E = e, A = a] P r[y = 0 E = e, A = a] = g(e)h(a) P r[y = 0 E = e, A = a]/p r[y = 0 E = e, A = 0] P r[y = 0 E = e, A = a] = g(e)h(a) P r[y = 1 E = e, A = a] = 1 g(e)h(a) Y = 0 Y = f( ) P DF U A U Y P DF P DF U A P DF U Y P DF 9.2 Y z=0,a = Y z=1,a
42 Y A L A L L 10.3
43 11.1 p i=0 θ ix i g{ } g{e[y X]} = p i=1 θ ix i log{e[y X]} = p θ i X i. i=1 E[Y X] p log{ 1 E[Y X] } = θ i X i. i=1 θ E[Y X] n i=1 E[Y X = x] x ω h(x X i )Y I i=1 nω h(x X i ω ) h (z) z = 0 0 z h ω p i=0 θ ix i p i=0 f i(x i )
44 f i ( ) k E[Y X = x] E[Y X = x] X x X X x E[Y X = x] E[Y X = x] X x E[Y X = x] X x h h = I(A = a)y ÊE[ ] f(a L) ÊE[ I(A=a)Y f(a L) ] ÊE[ I(A=a) f(a L) ]
45 12.2 g[a] f[a L] E[Y a ] E[ I(A = a) E[ ] = 1 f[a Y ] I(A = a)y E[ ] = E[Y a ] f[a Y ] E[ I(A=a)Y ] f[a Y ] E[ I(A=a) ] = E[Y a ] f[a Y ] E[ I(A=a)Y f[a Y ] E[ I(A=a) I(A = a)y f[a Y ] g(a)] f[a Y ] g(a)] = E[Y a ] g(a)] = E[Y a ]g(a) E[ I(A = a) g(a)] f[a Y ] A Y E[Y A = a, C = 0, L = l, D]
46 A = 1 A = 0 L 14.1 a V L E[Y a V ] = β 0 + β 1 a + β 2 av + β 3 V. E[Y a V ] = E[Y a=0 V ] + β 1 a + β 2 av E[Y a Y a=0 V ] = β 1 a + β 2 av 14.1 log( E[Y a A = a, L] E[Y a=0 A = a, L] ) = β 1a + β 2 L H(ϕ ) Y exp[ ϕ 1a ϕ 2L] (0, 1) Y = 1 L 1 Y logitp r[y a = 1 A = a, L] logitp t[y a=0 = 1 A = a, L] = β 1 a + β 2 L
47 14.2 β 1 H(ϕ ) H(ϕ ) A ϕ N i=1 I[C i = 0]W C i H i (ϕ )(A i E[A L i ]) = 0 H i (ϕ ) = Y i ϕ A i ϕ 1 = N i=1 I[C i = 0]W C i Y i (A i E[A L i ])/ N i=1 I[C i = 0]W C i A i (A i E[A L i ]) H i (ϕ ) H(ϕ ) H(ϕ ) E[H(ϕ ) L] ϕ E[H(ϕ ) L] E[A L] P r[c = 1 A, L] 15.1 b(l) L A L b(l) L b(l)
48 16.1 Z A Z Y Y a,z Z a, z Z 16.2 P r[y a=1 = 1] P r[y a=0 = 1] Z A Y A Z E[Y a=1 Y a=0 A = 1, Z] = β 0 + β 1 Z E[Y Y a=0 A, Z] = A(β 0 + β 1 Z) β 0 Z = 0
49 β 0 + β 1 Z = 1 Z β 1 = 0 β 0 E[Y a=0 Z = 1] = E[Y a=0 Z = 0] E[Y A(β 0 + β 1 ) Z = 1] = E[Y Aβ 0 Z = 0] β 1 = 0 β 0 = E[Y Z = 1] E[Y Z = 0] E[A Z = 1] E[A Z = 0] β 1 = 0 β 0 = E[Y a=1 Y a=0 A = 1, Z = z] = E[Y a=1 Y a=0 A = 1] z E[Y a=1 ] E[Y a=0 ] β 0 = E[Y a=1 ] E[Y a=0 ] E[Y a=1 ] E[Y a=0 ] 16.4 A Z E[Y a=1 A = 1, Z] E[Y a=0 A = 1, Z] = exp(β 0 + β 1 Z), E[Y A, Z] = E[Y a=0 A, Z]exp[A(β 0 + β 1 Z), exp(β 0 Z = 0 exp(β 0 + β 1 ) Z = 1
50 β 1 = 0 E[Y a=1 ]/E[Y a=0 ] = exp(β 0 ) E[Y a=1 ] E[Y a=0 ] = E[Y A = 0](1 E[A])[exp(β 0 ) 1] + E[Y A = 1]E[A][1 exp(β 0 )] Z E[Y (1)] E[Y (0)] Z 16.5 E[Y Y a=0 Z, A, V ] = γ(z, A, V, ψ ) E[Y a=0 Z = 1, V ] = E[Y a=0 Z = 0, V ]. E[Y Z, A, V ] = E[Y 0 Z, A, V ]exp[γ(z, A, V, ψ )] 16.6 E[Y a=1 Y a=0 A z=1 A z=0 = 1]
51 E[Y z=1 Y z=0 ] = E[Y z=1 Y z=0 A z=1 = 1, A z=0 = 1]P r[a z=1 = 1, A z=0 = 1] +E[Y z=1 Y z=0 A z=1 = 0, A z=0 = 0]P r[a z=1 = 0, A z=0 = 0] +E[Y z=1 Y z=0 A z=1 = 1, A z=0 = 0]P r[a z=1 = 1, A z=0 = 0] +E[Y z=1 Y z=0 A z=1 = 0, A z=0 = 1]P r[a z=1 = 0, A z=0 = 1]. E[Y z=1 Y z=0 ] = E[Y z=1 Y z=0 A z=1 = 1, A z=0 = 0]P r[a z=1 = 1, A z=0 = 0]. E[Y z=1 Y z=0 A z=1 = 1, A z=0 = 0] = E[Y a=1 Y a=0 A z=1 = 1, A z=0 = 0]. E[Y a=1 Y a=0 A z=1 = 1, A z=0 = 0] = E[Y z=1 Y z=0 ] P r[a z=1 = 1, A z=0 = 0]. Z E[Y z=1 Y z=0 ] = E[Y Z = 1] E[Y Z = 0]. P r[a z=1 A z=0 = 1] = P r[a = 1 Z = 1] P r[a = 1 Z = 0]. P r[a z=0 = 1] = P r[a = 1 Z = 0], P r[a z=1 = 0] = P r[a = 0 Z = 1]. P r[a z=1 A z=0 = 1] = 1 P r[a = 1 Z = 0] P r[a = 0 Z = 1] = 1 P r[a = 1 Z = 0] (1 P r[a = 1 Z = 1]) = P r[a = 1 Z = 1] P r[a = 1 Z = 0] Z Z U z U z
52 Z A Y U z U z U z Z U z 10.2
53
54 ... L p +E[Y z=1 Y z=0 A z=1 = 1, A z=0 = 0]P r[a z=1 = 1, A z=0 = 0]
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