advanced sem · introduction to mediation, moderation, and process control analysis: a...
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D1
REX B KLINE CONCORDIA D. MODERATION, MEDIATION
SEM ADVANCED
D2
X
1 DM M
1 DY
Y
D3
moderation
mmr
mpatop
ics
D4
cpm
mod. mediation
med. moderation top
ics
D5
cma
cause × mediator
most general top
ics
D6
MMR
X, W, Y are continuous
XW carries interaction
ˆX W XW
Y B X B W B XW A
D7
D8
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. 143–164). New York: Taylor &
Francis.
D9
Myth
You must center, to reduce extreme
collinearity
D10
Truth
Centering changes nothing
Optional, if 0 is not on scale
Center some, others not
D11
Myth
You must use hierarchical entry
D12
Truth
Not required
Possibly misleading
D13
Myth
You can ignore score reliability
Truth
D14
Truth
Score reliability is critical
rXX > .90
D15
Myth
ˆX W XW
Y B X B W B XW A
X, W are “main effects”
D16
Truth
X, W are linear only
D17
Myth
You can ignore curvilinear effects
D18
Truth
Estimate X2 and W2, too
D19
Myth
Small samples are fine
D20
Truth
Large samples needed
D21
X W Y
2 10 5
6 12 9
8 13 11
11 10 11
4 24 11
7 19 10
8 18 7
11 25 5
M 7.125 16.375
D22
ˆ .112 .064 8.873Y X W
2 .033R
D23
X W x w Y
2 10 −5.125 −6.375 5
6 12 −1.125 −4.375 9
8 13 .875 −3.375 11
11 10 3.875 −6.375 11
4 24 −3.125 7.625 11
7 19 −.125 2.625 10
8 18 .875 1.625 7
11 25 3.875 8.625 5
M 7.125 16.375 0 0
D24
ˆ .112 .064 8.873Y X W
ˆ .112 .064 8.625Y x w
2 .033R
D25
4
5
6
7
8
9
Y
10
11
1 5 4
X
2 3 6 7 8 9 10 11
D26
4
5
6
7
8
9
Y
10
11
1 5 4
X
2 3 6 7 8 9 10 11
W < MW
W > MW
D27
Analyses
Y on X, W, XW
Y on x, w, xw
Y on X, W, XWres
D28
XWres (1)
1. Regress XW on X, W
2. Create XW
3. Create XWres = XW − XW
D29
XWres (2)
1. Regress XW on X, W
2. Save residuals
3. Rename as XWres
D30
D31
D32
X W x w
XW .747 .706 xw −.138 .050
XWres 0 0
D33
Products
BXW = Bxw = BXWres
Same interaction
Same R2
D34
D35
ˆ .112 .064 8.873Y X W
Unconditional linear
2 .033R
D36
ˆ 1.768 .734 .108 3.118Y X W XW
2 .829R
D37
ˆ 1.768 .734 .108 3.118Y X W XW
If W ↑ 1pt,
slope Y on X ↓ .108
D38
ˆ 1.768 .734 .108 3.118Y X W XW
If X ↑ 1pt,
slope Y on W ↓ .108
D39
100
15
200
25
30
W
0
5
10
15
20
Y
2 4 6 8 10 12 14
X
ˆ 1.768 .734 .108 3.118Y X W XW
D40
ˆ 1.768 .734 .108 3.118Y X W XW
Conditional linear
Slope, Y on X is 1.768, if W = 0
Slope, Y on W is .734, if X = 0
D41
Centering
x = X − MX, w = W – MW
x = 0 says X = MX
w = 0 says X = MW
D42
ˆ .112 .064 8.625Y x w
2 .033R
ˆ .000 .035 .108 8.903Y x w xw
2 .829R
D43
ˆ .112 .064 8.873Y X W
2 .033R
resˆ .112 .064 .108 8.873Y X W XW
2 .829R
D44
Simple regressions
Simple slopes
Simple intercepts
Generate equations
D45
Y on X as a function of W
ˆ 1.768 .734 .108 3.118Y X W XW
ˆ 1.768 .108 .734 3.118Y X XW W
ˆ (1.768 .108 ) .(734 3.118)Y W X W
D46
ˆ (1.768 .108 ) .(734 3.118)Y W X W
16.38W
M
4.34 10.36 16.38 22.40 28.42
D47
ˆ (1.768 .108 ) .(734 3.118)Y W X W
22.40ˆ .651 13.324
WY X
D48
W
Level Score Regression equation
+2 SD 28.42 ˆ 1.301 17.712Y X
+1 SD 22.40 ˆ .651 13.324Y X
Mean 16.38 ˆ .001 8.905Y X
−1 SD 10.36 ˆ .649 4.486Y X
−2 SD 4.34 ˆ 1.299 .068Y X
D49 1 5 4
X
2 3 6 7 8 9 10 11 4
5
6
7
8
9
Y
10
11
MW
−2 SDW
+SDW
−SDW
+2 SDW
D50
MW
+1 SDW
+2 SDW
−1 SDW
−2 SDW
http://graph.seriesmathstudy.com/
D51
Other horizons
X, W, XW
X, X2, W, W2, XW
X, X2, W, W2, XW, X2W
D52
Other horizons
X, W, Z, XW, XZ, WZ, XWZ
E.g., XW over Z
Really?
D53
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, 917–926.
D54
(a) Regression perspective
BX
BW
BXW
Y
1 D
X
XW
W
(b) Compact symbolism
BX
BW
BXW
Y
1 D
X
W
D55
(d) W as focal variable,
X as moderator
BW
BX BXW
W
X
Y
1 D
(c) X as focal variable,
W as moderator
BX
BW BXW
X
W
Y
1 D
D56
D57
X
W
Y
1 D
X
W
Y
1 D
D58
Kline, R. B. (2015). The mediation myth. Basic
and Applied Social Psychology, 37, 202–
213.
Little, T. D. (2013). Longitudinal structural
equation modeling. New York: Guilford.
D59
Design
Time precedence: X → M → Y
Experimental X
What about M → Y?
D60
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,
30–43.
Stone–Romero, E. F., & Rosopa, P. J. (2011).
Experimental tests of mediation models:
Prospects, problems, and some solutions.
Organizational Research Methods, 14, 631–646.
D61
Design
Time precedence: X → M → Y
Longitudinal
D62
M1
O1
X1
1 D12
M2
O2
1 D22
a
b
D63
Selig, J. P., & Preacher, K. J. (2009).
Mediation models for longitudinal data in
developmental research. Research in
Human Development, 6, 144–164.
D64
No design
Indirect effect
Mediation
D65
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. 219–266). Greenwich,
CT: IAP.
Hayes, A. F. (2013b). Introduction to mediation,
moderation, and process control analysis: A
regression-based approach. New York: Guilford.
D66
CPM
Mediated moderation
Moderated mediation
Cause × mediator
D67
Mediated moderation
W
Y
1 DY
X
1 DM
M
D68
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, 163–175.
D69
D70
Moderated mediation (1)
1st-stage moderation, X → M → Y
X → M depends on W
W
Y
1 DY
X
1 DM
M
D71
Mediated moderation (2)
1st-stage moderation, W → M → Y
W → M depends on X
W
Y
1 DY
X
1 DM
M
D72
Moderated mediation
2nd-stage moderation, X → M → Y
M → Y depends on W
X
W
M 1
DM
Y
1 DY
D73
Edwards, J. R., & Lambert, L, S. (2007).
Methods for integrating moderation and
mediation: A general analytical
framework using moderated path
analysis. Psychological Methods, 12, 1–22.
D74
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 self-
determination theory. Journal of Sport &
Exercise Psychology, 35, 30–43.
D75
D76
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, 31–37.
D77
D78
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. 219–266). Greenwich, CT: IAP.
D79
Baron-Kenny
Continuous variables
Linear model
No interaction
D80
a
b c
X M
1 DM
Y
1 DY
D81
Product estimator
X → M, X → Y, M → Y
No omitted confounders
rXX = 1.0
D82
X
Y
1 DY
M
1 DM
D83
1 1M B X A
2 3 4 2Y B X B M B XM A
D84
X × M
No single direct
No single indirect, total
D85
X × M
Effect decomposition?
Nonlinear models?
D86
Pearl, J. (2014). Interpretation and
identification of causal mediation.
Psychological Methods, 19, 459–481.
D87
Causal mediation
Assumes X × M
Linear or nonlinear
Total = direct + indirect
D88
Causal mediation
Counterfactuals
What if Tx were not treated?
What if Cn were treated?
D89
Counterfactuals
Rubin Causal Model
Missing data inference
Latent variables
D90
Example
Experimental X = 0, 1
M, Y are continuous
D91
Direct effects
Controlled (CDE)
Natural (NDE)
No X × M? CDE = NDE
D92
CDE
How much Y changes
As X = 0 to X = 1
If M = m for all cases
D93
CDE
Estimate for m = M
Policy: Lift all to m
D94
NDE
How much Y changes
As X = 0 to X = 1
If M varies as under X = 0
D95
NIE
How much Y changes in X = 1
As M changes from in
X = 0 to X = 1
D96
Total Effect
TE = NDE + NIE
D97
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) ]
D98
Petersen, M. L., Sinisi, S. E., & van der Laan,
M. J. (2006). Estimation of direct causal
effects. Epidemiology, 17, 276–284.
D99
X = 0, control; X = 1, AVT
M = viral load
Y = CD4 T-cells
D100
CDE
Mean Δ T-cells if viral load were
the same for all cases
D101
NDE
Mean Δ T-cells if viral load were
as among untreated cases
D102
NIE
Mean Δ T-cells among treated if
viral load changed from
untreated to treated levels
D103
0 1ˆ β βM X
0 1 2 3ˆ θ θ θ θY X M XM
D104
1 3CDE θ θ m
1 3 0NDE θ θ β
2 3 1NIE (θ θ )β
D105
0 1 2 3ˆ θ θ θ θY X M XM
If θ3 = 0:
1CDE θ
1NDE θ
D106
ˆ 1.70 .20M X
ˆ 450.00 50.00 20.00 10.00Y X M XM
D107
β0 = 1.70 and β1 = −.20
θ0 = 450.00,
θ1 = 50.00, θ2 = −20.00,
and θ3 = −10.00
D108
CDE = 50.00 − 10.00 m
NDE = 50.00 − 10.00 (1.70) = 33.00
NIE = (−20.00 − 10.00) −.20 = 6.00
TE = 33.00 + 6.00 = 39.00
D109
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, 137–
150.
D110
Imai, K., Keele, L., & Tingley, D. (2010). A
general approach to causal mediation
analysis. Psychological Methods, 15, 309–
334.
D111
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