New developments in structural equation modeling
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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
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