SPSP 2010 1

Estimating Mediated Effects of Personality and Social

Psychological Processes

Patrick E. Shrout, Ph.D.NYU

Niall Bolger, Ph.D.Columbia U

SPSP 2010 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

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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

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B&K(1986) Step 1:Find an effect to explain

YX

M

e

• Bernstein et al (2009) showed that Exclusion led to increased preference for natural smiles. c=0.26

c

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B&K(1986) Step 2:Show X is related to mediator

YX

MeY

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

a

eM

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B&K(1986) Step 3:Show M is Related to Y

YX

MeY

• 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

b

eM

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B&K(1986) Step 4:Test the indirect effect

YX

MeY

• Indirect effect is quantified by the product a*b Formal test by Sobel test, joint-significance test,

bootstrap confidence interval

• Bernstein et al found indirect path was significant using Sobel test

a b

eM

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B&K (1986) Step 5: Distinguish Full from partial mediation

• Test direct effect, c’, while adjusting for M.• The adjusted (direct) effect in Bernstein example

was c’=0.18, which was not significantly different from zero Authors interpreted result as Full Mediation

YX

MeY

C’

eM

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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

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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

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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 actionYX

M

eY

C’

eM

a b

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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 actionYX

M

eY

C’

eM

a b

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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 actionYX

M

eY

C’

eM

a b

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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 actionYX

M

eY

C’

eM

a b

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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 actionYX

M

eY

C’

eM

a b

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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->Y: Exclusion experience (randomized) was related

to face preference X->M: Exclusion was also related to

• Self esteem (apparent mediator)• Efficacy needs (not found as mediator)

• M->Y: 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->Y

Y3

X1

M2

G

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If “third variable” is ignored, error terms are correlated

Y3

X1

M2However, the correlation can not be estimated in traditional Baron & Kenny Mediation model.

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Baseline Measures Can Reduce Confounding

Y3

X1

M2M1

Y1

a

b

c'

g1

g2

rmy

Design adds within person information so that change can be estimated.

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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.

Y3

X1

M2M1

Y1

ac'

g1

g2

rmy b

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Quantifying Bias: A Numerical Example

Y3

X1

M2M1

Y1

.70.28

g1

g2

rmy .40

Direct effect .28

Indirect effect .28

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Indirect Effect Bias

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 0.2 0.4 0.6 0.8 1

Baseline Corr of M and Y

Pro

du

ct a

*b

g=.2

If we ignore baseline, what do we estimate as indirect effect?

g=.0

g=.4

g=.6

g=.8

Y3

X1

M2M1

Y1

ac'

g1

g2

rmy b

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Direct Effect Bias

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 0.2 0.4 0.6 0.8 1

Baseline Corr of M and Y

Dir

ec

t E

ffe

ct

Quantifying Bias for Direct Effects

g=.0g=.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->Y 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 Y2) Show that X is related to Y.3) Show that X is related to M, the mediator4) *Show that M is measured with little error.5) *Identify plausible competing mediators and include

them in the model6) Show that M is related to Y adjusting for X7) *Adjust for correlation between M and Y that is prior to

causal process8) Show that indirect path (X->M->Y) is present9) Estimate/test direct effect of X->Y after adjusting for M.10)*Report ratio of mediated effect. If it is nearly 1 then

claim full mediation.

SPSP 2010 30

Time for a Ten Step Program?1) *Argue that X can be a causal agent of Y2) Show that X is related to Y.3) Show that X is related to M, the mediator4) *Show that M is measured with little error.5) *Identify plausible competing mediators and include

them in the model6) Show that M is related to Y adjusting for X7) *Adjust for correlation between M and Y that is prior to

causal process8) Show that indirect path (X->M->Y) is present9) Estimate/test direct effect of X->Y after adjusting for M.10)*Report ratio of mediated effect. If it is nearly 1 then

claim full mediation.

SPSP 2010 31

Time for a Ten Step Program?1) *Argue that X can be a causal agent of Y2) Show that X is related to Y.3) Show that X is related to M, the mediator4) *Show that M is measured with little error.5) *Identify plausible competing mediators and include

them in the model6) Show that M is related to Y adjusting for X7) *Adjust for correlation between M and Y that is prior to

causal process8) Show that indirect path (X->M->Y) is present9) Estimate/test direct effect of X->Y after adjusting for M.10)*Report ratio of mediated effect. If it is nearly 1 then

claim full mediation.

SPSP 2010 32

Help from our friends

• Margarita Krochik

• Turu Stadler

• Couples lab members at NYU and Columbia

• Grant R01-AA017672 from NIAAA

2010 SPSP 33

References• Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in

social 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, doi:10.1016/j.jesp2009.08.010.

• Cole DA, Maxwell SE. (2003). Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling. J. Abnormal Psychology, 112:558–577.

• Gollob, H.F. & Reichardt, C.S. (1987). Taking account of time lags in causal models. Child Development, 58(1), 80-92.

• Kraemer, H., Kiernan, M., Essex, M., & Kupfer, D. J. (2008). How and why criteria defining moderators and mediators differ between the Baron & Kenny and MacArthur approaches. Health Psychology, 27(2, Suppl), S101-S108

• MacKinnon DP (2008). Introduction to statistical mediation analysis. New York: LEA• Maxwell, S. E., & Cole, D. A. (2007). Bias in cross-sectional analyses of longitudinal

mediation. Psychological Methods, 12(1), 23-44.• Shrout, P.E. (in press). Integrating causal analysis into psychopathology research. In

Causality and Psychopathology: Finding the Determinants of Disorders and their Cures. P.E. Shrout, K. Keyes, K. Ornstein (Eds). New York: Oxford U. Press.

• Spencer, S.J., Zanna, M.P. & Fong, G.T. (2005). Establishing a causal chain: Why experiments are often more effective than mediational analyses in examining psychological processes. Journal of Personality and Social Psychology, 89(6), 845-851.