SEM REX B KLINE CONCORDIA D. MODERATION, MEDIATION

Transcription

1 ADVANCED SEM REX B KLINE CONCORDIA D1 D. MODERATION, MEDIATION

2 X 1 DY Y DM 1 M D2

3 topics moderation mmr mpa D3

4 topics cpm mod. mediation med. moderation D4

5 topics cma cause mediator most general D5

6 MMR X, W, Y are continuous XW carries interaction Yˆ B X B W B XW A X W XW D6

7 D7

8 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. D8

9 Myth You must center, to reduce extreme collinearity D9

10 Truth Centering changes nothing Optional, if 0 is not on scale Center some, others not D10

11 Myth You must use hierarchical entry D11

12 Truth Not required Possibly misleading D12

13 Myth You can ignore score reliability Truth D13

14 Truth Score reliability is critical rxx >.90 D14

15 Myth Yˆ B X B W B XW A X W XW X, W are main effects D15

16 Truth X, W are linear only D16

17 Myth You can ignore curvilinear effects D17

18 Truth Estimate X 2 and W 2, too D18

19 Myth Small samples are fine D19

20 Truth Large samples needed D20

21 X W Y M D21

22 Yˆ.112 X.064W R.033 D22

23 X W x w Y M D23

24 Yˆ.112 X.064W Yˆ.112 x.064 w R.033 D24

25 Y X D25

26 W < MW Y 8 7 W > MW X D26

27 Analyses Y on X, W, XW Y on x, w, xw Y on X, W, XWres D27

28 XWres (1) 1. Regress XW on X, W 2. Create XW 3. Create XWres = XW XW D28

29 XWres (2) 1. Regress XW on X, W 2. Save residuals 3. Rename as XWres D29

30 D30

31 D31

32 X W x w XW xw XW res 0 0 D32

33 Products BXW = Bxw = BXW res Same interaction Same R 2 D33

34 D34

35 Yˆ.112 X.064W Unconditional linear 2 R.033 D35

36 Yˆ X.734 W.108 XW R.829 D36

37 Yˆ X.734 W.108 XW If W 1pt, slope Y on X.108 D37

38 Yˆ X.734 W.108 XW If X 1pt, slope Y on W.108 D38

39 Yˆ X.734 W.108 XW Ŷ X W D39

40 Yˆ X.734 W.108 XW Conditional linear Slope, Y on X is 1.768, if W = 0 Slope, Y on W is.734, if X = 0 D40

41 Centering x = X MX, w = W MW x = 0 says X = MX w = 0 says X = MW D41

42 Yˆ.112 x.064 w R.033 Yˆ.000 x.035 w.108 xw R.829 D42

43 Yˆ.112 X.064W R.033 Yˆ.112 X.064 W.108 XW res 2 R.829 D43

44 Simple regressions Simple slopes Simple intercepts Generate equations D44

45 Y on X as a function of W Yˆ X.734 W.108 XW Yˆ X.108 XW.734W Yˆ ( W) X.(734 W 3.118) D45

46 Yˆ ( W) X.(734 W 3.118) M W D46

47 Yˆ ( W) X.(734 W 3.118) ˆ Y X W D47

48 W Level Score Regression equation +2 SD Yˆ 1.301X SD Yˆ.651X Mean Yˆ.001X SD Yˆ.649 X SD 4.34 Yˆ X.068 D48

49 SDW SDW 9 MW Y 8 7 +SDW SDW X D49

50 2 SDW 1 SDW MW +2 SDW +1 SDW D50

51 Other horizons X, W, XW X, X 2, W, W 2, XW X, X 2, W, W 2, XW, X 2 W D51

52 Other horizons X, W, Z, XW, XZ, WZ, XWZ E.g., XW over Z Really? D52

53 Dawson, J. F., & Richter, A. W. (2006). Probing three-way interactions in moderated multiple regression: Development and application of a slope difference test. Journal of Applied Psychology, 91, D53

54 (a) Regression perspective (b) Compact symbolism X B X 1 D X B X 1 D XW B XW Y B XW Y B W B W W W D54

55 (c) X as focal variable, W as moderator (d) W as focal variable, X as moderator W X B XW B W 1 D B XW B X 1 D X B X Y W B W Y D55

56 D56

57 W W 1 D 1 D X Y X Y D57

58 Kline, R. B. (2015). The mediation myth. Basic and Applied Social Psychology, 37, Little, T. D. (2013). Longitudinal structural equation modeling. New York: Guilford. D58

59 Design Time precedence: X M Y Experimental X What about M Y? D59

60 MacKinnon, D. P., & Pirlott, A. G. (2015). Statistical approaches for enhancing causal interpretation of the M to Y relation in mediation analysis. Personality and Social Psychology Review, 19, Stone Romero, E. F., & Rosopa, P. J. (2011). Experimental tests of mediation models: Prospects, problems, and some solutions. Organizational Research Methods, 14, D60

61 Design Time precedence: X M Y Longitudinal D61

62 X1 a 1 D 12 M1 b M2 1 D 22 O1 O2 D62

63 Selig, J. P., & Preacher, K. J. (2009). Mediation models for longitudinal data in developmental research. Research in Human Development, 6, D63

64 No design Indirect effect Mediation D64

65 Hayes, A. F. (2013a). Conditional process modeling: Using structural equation modeling to examine contingent causal processes. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.) (pp ). Greenwich, CT: IAP. Hayes, A. F. (2013b). Introduction to mediation, moderation, and process control analysis: A regression-based approach. New York: Guilford. D65

66 CPM Mediated moderation Moderated mediation Cause mediator D66

67 Mediated moderation X 1 DY 1 DM Y M W D67

68 Lance, C. E. (1988). Residual centering, exploratory and confirmatory moderator analysis, and decomposition of effects in path models containing interaction effects. Applied Psychological Measurement, 12, D68

69 D69

70 Moderated mediation (1) 1 st -stage moderation, X M Y X M depends on W X 1 DY 1 DM Y M W D70

71 Mediated moderation (2) 1 st -stage moderation, W M Y W M depends on X X 1 DY 1 DM Y M W D71

72 Moderated mediation 2 nd -stage moderation, X M Y M Y depends on W X DM 1 M Y 1 DY W D72

73 Edwards, J. R., & Lambert, L, S. (2007). Methods for integrating moderation and mediation: A general analytical framework using moderated path analysis. Psychological Methods, 12, D73

74 Curran, T., Hill, A. P., & Niemiec, C. P. (2013). A conditional process model of children's behavioral engagement and behavioral disaffection in sport based on selfdetermination theory. Journal of Sport & Exercise Psychology, 35, D74

75 D75

76 Desrosiers, A., Vine, V., Curtiss, J., & Klemanski, D. H. (2014). Observing nonreactively: A conditional process model linking mindfulness facets, cognitive emotion regulation strategies, and depression and anxiety symptoms. Journal of Affective Disorders, 165, D76

77 D77

78 Hayes, A. F., & Preacher, K. J. (2013). Conditional process modeling: Using structural equation modeling to examine contingent causal processes. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed.) (pp ). Greenwich, CT: IAP. D78

79 Baron-Kenny Continuous variables Linear model No interaction D79

80 1 DM X a M c b 1 DY Y D80

81 Product estimator X M, X Y, M Y No omitted confounders rxx = 1.0 D81

82 X 1 DY Y DM 1 M D82

83 ˆM B X A 1 1 Ŷ B X B M B XM A D83

84 X M No single direct No single indirect, total D84

85 X M Effect decomposition? Nonlinear models? D85

86 Pearl, J. (2014). Interpretation and identification of causal mediation. Psychological Methods, 19, D86

87 Causal mediation Assumes X M Linear or nonlinear Total = direct + indirect D87

88 Causal mediation Counterfactuals What if Tx were not treated? What if Cn were treated? D88

89 Counterfactuals Rubin Causal Model Missing data inference Latent variables D89

90 Example Experimental X = 0, 1 M, Y are continuous D90

91 Direct effects Controlled (CDE) Natural (NDE) No X M? CDE = NDE D91

92 CDE How much Y changes As X = 0 to X = 1 If M = m for all cases D92

93 CDE Estimate for m = M Policy: Lift all to m D93

94 NDE How much Y changes As X = 0 to X = 1 If M varies as under X = 0 D94

95 NIE How much Y changes in X = 1 As M changes from in X = 0 to X = 1 D95

96 Total Effect TE = NDE + NIE D96

97 Counterfactuals CDE = E [ Y (X = 1, M = m) ] E [ Y (X = 0, M = m) ] NDE = E [ Y (X = 1, M = m0) ] E [ Y (X = 0, M = m0) ] NIE = E [ Y (X = 1, M = m1) ] E [ Y (X = 1, M = m0) ] TE = E [ Y (X = 1) ] E [ Y (X = 0) ] D97

98 Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17, D98

99 X = 0, control; X = 1, AVT M = viral load Y = CD4 T-cells D99

100 CDE Mean Δ T-cells if viral load were the same for all cases D100

101 NDE Mean Δ T-cells if viral load were as among untreated cases D101

102 NIE Mean Δ T-cells among treated if viral load changed from untreated to treated levels D102

103 Mˆ β β 0 1 X Yˆ θ θ X θ M θ XM D103

104 CDE θ θ m 1 3 NDE θ θ β NIE (θ θ )β D104

105 Yˆ θ θ X θ M θ XM If θ3 = 0: CDE θ 1 NDE θ 1 D105

106 Mˆ X Yˆ X 20.00M 10.00XM D106

107 β0 = 1.70 and β1 =.20 θ0 = , θ1 = 50.00, θ2 = 20.00, and θ3 = D107

108 CDE = m NDE = (1.70) = NIE = ( ).20 = 6.00 TE = = D108

109 Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 2, D109

110 Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15, D110

111 D111