Estimating Mediated Effects of Personality and Social Psychological Processes

1
Estimating Mediated Effects of Personality and
Social Psychological Processes

• Patrick E. Shrout, Ph.D.
• NYU
• Niall Bolger, Ph.D.
• Columbia U

2
An Example Feeling Excluded

• Bernstein, Sacco, Brown, Young Claypool (JESP,
  2009)
• Randomly assigned Ss to write about exclusion
  experience or another experience
• Measured self esteem, belonging, control,
  meaningful existence
• Measured preference to 20 faces
• Duchenne smiles involving two muscle groups
• Non-Duchenne smiles involving one voluntary
  muscle group
• Summarized results as difference score

3
Exclusion affected face perception

• Those writing about exclusion were more likely to
  prefer genuine smiles to possibly staged
  smiles.
• BUT WHY?
• Self esteem seemed to mediate the Exclusion
  effect
• The fact that self-esteem alone fully mediated
  the effect warrants further discussion.
  Self-esteem is the mechanism by which Sociometer
  Theory operates (Leary et al.,1995). In this
  model, self-esteem acts as a gauge of
  belongingness, and when a threat occurs,
  individuals take actions to ameliorate that
  threat. Bernstein et al, (2009)
• Theory was tested using Baron Kenny mediation
  model

4
BK(1986) Step 1Find an effect to explain
e
c
Y
X
M

• Bernstein et al (2009) showed that Exclusion led
  to increased preference for natural smiles.
• c0.26

5
BK(1986) Step 2Show X is related to mediator
Y
X
a
M

• Bernstein et al showed that Exclusion was related
  to M Self-esteem was lower in the exclusion
  condition.
• a -.88

6
BK(1986) Step 3Show M is Related to Y
Y
X
M
b

• ADJUSTING for X, M must be related to Y
• Bernstein et al reported b -0.11.
• Increased self esteem decreased interest in
  natural smile, adjusting for Exclusion

7
BK(1986) Step 4Test the indirect effect
Y
X
a
M
b

• Indirect effect is quantified by the product ab
• Formal test by Sobel test, joint-significance
  test, bootstrap confidence interval
• Bernstein et al found indirect path was
  significant using Sobel test

8
BK (1986) Step 5 Distinguish Full from partial
mediation

• Test direct effect, c, while adjusting for M.
• The adjusted (direct) effect in Bernstein example
  was c0.18, which was not significantly
  different from zero
• Authors interpreted result as Full Mediation

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Mediation and Theory Construction

• When mediation is complete, researcher has
  explained the effect
• Other explanations apparently not needed
• Often those other explanations not tested
• Bernstein et al. (2009) did test theory-driven
  alternate mediators based on Williams (2007)
• Self esteem vs. belonging, efficacy needs

10
Some Vexing Problems

• Claiming complete mediation is too easy
• If the total effect is just significant, not much
  reduction is needed to make adjusted direct
  effect non-significant
• Multiple mediators are often of theoretical
  interest but not usually tested
• Estimates of indirect effects are often biased
• If based on mediators that are measured with
  error
• If based on wrong model

11
Model Specification

• Baron and Kenny (1986) assume model is correct
• What does this entail?
• Causal paths are interpretable
• Variables are measured without error
• Residual (error) values uncorrelated
• Implies that important causes are represented

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Causal Pathways and Time

• Causal Assumptions in Mediation
• X is prior to M and Y
• Change in X is associated with change in Y
• Change in X is associated with change in M
• Change in M is associated with change in Y
• Measurements taken at times that reflect causal
  action

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Causal Pathways and Time

• Causal Assumptions in Mediation
• X is prior to M and Y
• Change in X is associated with change in Y
• Change in X is associated with change in M
• Change in M is associated with change in Y
• Measurements taken at times that reflect causal
  action

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Causal Pathways and Time

• Causal Assumptions in Mediation
• X is prior to M and Y
• Change in X is associated with change in Y
• Change in X is associated with change in M
• Change in M is associated with change in Y
• Measurements taken at times that reflect causal
  action

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Causal Pathways and Time

• Causal Assumptions in Mediation
• X is prior to M and Y
• Change in X is associated with change in Y
• Change in X is associated with change in M
• Change in M is associated with change in Y
• Measurements taken at times that reflect causal
  action

16
Causal Pathways and Time

• Causal Assumptions in Mediation
• X is prior to M and Y
• Change in X is associated with change in Y
• Change in X is associated with change in M
• Change in M is associated with change in Y
• Measurements taken at times that reflect causal
  action

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Inferring Within-Person Change from
Between-Person Data

• Systematic consideration of time draws us to
  psychological process
• Within person changes
• Effects of manipulations on persons
• Traditional designs substitute between person
  differences for within person change
• Justified in experiments
• Harder to justify in surveys
• In nature, between person associations are rarely
  the same as within person associations

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Revisiting Bernstein et al. (2009)

• Randomized design makes temporal order clear
• X-gtY Exclusion experience (randomized) was
  related to face preference
• X-gtM Exclusion was also related to
• Self esteem (apparent mediator)
• Efficacy needs (not found as mediator)
• M-gtY Temporal relation of self-esteem and face
  preference not clear
• What might contribute the correlation between M
  Y?

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Possible Between Person Confounding of M-gtY
X1
M2
G
Y3
20
If third variable is ignored, error terms are
correlated
X1
M2
However, the correlation can not be estimated in
traditional Baron Kenny Mediation model.
Y3
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Baseline Measures Can Reduce Confounding
X1
Design adds within person information so that
change can be estimated.
c'
a
M2
M1
g1
rmy
b
Y3
Y1
g2
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But most ignore baseline

• What are implications?
• Total effect (c) is not biased.
• Effect on M (a) is not biased.
• BUT Effect of M on Y may be biased
• The more stable the processes (g1, g2), the more
  the bias for nonzero correlations of M and Y.
• The more the correlation of baseline M and Y the
  more the bias for stable processes.

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Quantifying Bias A Numerical Example
X1
Direct effect .28 Indirect effect .28
.28
.70
M2
M1
g1
rmy
.40
Y3
Y1
g2
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If we ignore baseline, what do we estimate as
indirect effect?
g.8
X1
g.6
c'
a
g.4
M2
M1
g1
g.2
rmy
b
g.0
Y3
Y1
g2
25
Quantifying Bias for Direct Effects
g.0
g.2
g.4
g.6
g.8
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Extensions

• Will correlations of M and Y error terms also
  cause problems in cross-sectional studies?
• You betcha!
• The M-gtY path needs to approximate within person
  change.
• Additional covariates will be needed
• But see Cole and Maxwell (2005) about
  plausibility of cross sectional models

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Objections

• What if taking baseline measures in experiments
  would prime processes that are left un-primed?
• Often possible to estimate Corr(M,Y) and the
  stability of M and Y in separate samples
• Combining the data from the two samples will
  require structural equation methods.

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Conclusions

• Social psychology theory is ready for next
  generation mediation analysis
• Will aid in communication with other scientists
• Will refine thinking about process
• Combination of new heuristic steps and systematic
  thinking about process will serve us well

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Time for a Ten Step Program?

1. Argue that X can be a causal agent of Y
2. Show that X is related to Y.
3. Show that X is related to M, the mediator
4. Show that M is measured with little error.
5. Identify plausible competing mediators and
   include them in the model
6. Show that M is related to Y adjusting for X
7. Adjust for correlation between M and Y that is
   prior to causal process
8. Show that indirect path (X-gtM-gtY) is present
9. Estimate/test direct effect of X-gtY after
   adjusting for M.
10. Report ratio of mediated effect. If it is
    nearly 1 then claim full mediation.

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Time for a Ten Step Program?

1. Argue that X can be a causal agent of Y
2. Show that X is related to Y.
3. Show that X is related to M, the mediator
4. Show that M is measured with little error.
5. Identify plausible competing mediators and
   include them in the model
6. Show that M is related to Y adjusting for X
7. Adjust for correlation between M and Y that is
   prior to causal process
8. Show that indirect path (X-gtM-gtY) is present
9. Estimate/test direct effect of X-gtY after
   adjusting for M.
10. Report ratio of mediated effect. If it is
    nearly 1 then claim full mediation.

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Time for a Ten Step Program?

1. Argue that X can be a causal agent of Y
2. Show that X is related to Y.
3. Show that X is related to M, the mediator
4. Show that M is measured with little error.
5. Identify plausible competing mediators and
   include them in the model
6. Show that M is related to Y adjusting for X
7. Adjust for correlation between M and Y that is
   prior to causal process
8. Show that indirect path (X-gtM-gtY) is present
9. Estimate/test direct effect of X-gtY after
   adjusting for M.
10. Report ratio of mediated effect. If it is
    nearly 1 then claim full mediation.

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Help from our friends

• Margarita Krochik
• Turu Stadler
• Couples lab members at NYU and Columbia
• Grant R01-AA017672 from NIAAA

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References

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  psychological research Conceptual, strategic and
  statistical considerations. Journal of
  Personality and Social Psychology, 51, 1173-1182.
  
• Bernstein, M.J. et al. (2009). A preference for
  genuine smiles following social exclusion.
  Journal of Experimental Social Psychology,
  doi10.1016/j.jesp2009.08.010.
• Cole DA, Maxwell SE. (2003). Testing mediational
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• Maxwell, S. E., Cole, D. A. (2007). Bias in
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