6. 因果推論 II - GitHub Pages...•selection bias = 0...

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計量経済学 6. 因果推論 II 矢内 勇生 2019年10月24日 高知工科大学 経済・マネジメント学群

Transcript of 6. 因果推論 II - GitHub Pages...•selection bias = 0...

Page 1: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

計量経済学

6. 因果推論 II

矢内 勇生

2019年10月24日

高知工科大学 経済・マネジメント学群

Page 2: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

今日の目標

• 因果推論の「根本問題」を解決する方法を考える

- 個体の因果効果は見えない

- 集団の因果効果を推定する

- なぜ実験が「最善」なのか?

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Page 3: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

前回のまとめ

•個体に関する因果効果(個体処置効果; ITE) - 潜在的結果の差 - 潜在的結果は最大で一つしか観察できない •個体に関する因果効果は観察できない:因果推論の根本問題

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Page 4: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

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潜在的結果      個体レベルの    因果効果観察対象

複数の個体を考える

•個体レベルの因果効果 (ITE) は観察不能 •では、何なら観察できる?

Page 5: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

集団の平均を考える•平均因果効果(平均処置効果; average treatment effect: ATE)

- :すべての個体が処置1を受けたときの結果の期待値

- :すべての個体が処置0を受けたときの結果の期待値

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Page 6: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

処置群と統制群•処置の値が2種類(0か1)しかないとき - 処置1を受ける:処置を受ける ‣ 処置を受けた個体のグループ:処置群 (treatment group)、実験群

- 処置0を受ける:処置を受けない ‣ 処置を受けなかった個体のグループ:統制群 (control group)、比較群

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Page 7: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

*期待値 (expected values)

•確率変数Xの期待値:E(X)

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確率

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E(X) =nX

i=1

xipi

= x1p1 + x2p2 + x3p3 + · · ·xnpn<latexit sha1_base64="KzXVnZnmYdEN9KvUWZvEWclmOro=">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</latexit><latexit sha1_base64="KzXVnZnmYdEN9KvUWZvEWclmOro=">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</latexit><latexit sha1_base64="KzXVnZnmYdEN9KvUWZvEWclmOro=">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</latexit><latexit sha1_base64="KzXVnZnmYdEN9KvUWZvEWclmOro=">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</latexit>

Page 8: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

*期待値の例 (1)•「公平な」サイコロを振ったときに出る目の期待値は?目 (X) 1 2 3 4 5 6

確率 1/6 1/6 1/6 1/6 1/6 1/6

E(X) = 1 · 16+ 2 · 1

6+ 3 · 1

6+ 4 · 1

6+ 5 · 1

6+ 6 · 1

6

= (1 + 2 + 3 + 4 + 5 + 6)1

6

=21

6=

7

2= 3.5

<latexit sha1_base64="Nj/Y3yoAABFfHUwxKpwaNJQoKcE=">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</latexit><latexit sha1_base64="Nj/Y3yoAABFfHUwxKpwaNJQoKcE=">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</latexit><latexit sha1_base64="Nj/Y3yoAABFfHUwxKpwaNJQoKcE=">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</latexit><latexit sha1_base64="Nj/Y3yoAABFfHUwxKpwaNJQoKcE=">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</latexit>

Page 9: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

*期待値の例 (2)•100分の1の確率で1万円が当たり、1000分の1の確率で10万円が当たるくじの賞金 (X) の期待値は?

E(X) = 100001

100+ 100000

1

1000= 100 + 100

= 200<latexit sha1_base64="p2MEN1uthCbydNKuQU4EvRsRPWU=">AAACpnicbZFbS8MwFMfTeq+3qY++BMekQ5RUBH0ZiCLoi3ib21jLTLN0hqUXklQYpR/NL+Gb38bMFtzcDgT+5/c/h+Sc+AlnUiH0bZgLi0vLK6tr1vrG5tZ2ZWf3VcapILRJYh6Lto8l5SyiTcUUp+1EUBz6nLb84fXYb31QIVkcvahRQr0QDyIWMIKVRr3KZ80NsXoXYXaTWxO66/YpV9iDDTgBO7ZTh8ewY6P6HMfT1hTSVdYfsNt1aB02oIN0QDcQmGROnuk0h0cFncYod92yoSgo0lOELFhEr1JFJ6jonBVOKaqgjIde5cvtxyQNaaQIx1J2HZQoL8NCMcJpbrmppAkmQzygXS0jHFLpZb9rzmFNkz4MYqFPpOAvnezIcCjlKPR15Xho+d8bw3leN1XBhZexKEkVjUhxUZByqGI4/jPYZ4ISxUdaYCKYfisk71gvSumftfQSnP8jz4rX0xNH68ez6uVVuY5VsA8OgA0ccA4uwS14AE1AjKpxZzwZz6Zt3ptNs1WUmkbZswemwnz7AYruwe4=</latexit><latexit sha1_base64="p2MEN1uthCbydNKuQU4EvRsRPWU=">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</latexit><latexit sha1_base64="p2MEN1uthCbydNKuQU4EvRsRPWU=">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</latexit><latexit sha1_base64="p2MEN1uthCbydNKuQU4EvRsRPWU=">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</latexit>

Page 10: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

平均因果効果 (ATE) は観察できる?

•全個体が処置1を受けたとき:   は観察(推定)可能 •全個体が処置0を受けたとき:   は観察(推定)可能

•処置1を受けた個体と処置0を受けた個体がいるとき:どちらの期待値も観察できない

•ATE も観察できない!10

ATE = E[Y (1)� Y (0)] = E[Y (1)]� E[Y (0)]<latexit sha1_base64="C2ct1el0BpnbagPeaQ9VGdGLgpU=">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</latexit><latexit sha1_base64="C2ct1el0BpnbagPeaQ9VGdGLgpU=">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</latexit><latexit sha1_base64="C2ct1el0BpnbagPeaQ9VGdGLgpU=">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</latexit><latexit sha1_base64="C2ct1el0BpnbagPeaQ9VGdGLgpU=">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</latexit>

E[Y (1)]<latexit sha1_base64="xkBF8AixII3hPRNuVn8t9GTHkiE=">AAACUXicbVFLSwMxGPy6vurWx6pHL8FSaA+WXRH0IlSl4LFCn7RLyaZpG5p9kGTFsvQvetCT/8OLB8X0AdrWgcAwMx/5MvEizqSy7feUsbG5tb2T3jUze/sHh9bRcV2GsSC0RkIeiqaHJeUsoDXFFKfNSFDse5w2vNH91G88USFZGFTVOKKujwcB6zOClZa61jDX8bEaCj8pT0zNvfA5ua2WJ+gG/RrtVt4poHPUytsFd91xtbUk6ZS5mulaWbtoz4DWibMgWVig0rVeO72QxD4NFOFYyrZjR8pNsFCMcDoxO7GkESYjPKBtTQPsU+kms0YmKKeVHuqHQp9AoZn6dyLBvpRj39PJ6Z5y1ZuK/3ntWPWv3YQFUaxoQOYX9WOOVIim9aIeE5QoPtYEE8H0rogMscBE6U8wdQnO6pPXSf2i6Gj+eJkt3S3qSMMpnEEeHLiCEjxABWpA4AU+4Au+U2+pTwMMYx41UouZE1iCkfkBt0Svow==</latexit><latexit sha1_base64="xkBF8AixII3hPRNuVn8t9GTHkiE=">AAACUXicbVFLSwMxGPy6vurWx6pHL8FSaA+WXRH0IlSl4LFCn7RLyaZpG5p9kGTFsvQvetCT/8OLB8X0AdrWgcAwMx/5MvEizqSy7feUsbG5tb2T3jUze/sHh9bRcV2GsSC0RkIeiqaHJeUsoDXFFKfNSFDse5w2vNH91G88USFZGFTVOKKujwcB6zOClZa61jDX8bEaCj8pT0zNvfA5ua2WJ+gG/RrtVt4poHPUytsFd91xtbUk6ZS5mulaWbtoz4DWibMgWVig0rVeO72QxD4NFOFYyrZjR8pNsFCMcDoxO7GkESYjPKBtTQPsU+kms0YmKKeVHuqHQp9AoZn6dyLBvpRj39PJ6Z5y1ZuK/3ntWPWv3YQFUaxoQOYX9WOOVIim9aIeE5QoPtYEE8H0rogMscBE6U8wdQnO6pPXSf2i6Gj+eJkt3S3qSMMpnEEeHLiCEjxABWpA4AU+4Au+U2+pTwMMYx41UouZE1iCkfkBt0Svow==</latexit><latexit sha1_base64="xkBF8AixII3hPRNuVn8t9GTHkiE=">AAACUXicbVFLSwMxGPy6vurWx6pHL8FSaA+WXRH0IlSl4LFCn7RLyaZpG5p9kGTFsvQvetCT/8OLB8X0AdrWgcAwMx/5MvEizqSy7feUsbG5tb2T3jUze/sHh9bRcV2GsSC0RkIeiqaHJeUsoDXFFKfNSFDse5w2vNH91G88USFZGFTVOKKujwcB6zOClZa61jDX8bEaCj8pT0zNvfA5ua2WJ+gG/RrtVt4poHPUytsFd91xtbUk6ZS5mulaWbtoz4DWibMgWVig0rVeO72QxD4NFOFYyrZjR8pNsFCMcDoxO7GkESYjPKBtTQPsU+kms0YmKKeVHuqHQp9AoZn6dyLBvpRj39PJ6Z5y1ZuK/3ntWPWv3YQFUaxoQOYX9WOOVIim9aIeE5QoPtYEE8H0rogMscBE6U8wdQnO6pPXSf2i6Gj+eJkt3S3qSMMpnEEeHLiCEjxABWpA4AU+4Au+U2+pTwMMYx41UouZE1iCkfkBt0Svow==</latexit><latexit sha1_base64="xkBF8AixII3hPRNuVn8t9GTHkiE=">AAACUXicbVFLSwMxGPy6vurWx6pHL8FSaA+WXRH0IlSl4LFCn7RLyaZpG5p9kGTFsvQvetCT/8OLB8X0AdrWgcAwMx/5MvEizqSy7feUsbG5tb2T3jUze/sHh9bRcV2GsSC0RkIeiqaHJeUsoDXFFKfNSFDse5w2vNH91G88USFZGFTVOKKujwcB6zOClZa61jDX8bEaCj8pT0zNvfA5ua2WJ+gG/RrtVt4poHPUytsFd91xtbUk6ZS5mulaWbtoz4DWibMgWVig0rVeO72QxD4NFOFYyrZjR8pNsFCMcDoxO7GkESYjPKBtTQPsU+kms0YmKKeVHuqHQp9AoZn6dyLBvpRj39PJ6Z5y1ZuK/3ntWPWv3YQFUaxoQOYX9WOOVIim9aIeE5QoPtYEE8H0rogMscBE6U8wdQnO6pPXSf2i6Gj+eJkt3S3qSMMpnEEeHLiCEjxABWpA4AU+4Au+U2+pTwMMYx41UouZE1iCkfkBt0Svow==</latexit>

E[Y (0)]<latexit sha1_base64="ZSNXfGk3GzzncnEjrxB8/pBpsvU=">AAACUXicbZFLSwMxFIVvx1ed+hh16SZYCu3CMiOCboSqFFxW6JN2KJk0bUMzD5KMWIb+RRe68n+4caGYPkDbeiHwcc695ObEiziTyrbfU8bG5tb2TnrXzOztHxxaR8d1GcaC0BoJeSiaHpaUs4DWFFOcNiNBse9x2vBG91O/8USFZGFQVeOIuj4eBKzPCFZa6lrDXMfHaij8pDwxNXvhc3JbLU/QDfo12q28U0DnqJW3C+6642prSdJd5qrQtbJ20Z4VWgdnAVlYVKVrvXZ6IYl9GijCsZRtx46Um2ChGOF0YnZiSSNMRnhA2xoD7FPpJrNEJiinlR7qh0KfQKGZ+nciwb6UY9/TndM95ao3Ff/z2rHqX7sJC6JY0YDML+rHHKkQTeNFPSYoUXysARPB9K6IDLHAROlPMHUIzuqT16F+UXQ0P15mS3eLONJwCmeQBweuoAQPUIEaEHiBD/iC79Rb6tMAw5i3GqnFzAkslZH5AbW+r6I=</latexit><latexit sha1_base64="ZSNXfGk3GzzncnEjrxB8/pBpsvU=">AAACUXicbZFLSwMxFIVvx1ed+hh16SZYCu3CMiOCboSqFFxW6JN2KJk0bUMzD5KMWIb+RRe68n+4caGYPkDbeiHwcc695ObEiziTyrbfU8bG5tb2TnrXzOztHxxaR8d1GcaC0BoJeSiaHpaUs4DWFFOcNiNBse9x2vBG91O/8USFZGFQVeOIuj4eBKzPCFZa6lrDXMfHaij8pDwxNXvhc3JbLU/QDfo12q28U0DnqJW3C+6642prSdJd5qrQtbJ20Z4VWgdnAVlYVKVrvXZ6IYl9GijCsZRtx46Um2ChGOF0YnZiSSNMRnhA2xoD7FPpJrNEJiinlR7qh0KfQKGZ+nciwb6UY9/TndM95ao3Ff/z2rHqX7sJC6JY0YDML+rHHKkQTeNFPSYoUXysARPB9K6IDLHAROlPMHUIzuqT16F+UXQ0P15mS3eLONJwCmeQBweuoAQPUIEaEHiBD/iC79Rb6tMAw5i3GqnFzAkslZH5AbW+r6I=</latexit><latexit sha1_base64="ZSNXfGk3GzzncnEjrxB8/pBpsvU=">AAACUXicbZFLSwMxFIVvx1ed+hh16SZYCu3CMiOCboSqFFxW6JN2KJk0bUMzD5KMWIb+RRe68n+4caGYPkDbeiHwcc695ObEiziTyrbfU8bG5tb2TnrXzOztHxxaR8d1GcaC0BoJeSiaHpaUs4DWFFOcNiNBse9x2vBG91O/8USFZGFQVeOIuj4eBKzPCFZa6lrDXMfHaij8pDwxNXvhc3JbLU/QDfo12q28U0DnqJW3C+6642prSdJd5qrQtbJ20Z4VWgdnAVlYVKVrvXZ6IYl9GijCsZRtx46Um2ChGOF0YnZiSSNMRnhA2xoD7FPpJrNEJiinlR7qh0KfQKGZ+nciwb6UY9/TndM95ao3Ff/z2rHqX7sJC6JY0YDML+rHHKkQTeNFPSYoUXysARPB9K6IDLHAROlPMHUIzuqT16F+UXQ0P15mS3eLONJwCmeQBweuoAQPUIEaEHiBD/iC79Rb6tMAw5i3GqnFzAkslZH5AbW+r6I=</latexit><latexit sha1_base64="ZSNXfGk3GzzncnEjrxB8/pBpsvU=">AAACUXicbZFLSwMxFIVvx1ed+hh16SZYCu3CMiOCboSqFFxW6JN2KJk0bUMzD5KMWIb+RRe68n+4caGYPkDbeiHwcc695ObEiziTyrbfU8bG5tb2TnrXzOztHxxaR8d1GcaC0BoJeSiaHpaUs4DWFFOcNiNBse9x2vBG91O/8USFZGFQVeOIuj4eBKzPCFZa6lrDXMfHaij8pDwxNXvhc3JbLU/QDfo12q28U0DnqJW3C+6642prSdJd5qrQtbJ20Z4VWgdnAVlYVKVrvXZ6IYl9GijCsZRtx46Um2ChGOF0YnZiSSNMRnhA2xoD7FPpJrNEJiinlR7qh0KfQKGZ+nciwb6UY9/TndM95ao3Ff/z2rHqX7sJC6JY0YDML+rHHKkQTeNFPSYoUXysARPB9K6IDLHAROlPMHUIzuqT16F+UXQ0P15mS3eLONJwCmeQBweuoAQPUIEaEHiBD/iC79Rb6tMAw5i3GqnFzAkslZH5AbW+r6I=</latexit>

Page 11: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

ATEの観察に失敗する例:手術 vs 投薬治療

• 手術のATE(平均処置効果) = 2

‣ 手術すると余命が平均2年延びる11

ガン患者の余命潜在的結果 因果効果

患者ID 手術 手術薬 薬

平均

Page 12: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

処置の割り当て•善良で優秀な医者

‣ 潜在的結果を(ある程度正確に)知っている

‣ 患者の余命を延ばそうとする

‣ それぞれの患者にとって最もいい治療法を選択する

12

患者 処置 観察される結果手術

手術薬

• 「誤った」因果推論:手術を受けた人の平均余命は6 < 投薬を受けた人の平均余命は7:手術は平均余命は1年縮める!

Page 13: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

どこで間違った?• 処置が患者の特性(共変量)によって変わる

‣ 手術を受けた人たちと手術を受けなかった(投薬された)人たちに違いがある

13

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) E[Y (1)] 6= E[Y (1) | D = 1],E[Y (0)] 6= E[Y (0) | D = 0]<latexit sha1_base64="fmpQ0bhlaxCI7PLaNXaub6uMjdY=">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</latexit><latexit sha1_base64="fmpQ0bhlaxCI7PLaNXaub6uMjdY=">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</latexit><latexit sha1_base64="fmpQ0bhlaxCI7PLaNXaub6uMjdY=">AAACsXicbVFbT9swFHYCjC6wUdjjXiyqSq0EVcImwQtS2Ya0R4ba0qoxneO6rVVfgu2wVVH/3573tn8zt1QCmh7J0qfvcnx8nKScGRuG/zx/a3vnzW7pbbC3/+79QfnwqGNUpgltE8WV7ibYUM4kbVtmOe2mmmKRcHqXTL8u9LtHqg1TsmVnKUUCjyUbMYKtowblP9VYYDvRIr+eBw4n6nd+1bqew0v4LPR7tagOT2GvFtZRUUFOekU5VxDfsvHEYq3Vr6DgjyV9KPSPBRvCb659hE4K/TZEwheREA3KlbARLgsWQbQCFbCqm0H5bzxUJBNUWsKxMf0oTC3KsbaMcDoP4szQFJMpHtO+gxILalC+3PgcVh0zhCOl3ZEWLtmXiRwLY2Yicc7FyGZdW5CbtH5mRxcoZzLNLJXk6aJRxqFVcPF9cMg0JZbPHMBEMzcrJBOsMbHukwO3hGj9yUXQOWtEDv/4XGl+Wa2jBD6CY1ADETgHTfAd3IA2IF7Da3nIu/c/+T3/p588WX1vlfkAXpU//Q9AL8yw</latexit><latexit sha1_base64="fmpQ0bhlaxCI7PLaNXaub6uMjdY=">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</latexit>

Page 14: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

観察したいものと観察できるもの•観察したいもの: -     : 全個体が処置1を受けたときの結果の期待値 -     : 全個体が処置0を受けたときの結果の期待値 •観察できる期待値: - :実際に処置1を受けた個体が処置1を受けたときの結果の平均値

- :実際に処置0を受けた個体が処置0を受けたときの結果の平均値

14

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E[Y (1) | D = 1]<latexit sha1_base64="3hj17DEjHVQI/qo3cuvslEodNJc=">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</latexit><latexit sha1_base64="3hj17DEjHVQI/qo3cuvslEodNJc=">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</latexit><latexit sha1_base64="3hj17DEjHVQI/qo3cuvslEodNJc=">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</latexit><latexit sha1_base64="3hj17DEjHVQI/qo3cuvslEodNJc=">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</latexit>

E[Y (0) | D = 0]<latexit sha1_base64="jlYgxiHnbXoCShy25D1d1gVBexc=">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</latexit><latexit sha1_base64="jlYgxiHnbXoCShy25D1d1gVBexc=">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</latexit><latexit sha1_base64="jlYgxiHnbXoCShy25D1d1gVBexc=">AAACz3icfVLLSgMxFM2M7/FVdekmWAoVVGZE0I3gq+DCRRXrg85QMmnaBvMYk4xaxopbf8+dP+B3mNaCjxEvBA7n3HPvzU3ihFFtfP/NcUdGx8YnJqe86ZnZufnCwuKFlqnCpIYlk+oqRpowKkjNUMPIVaII4jEjl/HNYV+/vCNKUynOTTchEUdtQVsUI2OpRuG9FHJkOopnlZ5ncSwfsv3zSg/uwi+hfl0OVuE6vC77q1Feiaz0g7JZttYZbXcMUkree6WcIxTkNtch5LQJj2yDIFrLVfzD4n+z+JH3j9YoFP0NfxAwD4IhKIJhVBuF17ApccqJMJghreuBn5goQ8pQzEjPC1NNEoRvUJvULRSIEx1lg/fowZJlmrAllT3CwAH73ZEhrnWXxzazP7L+rfXJv7R6alo7UUZFkhoi8GejVsqgkbD/uLBJFcGGdS1AWFE7K8QdpBA29gt4dgnB7yvnwcXmRmDx6VZx72C4jkmwDFZAGQRgG+yBY1AFNYCdE0c5mfPonrr37pP7/JnqOkPPEvgR7ssHJhnWqw==</latexit><latexit sha1_base64="jlYgxiHnbXoCShy25D1d1gVBexc=">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</latexit>

Page 15: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

何が計算できるか (1)

•ATT (average treatment effect on the treated):処置群における平均処置効果

15

E[Y (1) | D = 1]� E[Y (0) | D = 0]

=E[Y (1) | D = 1]� E[Y (0) | D = 0]

+ (E[Y (0) | D = 1]� E[Y (0) | D = 1])

=E[Y (1) | D = 1]� E[Y (0) | D = 1]

+ E[Y (0) | D = 1]� E[Y (0) | D = 0]

=ATT+ selection bias<latexit sha1_base64="OjGXZ7KxlkT5ITwgkiXNxjKZV1o=">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</latexit><latexit sha1_base64="OjGXZ7KxlkT5ITwgkiXNxjKZV1o=">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</latexit><latexit sha1_base64="OjGXZ7KxlkT5ITwgkiXNxjKZV1o=">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</latexit><latexit sha1_base64="OjGXZ7KxlkT5ITwgkiXNxjKZV1o=">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</latexit>

Page 16: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

何が計算できるか (2)

•ATC (average treatment effect on the controlled):統制群における平均処置効果

16

E[Y (1) | D = 1]� E[Y (0) | D = 0]

=E[Y (1) | D = 1]� E[Y (0) | D = 0]

+ (E[Y (1) | D = 0]� E[Y (1) | D = 0])

=E[Y (1) | D = 0]� E[Y (0) | D = 0]

+ E[Y (1) | D = 1]� E[Y (1) | D = 0]

=ATC+ selection bias<latexit sha1_base64="inkT/gUdw3r9lD7iGxygFaQU7FU=">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</latexit><latexit sha1_base64="inkT/gUdw3r9lD7iGxygFaQU7FU=">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</latexit><latexit sha1_base64="inkT/gUdw3r9lD7iGxygFaQU7FU=">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</latexit><latexit sha1_base64="inkT/gUdw3r9lD7iGxygFaQU7FU=">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</latexit>

Page 17: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

Selection Bias•セレクションバイアス •処置を受ける(処置1)か処置を受けない(処置0)かが、結果の値によって異なる

- 例:手術がうまくいきそうな人ほど手術を受け、手術が失敗しそうな人ほど手術を避ける

- 例:いい成績が取れそうな人ほど勉強する - 例:就職できい人ほど職業訓練を受けやすい

17

Page 18: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

観察データのバイアス

•観察された値の平均値を比較しても、結果にバイアス(体系的な偏り)が混ざっている

- バイアスを取り除きたい - どうすればいい?

18

Page 19: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

ATTを知りたいとき

•selection bias = 0 なら、観察できる期待値の差がATT

•処置群 (D=1)と統制群 (D=0) で処置を受けない場合の潜在的結果の期待値が同じなら、ATTが推定できる

19

E[Y (1) | D = 1]� E[Y (0) | D = 0] = ATT+ selection bias<latexit sha1_base64="m8ONhVGYXdK5lTRQDZNEc4KFgng=">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</latexit><latexit sha1_base64="m8ONhVGYXdK5lTRQDZNEc4KFgng=">AAACl3icfVFbS8MwGE3rvd7m5UV8CY7BRBytCIowvMseFTadrGWkWTaDSVqSVByl/iR/jG/+G9M5xKnzg8DhnO+W84Uxo0q77rtlT0xOTc/MzjnzC4tLy4WV1VsVJRKTBo5YJJshUoRRQRqaakaasSSIh4zchY/nuX73RKSikajrfkwCjnqCdilG2lDtwqvPkX6QPL3MWvdlbxv6nHbgRdUL4C4c0dwvzQ1g1eAwek5P6/UM7nwlmj0Izhu/hBSpzCmNFarjmv8/uF0ouhV3EPA38IagCIZx3S68+Z0IJ5wIjRlSquW5sQ5SJDXFjGSOnygSI/yIeqRloECcqCAd+JrBkmE6sBtJ84SGA/Z7RYq4Un0emsx8YfVTy8m/tFaiu4dBSkWcaCLw56BuwqCOYH4k2KHS2MX6BiAsqdkV4gckEdbmlI4xwfv55d/gdq/iGXyzXzw5G9oxCzbBFigDDxyAE1AD16ABsLVuHVnn1oW9YR/bV3btM9W2hjVrYCTsmw8gzMVf</latexit><latexit sha1_base64="m8ONhVGYXdK5lTRQDZNEc4KFgng=">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</latexit><latexit sha1_base64="m8ONhVGYXdK5lTRQDZNEc4KFgng=">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</latexit>

selection bias = E[Y (0) | D = 1]� E[Y (0) | D = 0] = 0<latexit sha1_base64="Uu2RBRln6wEOMp3K2V9Kydoc3fQ=">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</latexit><latexit sha1_base64="Uu2RBRln6wEOMp3K2V9Kydoc3fQ=">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</latexit><latexit sha1_base64="Uu2RBRln6wEOMp3K2V9Kydoc3fQ=">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</latexit><latexit sha1_base64="Uu2RBRln6wEOMp3K2V9Kydoc3fQ=">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</latexit>

() E[Y (0) | D = 1] = E[Y (0) | D = 0]<latexit sha1_base64="GNNHPZHdPS+fCwShBqmCbFrDfyo=">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</latexit><latexit sha1_base64="GNNHPZHdPS+fCwShBqmCbFrDfyo=">AAAC13ichVLbSsMwGE7ruZ6mXnoTHANFlFQEvRl4BC8VNg+sZaRZ6oJJW5JUnKV6oYi3vpp3voTPYDqHeJr+EPj4vv/8J0g4UxqhF8seGBwaHhkdc8YnJqemSzOzxypOJaF1EvNYngZYUc4iWtdMc3qaSIpFwOlJcLFb6CeXVCoWRzXdSagv8HnEQkawNlSz9FrxBNZtKbL9vHG26C5BT7AW3Ku6PlyBXzT0oSEfVg0O4qtsu1bL4fKHo2mEkiLzTcCwyp1KX6HaL/m/hZHjsTD8I7xvauQ3S2W0iroGfwK3B8qgZ4fN0rPXikkqaKQJx0o1XJRoP8NSM8Jp7nipogkmF/icNgyMsKDKz7p3yWHFMC0YxtK8SMMu+zkiw0KpjgiMZ9Gw+q4V5G9aI9Xhpp+xKEk1jch7oTDlUMewODJsMWm2zTsGYCKZ6RWSNpaYaPMVHLME9/vIP8Hx2qpr8NF6eWunt45RMA8WwCJwwQbYAgfgENQBsWrWtXVn3dtn9q39YD++u9pWL2YOfDH76Q1PCttg</latexit><latexit sha1_base64="GNNHPZHdPS+fCwShBqmCbFrDfyo=">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</latexit><latexit sha1_base64="GNNHPZHdPS+fCwShBqmCbFrDfyo=">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</latexit>

Page 20: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

ATCを知りたいとき

•selection bias = 0 なら、観察できる期待値の差がATC

•処置群 (D=1)と統制群 (D=0) で処置を受けた場合の潜在的結果の期待値が同じなら、ATCが推定できる

20

E[Y (1) | D = 1]� E[Y (0) | D = 0] = ATC+ selection bias<latexit sha1_base64="iBM+9DKOjbozbC1b/xW/lgF4/LU=">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</latexit><latexit sha1_base64="iBM+9DKOjbozbC1b/xW/lgF4/LU=">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</latexit><latexit sha1_base64="iBM+9DKOjbozbC1b/xW/lgF4/LU=">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</latexit><latexit sha1_base64="iBM+9DKOjbozbC1b/xW/lgF4/LU=">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</latexit>

selection bias = E[Y (1) | D = 1]� E[Y (1) | D = 0] = 0<latexit sha1_base64="bHzJuGYZDU9pDEB4E0SB1unuk2s=">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</latexit><latexit sha1_base64="bHzJuGYZDU9pDEB4E0SB1unuk2s=">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</latexit><latexit sha1_base64="bHzJuGYZDU9pDEB4E0SB1unuk2s=">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</latexit><latexit sha1_base64="bHzJuGYZDU9pDEB4E0SB1unuk2s=">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</latexit>

() E[Y (1) | D = 1] = E[Y (1) | D = 0]<latexit sha1_base64="D+47qvRUq+sYWVIAIPFeBkGDMxM=">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</latexit><latexit sha1_base64="D+47qvRUq+sYWVIAIPFeBkGDMxM=">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</latexit><latexit sha1_base64="D+47qvRUq+sYWVIAIPFeBkGDMxM=">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</latexit><latexit sha1_base64="D+47qvRUq+sYWVIAIPFeBkGDMxM=">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</latexit>

Page 21: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

セレクションバイアスをなくす•                をどうやって実現する?

•                をどうやって実現する?

•最も簡単な方法: - 個体を処置群と統制群に無作為に振り分ける - Dの値をランダムに決める

21

E[Y (1) | D = 1] = E[Y (1) | D = 0]<latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit>

E[Y (0) | D = 1] = E[Y (0) | D = 0]<latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit>

Page 22: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

処置のランダム割当の効果 (1)•処置Dの値をランダムに割り当てる:

22

E[Y (1) | D = 1] = E[Y (1) | D = 0]<latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit><latexit sha1_base64="TwqEKIjVmrqXQTEYEpbg9/35WSU=">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</latexit>

E[Y (0) | D = 1] = E[Y (0) | D = 0]<latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">AAAC0nicjVJdS8MwFE3rd/2q+uhLcAwUURoR9GXgJ/imwjaVrYw0y2YwaUuSirNUEV/9db75E/wXptsQNx14IXA4597ck3sTxJwp7Xkflj02PjE5NT3jzM7NLyy6S8tVFSWS0AqJeCSvA6woZyGtaKY5vY4lxSLg9Cq4O871q3sqFYvCsu7E1Be4HbIWI1gbquF+FusC61sp0tOsdrOONmBdsCY8KSEfbsEBzfvWPB+WDA6ih/SwfJzBze9EY4SS/OangGGVOcWRQgn+uzEabOw5I2yhnq0Rlhtuwdv2ugF/A9QHBdCPi4b7Xm9GJBE01IRjpWrIi7WfYqkZ4TRz6omiMSZ3uE1rBoZYUOWn3ZVksGiYJmxF0pxQwy77syLFQqmOCExmblgNazn5l1ZLdGvfT1kYJ5qGpNeolXCoI5jvFzaZNIPmHQMwkcx4heQWS0y0+QWOGQIafvJvUN3ZRgZf7hYOjvrjmAarYA2sAwT2wAE4AxegAoh1biXWk/Vsl+1H+8V+7aXaVr9mBQyE/fYFUvLZbg==</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit><latexit sha1_base64="VQstsse6b0iVYlGrGx5pPR4iPkQ=">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</latexit>

かつ

E[Y (1)] = E[Y (1) | D = 1] = E[Y (1) | D = 0]<latexit sha1_base64="JrIt5QOwweehZcufatGqPWjaxjQ=">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</latexit><latexit sha1_base64="JrIt5QOwweehZcufatGqPWjaxjQ=">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</latexit><latexit sha1_base64="JrIt5QOwweehZcufatGqPWjaxjQ=">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</latexit><latexit sha1_base64="JrIt5QOwweehZcufatGqPWjaxjQ=">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</latexit>

E[Y (0)] = E[Y (0) | D = 1] = E[Y (0) | D = 0]<latexit sha1_base64="0WRsj7cABQHR4jmSPhWwa0HN/No=">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</latexit><latexit sha1_base64="0WRsj7cABQHR4jmSPhWwa0HN/No=">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</latexit><latexit sha1_base64="0WRsj7cABQHR4jmSPhWwa0HN/No=">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</latexit><latexit sha1_base64="0WRsj7cABQHR4jmSPhWwa0HN/No=">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</latexit>

かつ

Page 23: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

処置のランダム割当の効果 (2)•したがって、

23

E[Y (1) | D = 1]� E[Y (0) | D = 0]

=E[Y (1)]� E[Y (0)]

=ATE<latexit sha1_base64="pOAm7M2HyzRnFz9oZ+MDhdoZRMQ=">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</latexit><latexit sha1_base64="pOAm7M2HyzRnFz9oZ+MDhdoZRMQ=">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</latexit><latexit sha1_base64="pOAm7M2HyzRnFz9oZ+MDhdoZRMQ=">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</latexit><latexit sha1_base64="pOAm7M2HyzRnFz9oZ+MDhdoZRMQ=">AAADR3iclVJNS+wwFE3rd59PR126CQ4jPh5PGhF0M+AnuFRw/GBahjST0WDSliQVh1J/nRu37vwLblwo4tJ0poozOvC8EDicc2/uyc0NYs6Udt17yx4aHhkdG59wfk3+npouzcweqSiRhNZIxCN5EmBFOQtpTTPN6UksKRYBp8fBxXauH19SqVgUHup2TH2Bz0LWYgRrQzVmLL/iCazPpUh3s/rpEvoDPcGacKeKfPgP9mjuh+b6sGpwEF2lm4fbGfz7kWicUJJffR0wrDKnMlCowv9ujHobu05lgC/U9TXAs7P486fm7XzoeU51sd/TN0VF5vtkdrNGqewuu52AXwEqQBkUsd8o3XnNiCSChppwrFQdubH2Uyw1I5xmjpcoGmNygc9o3cAQC6r8tLMHGawYpglbkTQn1LDDfq5IsVCqLQKTmftW/VpOfqfVE91a91MWxommIek2aiUc6gjmSwWbTJrP5W0DMJHMeIXkHEtMtFk9xwwB9T/5KzhaWUYGH6yWN7aKcYyDebAAlgACa2AD7IF9UAPEurEerCfr2b61H+0X+7WbaltFzRzoiSHrDWpY/+A=</latexit>

•観察したものから、ATEが推測できる!

Page 24: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

無作為化比較実験 (RCTs)• 対象集団を無作為(ランダム)に2つに分ける!

- 無作為 (random):確率が等しい

• 無作為に作られる2つの集団:よく似ている(集団としては交換可能な)はず

- 処置群(実験群):実験の刺激を与えられる集団(例:アスピリンを飲む)

- 統制群(比較群):比較の対象となる集団(例:アスピリンを飲まない)

24

無作為化比較実験 (Randomized Controlled Trials: RCTs)

Page 25: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

RCTで何をするか:頭痛とアスピリンの例

• 処置群と統制群:アスピリンを飲むかどうか以外に差はない(無作為に選んでいるため)

25

頭痛がある人々

処置群

統制群

無作為に振り分ける

アスピリンを飲む

アスピリンを飲まない

頭痛が残っている人の割合?

頭痛が残っている人の割合?

比較する

• もし結果に違いがあれば、考えられる要因はアスピリンの有無のみ

• 平均的な因果関係を確かめられる﹅ ﹅ ﹅ ﹅

Page 26: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

実験できないとき:調査・観察研究

•調査・観察データを使った因果推論は難しい - 例:手術 vs 投薬 •なぜ難しいか? - 処置を受ける人と受けない人が「同じ」ではない

26

Page 27: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

交絡 (confounder)•交絡変数 Z: 処置 D(処置を受ける確率)と結果 Yの両者に影響を与える変数

27

Z

D

Y

Page 28: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

架空の例•「スポーツをする人ほど寿命が短い」説 - 処置 (D):「週に3回以上運動をするかどうか」 ‣ している人は1、していない人は0

- 結果 (Y):生存年数(何歳で死ぬか)

28

D Y負の因果効果?

E[Y (1)] < E[Y (0)]<latexit sha1_base64="URte0X/1pbEi0bqpc2XV3nhRQfM=">AAACDHicbVDLSgMxFL1TX7W+qi7dBIvQbsqMCLpwURTBZQX7kOlQMmnahmYyQ5IRytAPcOOvuHGhiFs/wJ1/Y6adhW09EDiccy659/gRZ0rb9o+VW1ldW9/Ibxa2tnd294r7B00VxpLQBgl5KNs+VpQzQRuaaU7bkaQ48Dlt+aPr1G89UqlYKO71OKJegAeC9RnB2kjdYqkTYD2UQXIzcR/KTsVDl2hOsiueSdlVewq0TJyMlCBDvVv87vRCEgdUaMKxUq5jR9pLsNSMcDopdGJFI0xGeEBdQwUOqPKS6TETdGKUHuqH0jyh0VT9O5HgQKlx4Jtkuqda9FLxP8+Ndf/CS5iIYk0FmX3UjznSIUqbQT0mKdF8bAgmkpldERliiYk2/RVMCc7iycukeVp17Kpzd1aqXWV15OEIjqEMDpxDDW6hDg0g8AQv8Abv1rP1an1Yn7NozspmDmEO1tcvcOeZ7g==</latexit><latexit sha1_base64="URte0X/1pbEi0bqpc2XV3nhRQfM=">AAACDHicbVDLSgMxFL1TX7W+qi7dBIvQbsqMCLpwURTBZQX7kOlQMmnahmYyQ5IRytAPcOOvuHGhiFs/wJ1/Y6adhW09EDiccy659/gRZ0rb9o+VW1ldW9/Ibxa2tnd294r7B00VxpLQBgl5KNs+VpQzQRuaaU7bkaQ48Dlt+aPr1G89UqlYKO71OKJegAeC9RnB2kjdYqkTYD2UQXIzcR/KTsVDl2hOsiueSdlVewq0TJyMlCBDvVv87vRCEgdUaMKxUq5jR9pLsNSMcDopdGJFI0xGeEBdQwUOqPKS6TETdGKUHuqH0jyh0VT9O5HgQKlx4Jtkuqda9FLxP8+Ndf/CS5iIYk0FmX3UjznSIUqbQT0mKdF8bAgmkpldERliiYk2/RVMCc7iycukeVp17Kpzd1aqXWV15OEIjqEMDpxDDW6hDg0g8AQv8Abv1rP1an1Yn7NozspmDmEO1tcvcOeZ7g==</latexit><latexit sha1_base64="URte0X/1pbEi0bqpc2XV3nhRQfM=">AAACDHicbVDLSgMxFL1TX7W+qi7dBIvQbsqMCLpwURTBZQX7kOlQMmnahmYyQ5IRytAPcOOvuHGhiFs/wJ1/Y6adhW09EDiccy659/gRZ0rb9o+VW1ldW9/Ibxa2tnd294r7B00VxpLQBgl5KNs+VpQzQRuaaU7bkaQ48Dlt+aPr1G89UqlYKO71OKJegAeC9RnB2kjdYqkTYD2UQXIzcR/KTsVDl2hOsiueSdlVewq0TJyMlCBDvVv87vRCEgdUaMKxUq5jR9pLsNSMcDopdGJFI0xGeEBdQwUOqPKS6TETdGKUHuqH0jyh0VT9O5HgQKlx4Jtkuqda9FLxP8+Ndf/CS5iIYk0FmX3UjznSIUqbQT0mKdF8bAgmkpldERliiYk2/RVMCc7iycukeVp17Kpzd1aqXWV15OEIjqEMDpxDDW6hDg0g8AQv8Abv1rP1an1Yn7NozspmDmEO1tcvcOeZ7g==</latexit><latexit sha1_base64="URte0X/1pbEi0bqpc2XV3nhRQfM=">AAACDHicbVDLSgMxFL1TX7W+qi7dBIvQbsqMCLpwURTBZQX7kOlQMmnahmYyQ5IRytAPcOOvuHGhiFs/wJ1/Y6adhW09EDiccy659/gRZ0rb9o+VW1ldW9/Ibxa2tnd294r7B00VxpLQBgl5KNs+VpQzQRuaaU7bkaQ48Dlt+aPr1G89UqlYKO71OKJegAeC9RnB2kjdYqkTYD2UQXIzcR/KTsVDl2hOsiueSdlVewq0TJyMlCBDvVv87vRCEgdUaMKxUq5jR9pLsNSMcDopdGJFI0xGeEBdQwUOqPKS6TETdGKUHuqH0jyh0VT9O5HgQKlx4Jtkuqda9FLxP8+Ndf/CS5iIYk0FmX3UjznSIUqbQT0mKdF8bAgmkpldERliiYk2/RVMCc7iycukeVp17Kpzd1aqXWV15OEIjqEMDpxDDW6hDg0g8AQv8Abv1rP1an1Yn7NozspmDmEO1tcvcOeZ7g==</latexit>

Page 29: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

交絡の疑い•性別 (Z) が影響する? - 男性の方が「週に3回以上運動する」確率が高いかも - 男性の方が生物学的に寿命が短いかも

29

D Y

負の効果?Z

正の効果?

???

Page 30: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

何が問題なのか?•仮定をおく(単なる例であり、事実とは異なる) - 女性の平均寿命 = 81, 男性の平均寿命 = 75 - 人口の男女比は1:1 - 運動は、男性の方が2倍しやすい •処置群の男女比は 2:1 •統制群の男女比は 1:2 •運動が寿命にまったく影響を与えないとすると - 処置群の平均寿命: - 統制群の平均寿命:

30

75 · 2/3 + 81 · 1/3 = 77<latexit sha1_base64="2SxWHbhnAsEKxPRjDllfhOXqwyA=">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</latexit><latexit sha1_base64="2SxWHbhnAsEKxPRjDllfhOXqwyA=">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</latexit><latexit sha1_base64="2SxWHbhnAsEKxPRjDllfhOXqwyA=">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</latexit><latexit sha1_base64="2SxWHbhnAsEKxPRjDllfhOXqwyA=">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</latexit>

75 · 1/3 + 81 · 2/3 = 79<latexit sha1_base64="HN3u0hJ9ImRJHbKpnkqSBn/lP6M=">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</latexit><latexit sha1_base64="HN3u0hJ9ImRJHbKpnkqSBn/lP6M=">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</latexit><latexit sha1_base64="HN3u0hJ9ImRJHbKpnkqSBn/lP6M=">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</latexit><latexit sha1_base64="HN3u0hJ9ImRJHbKpnkqSBn/lP6M=">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</latexit>

差がある!

Page 31: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

一つの対処法:交絡をブロックする

•ブロッキング (blocking)、細分類化 (subclassification)

- 交絡変数の値によって、分析対象をグループ分けして分析する

•性別が交絡なら、男性と女性を別に分析する

31

Page 32: 6. 因果推論 II - GitHub Pages...•selection bias = 0 なら、観察できる期待値の差がATT • 処置群 (D=1)と統制群 (D=0) で処置を受けない場合の 潜在的結果の期待値が同じなら、ATTが推定できる

細分類化のイメージ

運動 寿命

性別

女性

男性

運動 寿命

平均因果効果は?

平均因果効果は?