New developments in structural equation modeling

Transcription

1 New developments in structural equation modeling Rex B Kline Concordia University Montréal Set B: Mediation A UNL Methodology Workshop

2 A2

3 Topics o Mediation: Design requirements Conditional process modeling Cause mediator A3

4 Design o Baron, R. M., & Kenny, D. A. (986). The moderatormediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 5, A4

5 D a Y c b D2 Y2 Y Y2 = ab c' A5

6 D a Y c b D2 c D2 Y2 Y2 c, a * * * c not (c < c) ab A6

7 Design o Newer view: * insufficient Time precedence Changes A7

8 Mediation refers to the causal hypothesis that one variable causes changes in another variable, which in turn leads to changes in the outcome variable. Little (203) A8

9 Half longitudinal mediation a D2 M b M2 D22 O2 O22 A9

10 Full longitudinal mediation a 2 3 M M2 b M3 O O2 O3 A0

11 Design o Concurrent design o Uncertain directionality o Equivalent models A

12 Concurrent measurement () D D2 D Y Y2 Y2 D2 D D Y2 Y Y D D2 D Y2 Y Y Y2 Y D D D2 Y2 A2

13 Concurrent measurement (2) D D2 D Y Y2 Y2 D2 D D Y2 Y Y D D2 D Y2 Y Y Y2 Y D D D2 Y2 A3

14 Concurrent measurement* (3) D D2 D Y Y2 Y2 D2 D D Y2 Y Y D D2 D Y2 Y Y Y2 Y D D D2 *Equality-constrained reciprocal effects Y2 A4

15 Design o Minimal: Time precedence is manipulated M, Y are nonexperimental A5

16 M M U Y Y M Y M Y M U Y A6

17 Design o Bullock, J. G., Green, D. P., & Ha, S. E. (200). Yes, but what s the mechanism? (Don t expect an easy answer). Journal of Personality and Social Psychology, 98, A7

18 Moderation o, W, Z are continuous o Moderated MR o Yˆ = B + B W + B W + A W W A8

19 Moderation o Edwards, J. R. (2009). Seven deadly myths of testing moderation in organizational research. In C. E. Lance & R. J. Vandenberg (Eds), Statistical and methodological myths and urban legends: Doctrine, verity and fable in the organizational and social sciences (pp ). New York: Taylor & Francis. A9

20 Myths You must center, to reduce extreme collinearity A20

21 Truths Centering changes nothing Optional, if 0 is not on scale Center some, others not A2

22 Myth You must use hierarchical entry A22

23 Truths Not required Possibly misleading A23

24 Myth You can ignore score reliability Truth A24

25 Truth Score reliability is critical r >.90 A25

26 Myth Yˆ = B + B W + B W + A W W, W are main effects A26

27 Truth, W are linear only A27

28 W Y M A28

29 Yˆ =.2.064W R =.033 A29

30 0 9 Y A30

31 0 9 W < MW Y 8 7 W > MW A3

32 Yˆ =.2.064W R =.033 Yˆ = W.08W R =.829 A32

33 Yˆ = W.08W 3.8 A33

34 Centering o W with, W o x = M, w = w Mw o xw with x, w A34

35 Yˆ = W.08W 3.8 Yˆ =.000 x.035 w.08xw R =.829 A35

36 Y on as a function of W Yˆ = W.08W 3.8 Yˆ = W +.734W 3.8 Yˆ = ( W) +.(734W 3.8) A36

37 Yˆ = ( W) + (.734W 3.8) M = W A37

38 Yˆ = ( W) +.(734W 3.8) 4.34, 0.36, 6.38, 22.40, and Y ˆ = = ( * 22.40) + (.734* ) W Yˆ = W= A38

39 W Level Score Regression equation +2 SD Yˆ = SD Yˆ = Mean 6.38 Yˆ = SD 0.36 Yˆ = SD 4.34 Yˆ = A39

40 2 SDW SDW MW +2 SDW + SDW A40

41 Path models o Diagram options:. Include W 2. Moderated path A4

42 DY W Y W BW W BW DY BW DY W Y Y A42

43 Process modeling o Both:. Mediated moderation 2. Moderated mediation (conditional indirect) A43

44 Mediated moderation DM W M DY Y W A44

45 Process modeling o Moderated mediation:. st stage 2. 2 nd stage 3. st and 2 nd stage A45

46 st stage M depends on W DM W M DY W Y A46

47 2 nd stage M Y depends on W DY DM M Y W MW A47

48 st and 2 nd stage M, M Y depend on W DM W M DY W Y A48

49 Mediation in SCM o Nonparametric model o Consistent definition o Linear or nonlinear models A49

50 Mediation in SCM o Assumes M: Conditional direct, indirect Equations, not diagrams A50

51 Mediation in SCM o Assumes M: > direct, indirect Counterfactuals (PO) A5

52 Mediation in SCM o Direct effect: Controlled (CDE) Natural (NDE) A52

53 Mediation in SCM o Total effect: TE = NDE + NIE A53

54 Mediation in SCM o CDE: How much Y changes Given = 0 to = If M = m for all cases A54

55 Mediation in SCM o CDE: Different value of DE For every value of M Mean Y change over M A55

56 Mediation in SCM o NDE: Allows for variation in M But at values that would be observed in control A56

57 Mediation in SCM o NDE: How much Y changes Given = 0 to = If M varies as under = 0 A57

58 Mediation in SCM o NIE: How much Y changes in = If M changes from values observed in = 0 to values it would be obtained in = A58

59 Counterfactuals CDE = E [ Y ( =, M = m) ] E [ Y ( = 0, M = m) ] NDE = E [ Y ( =, M = m0) ] E [ Y ( = 0, M = m0) ] NIE = E [ Y ( =, M = m) ] E [ Y ( =, M = m0) ] TE = E [ Y ( = ) ] E [ Y ( = 0) ] A59

60 Petersen, et al. (2006) = 0, control; =, anti-viral therapy M = viral load Y = CD4 T-cells A60

61 CDE Mean T-cells if viral load is same for all cases NDE Mean T-cells if viral load were among untreated cases A6

62 NIE Mean T-cells among treated if viral load changed from untreated to treated levels A62

63 Mediation in SCM o Valeri & VanderWeele (203) SAS/STAT, SPSS o Muthén (20) Mplus A63

64 Mediation in SCM o Hicks & Tingley (202) Stata o Tingley et al. (204) R A64

65 A65