advanced sem · introduction to mediation, moderation, and process control analysis: a...
TRANSCRIPT
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REX B KLINE CONCORDIA D. MODERATION, MEDIATION
SEM ADVANCED
D2
X
1 DM M
1 DY
Y
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moderation
mmr
mpatop
ics
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cpm
mod. mediation
med. moderation top
ics
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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
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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
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Myth
Small samples are fine
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Truth
Large samples needed
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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
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ˆ .112 .064 8.873Y X W
2 .033R
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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
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ˆ .112 .064 8.873Y X W
ˆ .112 .064 8.625Y x w
2 .033R
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4
5
6
7
8
9
Y
10
11
1 5 4
X
2 3 6 7 8 9 10 11
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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
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Analyses
Y on X, W, XW
Y on x, w, xw
Y on X, W, XWres
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XWres (1)
1. Regress XW on X, W
2. Create XW
3. Create XWres = XW − XW
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XWres (2)
1. Regress XW on X, W
2. Save residuals
3. Rename as XWres
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X W x w
XW .747 .706 xw −.138 .050
XWres 0 0
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Products
BXW = Bxw = BXWres
Same interaction
Same R2
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ˆ .112 .064 8.873Y X W
Unconditional linear
2 .033R
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ˆ 1.768 .734 .108 3.118Y X W XW
2 .829R
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ˆ 1.768 .734 .108 3.118Y X W XW
If W ↑ 1pt,
slope Y on X ↓ .108
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ˆ 1.768 .734 .108 3.118Y X W XW
If X ↑ 1pt,
slope Y on W ↓ .108
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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
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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
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Centering
x = X − MX, w = W – MW
x = 0 says X = MX
w = 0 says X = MW
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ˆ .112 .064 8.625Y x w
2 .033R
ˆ .000 .035 .108 8.903Y x w xw
2 .829R
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ˆ .112 .064 8.873Y X W
2 .033R
resˆ .112 .064 .108 8.873Y X W XW
2 .829R
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Simple regressions
Simple slopes
Simple intercepts
Generate equations
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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
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ˆ (1.768 .108 ) .(734 3.118)Y W X W
16.38W
M
4.34 10.36 16.38 22.40 28.42
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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
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MW
+1 SDW
+2 SDW
−1 SDW
−2 SDW
http://graph.seriesmathstudy.com/
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Other horizons
X, W, XW
X, X2, W, W2, XW
X, X2, W, W2, XW, X2W
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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.
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(a) Regression perspective
BX
BW
BXW
Y
1 D
X
XW
W
(b) Compact symbolism
BX
BW
BXW
Y
1 D
X
W
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(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
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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.
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Design
Time precedence: X → M → Y
Longitudinal
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M1
O1
X1
1 D12
M2
O2
1 D22
a
b
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Selig, J. P., & Preacher, K. J. (2009).
Mediation models for longitudinal data in
developmental research. Research in
Human Development, 6, 144–164.
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No design
Indirect effect
Mediation
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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.
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CPM
Mediated moderation
Moderated mediation
Cause × mediator
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Mediated moderation
W
Y
1 DY
X
1 DM
M
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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.
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Moderated mediation (1)
1st-stage moderation, X → M → Y
X → M depends on W
W
Y
1 DY
X
1 DM
M
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Mediated moderation (2)
1st-stage moderation, W → M → Y
W → M depends on X
W
Y
1 DY
X
1 DM
M
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Moderated mediation
2nd-stage moderation, X → M → Y
M → Y depends on W
X
W
M 1
DM
Y
1 DY
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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.
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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
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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
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a
b c
X M
1 DM
Y
1 DY
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Product estimator
X → M, X → Y, M → Y
No omitted confounders
rXX = 1.0
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X
Y
1 DY
M
1 DM
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1 1M B X A
2 3 4 2Y B X B M B XM A
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X × M
No single direct
No single indirect, total
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X × M
Effect decomposition?
Nonlinear models?
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Pearl, J. (2014). Interpretation and
identification of causal mediation.
Psychological Methods, 19, 459–481.
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Causal mediation
Assumes X × M
Linear or nonlinear
Total = direct + indirect
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Causal mediation
Counterfactuals
What if Tx were not treated?
What if Cn were treated?
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Counterfactuals
Rubin Causal Model
Missing data inference
Latent variables
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Example
Experimental X = 0, 1
M, Y are continuous
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Direct effects
Controlled (CDE)
Natural (NDE)
No X × M? CDE = NDE
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CDE
How much Y changes
As X = 0 to X = 1
If M = m for all cases
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CDE
Estimate for m = M
Policy: Lift all to m
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NDE
How much Y changes
As X = 0 to X = 1
If M varies as under X = 0
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NIE
How much Y changes in X = 1
As M changes from in
X = 0 to X = 1
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Total Effect
TE = NDE + NIE
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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
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CDE
Mean Δ T-cells if viral load were
the same for all cases
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NDE
Mean Δ T-cells if viral load were
as among untreated cases
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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.
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