???????????????????

1
?????????????
??????????????????? KBS?? ???????2003?3?4?(?)
1330-1730 ????????

• ?? ????? ?????????
• ???????????

2
Agenda

• ???????????
• ?????
• ?????Rubin????
• ???
• (Lord???????????)

3
???????????
4
?????????????????---????????---
????

• ???????????????????????
• ????????????????????????

5
??????
6
??????????????(Instrumental variable method)
????
????
7
????????????????
??????
??????
X?Y ???????????
8
???????

• X,Y????????????,???????????????Z(????)?????
• X,Y,Z???????,X?Y or X?Y ?????

9
????????(??????)
10
?1?????????
??Asher(1976). Causal Modeling. Sage
11
?2Attractiveness implies perceived academic
ability?
?? AMOS?????
12
?????????????
13
???????????
14
?????????????

• X,Y?,?????(0)????????,??????,???????????
• ???????????B???
• X?Y?????????????????

15
??????????????????

• ?????????????
• ??????????
• ???????????
• ???????????????????????????
• ????????????(?????)???

16
???

• ?????????
• ?????
• X?Y,X?Y,X??Y?????
• ????????
• X?Y,X?Y,X??Y, ?????????
• ?????,????????????
• ????
• ?????????????????
• ??????
• R2?????????
• R20.1??????????
• X?Y???????????????

17
?1????????
??(1986,?????)
18
?2??????????
???Y?X????????
19
?????????

• 2?????????,????????
• ????????? or ?????????

Lord ???????
20
???

• ???????????,?????????????????????
• X?Y or Y? X?????????????
• ??????????????????
• ?????
• ??
• ??????????????
• ?????????????????????
• ????????????????????????????????

21
?????
22
?????

• ??(or ??)??????
• X???????
• Y????(??)
• Z1,Z2, ????
• ?????(propensity score)
• by Rosenbaum-Rubin (Biometrika, 1983)
• e(z)EX1Z1,Z2,
• X Z e(z)

23
????????
Given e(Z1,Z2,)

• ?Z?Y????????????
• ?X?Y??????????????????

24
????????
????
e(z)0.8
e(z)0.5
e(z)0.2
X0 X1??? ??
25
????????

• ????z??????e(z)??????
• ???????
• e(z)????????????????X0,1???
• ?????
• e(z)?????????X0?X1?????????????,??????????????
• e(z)???
• ??????????????
• strongly ignorable???
• z??????,??????????????????
• z???????????????

26
????????????

• ??????????????????????
• Mx, EQS, LISREL
• z?Y??????????(??)?????

27
???

• ?????
• ????????z?1??????
• ???????????????????
• z??Y??????????
• ?????????????,??????
• SEM
• z?????????????
• ?????
• z?X???????????

28
?????Rubin????
29
Rubin????(1)

• ????????????????
• ?
• P??(Y1)???? vs P??(Y1)????
• ??Y?????? vs ??Y?????
• ??
• ???P
• ????????(unit)u
• Yx0(u) vs Yx1(u)
• X0 control, X1 treatment
• Unit-level Causal Effect

30
??????????

• Unit-level Causal Effect
• ??????????????????????????
• ???????
• ?????????????(e.g., Holland 1986)(fundamental
  problem of causal inference)

31
Rubin????(2)

• Average Causal Effect
• EPYx0 vs EPYx1
• P?unit????X0 ? X1? ?????
• ??????????????
• ??????????????????
• ?????????????
• ???????

32
?????????
?????
z???
33
Average Causal Effect???

• ???????????????
• ???????? or ????????????
• ???????????????
• MCAR
• X0,1??????????????
• MAR???????,???????????
• z?????????
• ??????????????

34
?????????

• Missing Completely At Random (MCAR)
• ????????????????????
• Missing At Random (MAR)
• ??????????????????????,????????????
• ???(FIML)?????????
• Non-ignorable Missing
• ?????????????????????
• ?????????????????

35
??(???)????
MCAR X0,1?????????
MAR X0,1?Z????????
36
MAR??

• ????????????
• ??????????
• ???????????

37
Average Causal Effect???---MAR???---

• strongly ignorable given z (Rosenbaum-Rubin,1983)
• z?????????
• Missing Completely At Random
• (????)?????? X0,1 ?????????
• X0,1?,z??????Y?????????
• Missing At Random
• ??????

38
???
39
SEM????
?????????????SEM
????????????
40
Rubin????????

• ??????????(??)????
• ??????????????????
• ????????????
• ????????
• ????????????
• Unit-level Causal Effect
• Average Causal Effect
• ????????????,???????????????????

41
?????????

• ?????????
• MCAR??????
• MAR????????z??????
• strongly ignorable given z
• z??????????????
• ????????z????????
• ????
• MCARz????????
• MAR ????????????
• SEM???
• MAR???,??????????

42
???

• ?????????????
• ???????????????????
• ??????????,X??????????.?????????????
• ??X?????????????.??????????
• ???????
• ????????,????????????????????
• ????????????,?????????

43

• ??????????????
• ????????????
• ?????????????????
• ???????????????????
• ???????????????????????
• SEM?????????,?????????????????????
• ?????????,???????????,?????????????????????
• ??????????
• ???????????????

44

• Rubin???
• ??????????????
• ?????????
• ????????????
• ????????
• ??????????
• ??????????(MAR)???

45
????

• Bollen, K. A. (1989). Structural Equations with
  Latent Variables. Wiley New York
• Bullock, H. E., Harlow, L. L. Mulaik, S. A.
  (1994). Causal issues in structural equation
  modeling research. Structural Equation Modeling,
  1, 253-267
• Holland, P. W. (1986). Statistics and causal
  inference (with discussion). Journal of the
  American Statistical Association, 81, 945-970
• Holland, P. M. Rubin, D. B. (1983). On Lords
  Paradox. In Principles of Modern Psychological
  Measurement (Wainer Messick, Eds.), pp.3-35.
  Erbaum.
• Lord, F. M. (1967). A paradox in the
  interpretation of group comparison. Psych. Bull.
  68, 304-305.
• Mulaik, S. A. James, L. R. (1995). Objectivity
  and reasoning in science and structural equation
  modeling. In Structural Equation Modeling
  Concepts, Issues, and Applications, (Hoyle, H.,
  Ed.), pp.118-137. Sage Publications CA

46

• Rosenbaum, P. R. Rubin, D. B. (1983). The
  central role of the propensity score in
  observational studies for causal effects.
  Biometrika, 70, 41-55
• Wainer, H.(1991). Adjusting for differential base
  rate Lord's paradox again. Psych. Bull. 109,
  147-151.
• ?? ?(2002). ???????????.???????
• ??? (2002). ???????????,????,???????? ??? (??)
  ???????? -- ????????????? Part II.????
• ??????? (2002). ???????????????? ??? (??)
  ???????? -- ????????????? Part III.????
• ???? (1986). ?????????????? ---
  ?????????loop?????.?????,14, 71-78
• ???(1986). ??????????.?????,14, 85-90
• ????(1998). ??????????.????
• ???? (1997). ???????????.????

47
MAR???????

• Missing At Random (MAR)
• ??????????????????????,????????????
• ???(FIML)?????????

48
???
49
Lord ???????????

• Lord(1967) Psych. Bull.
• Holland Rubin (1983)
• Wainer (1991) Psych. Bull.

50
??

• ??????????????????????????
• ???
• ???????1?????
• ??

51
??

• Statistician 1 not significant
• Statistician 2 significant

52
???
1?????
?


?
??????
0
53
???(??)??

• Statistician 1
• ?????????????????????
• Statistician 2
• ????????????????1????????????
• ????
• ????????????????????

54
Statistician 2???
1?????
?


??????
?
??????
0
55
????????

• ???????????Stat2???????????
• ?????????,?????????
• ??????????????????????????
• ???????????
• ????????????
• ??????????????????????????

56
Rubin????

• ??? ???????
• ?? ???????(x1)
• ?????? ????????(x0)
• ??? ?????????(x1)
• ???
• ??. G1,2(male or female)
• Y ... 1?????
• Z ... ??????

57
Rubin?????Statistician1

• Average Causal Effect
• ??????? MEPYx1 ? - EPYx0 ?
• ??????? FEPYx1 ? - EPYx0 ?
• ????? M-F ????????
• Statistician 1
• EPYx1 -Z? vs EPYx1 -Z?
• ???????????
• Yx0 Z

58
Rubin?????Statistician2

• Average Causal Effect
• ??????? MEPYx1 ? - EPYx0 ?
• ??????? FEPYx1 ? - EPYx0 ?
• ????? M-F ????????
• Statistician 2
• EPYx1 -(abZ)? vs EPYx1 -(abZ)?
• ???????????
• Yx0 abZ

59
????

• ??????????
• ??1 Yx0 Z
• ??2 Yx0 abZ
• ??????????
• ??1????,??????????????????????
• ??2????,?????????????????????,??????????????
• ?????????????,????????????,????(??)????????????
• ?????????????????

60
Statistician 2???
1?????
?


??????
?
??????
0
61
2????(1)

• ?????????????????
• ??????,???,????

???????? ??????
??? 1??
??? 1??
Yx0 Z Yx0 abZ
62
2????(2)

• Yx0 abZ?????????
• ????????
• ?????????????Yx1??????????????
• a?b?,Yx1?Z??????????

??? 1??
63
Lord???????????

• ????????????
• 1????????????
• 2????z?????,?????????
• ????????
• ??????????????????
• ??????????????????????????

64

• ???????
• ?????,?????????????????
• 1 Yx0 Z
• 2 Yx0 abZ
• ?????????
• ?????????????
• ??Yx0 abZ?????????????????