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Unbearable Lightness of b: Approaches to Causal Interpretation

of the M to Y relationDavid P. MacKinnon, Angela Pirlott, & Stephanie Moser

Society for Personality and Social Psychology

Friday, January 29, 2010

Las Vegas, Nevada

Causal Inference Criticisms of Mediation AnalysisStatistical Approaches to Addressing CriticismsDesigns to Address Criticisms

Acknowledgements: National Institute on Drug Abuse, Arizona State University Social Psychology Research Institute

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Single Mediator Model

MEDIATOR

M

INDEPENDENT VARIABLE

X Y

DEPENDENT VARIABLE

a b

c’

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Mediation Regression Equations

Tests of mediation for a single mediator use information from some or all of three equations.

The coefficients in the equations may be obtained using methods such as ordinary least squares regression, covariance structure analysis, or logistic regression.

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Equation 1

MEDIATOR

M

INDEPENDENT VARIABLE

X Y

DEPENDENT VARIABLE

c

1. The independent variable is related to the dependent variable:Y i c X e 1 1

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Equation 2

MEDIATOR

M

INDEPENDENT VARIABLE

X Y

DEPENDENT VARIABLE

2. The independent variable is related to the potential mediator:

a

M i aX e 2 2

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Equation 3

MEDIATOR

M

INDEPENDENT VARIABLE

X Y

DEPENDENT VARIABLE

a

3. The mediator is related to the dependent variable controlling for exposure to the independent variable:

b

c’

Y i c X b M e 3 3 '

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Mediated Effect Measures

Indirect Effect = Mediated effect = ab = c-c’

Direct effect= c’ Total effect= ab+c’=c

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Mediated Effect, ab, Standard Error

Mediated effect=ab Standard error=

Multivariate delta method standard error (Sobel 1982; Folmer 1981)

Test for significant mediation:

z’= Compare to normal distribution or use

product distribution/bootstrap

2 22 2aba bs s

ab2 22 2

aba bs s

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Common Mediation Design • X is a randomized manipulation.• M and Y are measured, usually on the same

occasion.• Methods described earlier are applied to estimate

the mediated effect and its standard error.• Because X is randomized, the relation of X to M, a,

and X to Y, c, have a causal interpretation. • Note that the relation of M to Y adjusted for X, b,

and X to Y adjusted for M, c’, are correlational.• Are there methods that improve interpretation of

the M to Y relation?

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Causal Inference for MediationThe Rubin Causal Model (RCM, Rubin, 1974) and

other causal inference approaches (Robins & Greenland 1992; Pearl 2009) provide ways to interpret evidence for causal relations for non-experimental as well as experimental research.

Helpful because these methods display limits and

strengths of models, including mediation.

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Counterfactual

Counterfactual is central to modern causal inference. The counterfactual refers to conditions in which a participant could serve, not just the condition in which they did serve.

For example, for a participant in the treatment group, the counterfactual is the same participant in the control group. For a participant in the control group, the counterfactual is the same participant in the treatment group.

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Why b and c’ do not reflect a causal relation?

Because M is not under direct experimental control, b and c’ do not necessarily represent causal effects.

Need: -The relation between M and Y for participants in the

treatment group if they were in the control group-The relation between M and Y for control participants if

they instead were in the treatment group. -Also need these values for every value of M! Coefficients b and c’ are not causal effects, because the

counterfactuals for these relations are complicated because M is not randomly assigned.

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Statistical Approaches to Causal Inference

Statistical approaches to improving causal inference from a mediation study:

1. Instrumental Variable Methods (Holland, 1988; Sobel 2006)

2. Principal Stratification and Latent Classes (Frangakis & Rubin, 2002; Jo, 2006)

3. G-estimation, Marginal Structural Models (Robins, 1999; Robins & Greenland, 1992)

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Design Approaches to Improving Causal Inference

Statistical mediation analysis answers the following question, “How does a researcher use measures of the hypothetical intervening process to increase the amount of information from a research study?”

Another question is, “What is the best next study or studies to conduct after a statistical mediation analysis to test mediation theory.”

Three general approaches: (1) Double randomization designs.(2) Designs to address Consistency of the mediation relation.(3) Designs to address Specificity of the mediation relation.

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(1) Double RandomizationIf the problem with the b path is that M is not

randomly assigned, then how about randomizing both X in the X to M relation and randomizing M in the M to Y relation.

Say X was randomized and there is a significant effect of X on M in Study 1. In Study 2, an experiment is set up so that M was randomized to levels defined by how X changed M in Study 1. If there is a significant relation of M to Y in Study 2, then there is more evidence for mediation.

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Double Randomization ExampleWord et al. (1974)

Study of self-fulfilling prophecy in interviews cited in Spencer et al., (2005).

Race (X) predicts quality of interview (M) which predicts performance (Y).

Confederates were used to manipulate factors. Confederate applicants were used in Study 1 for the X to M relation and confederate interviewers were used in Study 2 for the M to Y relation.

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Study 1. White participants interviewed either Black or White confederate applicants (X). The dependent variable M, was interview quality and participants with Black confederate applicants gave poorer quality interviews (M).

Study 2. Confederates gave either an interview (M) like White applicants were interviewed in Study 1 or like Black applicants in Study 1. This manipulation had a significant effect on applicant performance (Y).

So randomization was used for the X to M relation and the M to Y relation.

Double Randomization ExampleWord et al. (1974)

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Prevention Example (MacKinnon et al., 2002)

Norms increase exercise which decreases depression.

Study 1, X to M: Similar to existing prevention studies, participants either receive a social norm manipulation to increase exercise or not (X) and exercise is measured (M).

Study 2, M to Y: Participants are randomly assigned to conduct an amount of exercise (M) obtained in the program or the control group from Study 1 and depression is measured (Y).

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Double Randomization Problems

Most problems center around the randomization of the mediator in the M to Y study so that it corresponds to the change in the mediator in the X to M study.

Study 2 is a mediation X to M to Y study with a manipulation (X) that should change M in the same way as X changed M in Study 1. So Study 2 data is analyzed with statistical mediation analysis with the same problems of interpretation.

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(2) Consistency Mediation DesignsConsistency designs replicate mediation relations in new

settings, groups, species (animals, humans), and times.

Consistency designs also replicate mediation relations with alternative manipulations (X), alternative measures of the same mediator (M), and other dependent measures (Y).

Overall, consistency designs provide evidence that the mediation relation is consistently observed across many domains and variables.

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Consistency Design ExampleSocial-influences school-based substance use prevention

research provides examples of consistency designs.

Mediation effects on groups defined by age, ethnicity, and location.

Mediation effects on related dependent variables, tobacco, alcohol, and marijuana.

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(3) Specificity Mediation DesignsEvidence for specificity of a mediation relation is obtained by

comparing between groups (or variables) to demonstrate that the mediation relation is present in the predicted groups (or variables) but not present in other groups (or variables).

Specificity designs demonstrate that mediation relations can be changed by different manipulations (X), mediation relations are observed for some mediators (M) but not others, and mediation is observed for some dependent measures (Y) but not others in a way that demonstrates a pattern of results consistent mediation theory.

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Specificity in X, M, Y

Specificity for X: a norm change manipulation for alcohol results in a mediation effect for alcohol but not tobacco use.

Specificity for M: Changes in beliefs about positive

consequences is an observed mediator but changes in beliefs about negative consequences is not.

Specificity for Y: a mediation relation is observed for one dependent variable but not another. For example, change in beliefs about positive consequences of alcohol use is a mediator for alcohol use but not for tobacco use.

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Blockage Specificity Designs

The goal of blockage designs is to test a mediation relation with a manipulation that blocks the mediator from operating.

For example, let’s say that an exercise program appears to reduce depression by increasing endorphin levels-- the hypothesized mediator. A blockage manipulation would administer a drug to prevent endorphin production so that persons receiving the exercise program would no longer experience reduced depression if the endorphin level is the mediator.

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Blockage Design Example 1

Cahill et al., (1994). Memory associated with emotional arousal is through beta-adrenergic stress hormone systems. Participants received a beta-blocker, propranol. Memory for an emotionally arousing versus an emotionally neutral story was recorded.

Propranol impaired memory for the emotionally arousing story but did not affect memory for the emotionally neutral story.

The implication is that the stress hormone system was the mediator because its effects were blocked as expected.

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Blockage Design Example 2Insel & Hulihan, (1995). Tested whether partner

preference was through the hormone oxytocin, not vasopressin, in female prairie voles. Half of female voles received an oxytocin blocker, half received a vasopressin blocker. Female voles in oxytocin condition showed no partner preference for mates. Voles in vasopressin condition showed clear preference for mates.

The implication is that oxytocin is the mediator because its effects were blocked as expected but vasopressin did not block effects.

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Enhancement Specificity Designs

The goal of enhancement designs is to test interventions that enhance the effects of a hypothesized mediator.

For example, let’s say that an addiction treatment program reduces remission by improving social support. An enhancement design would increase social support even more to demonstrate a larger effect on remission. Social support may be increased by more exposure to a therapist, additional contact with friends and family etc.

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Emotional events are remembered more vividly because of arousal. O’Carroll et al. (1999) randomly assigned participants to receive a stimulant to enhance arousal, a drug to block arousal or a placebo. All saw a slide show of a boy in an accident.

Obtained predicted effects on average heart rate and memory; participants who took the stimulant had better memory than placebo and placebo had better memory than blockage condition participants.

Same study demonstrated that enhancement and blockage of arousal led to the expected pattern of results on memory.

Blockage and Enhancement Design Example

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Summary-Problems with causal inference for mediation relations b and c’ because M is not directly randomized.

-Double Randomization, Consistency, and Specificity research designs are available to investigate mediation hypotheses experimentally. The designs improve evidence for a causal relation between M and Y.

-Best to have programs of research designed to address the many aspects of a mediation relation.

-Easier task in psychology where we can run more experiments than community medicine, for example.

-Other examples? David.MacKinnon@asu.edu

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Hypothesized Effects of SPSP talk on Mediation Designs

SPSP Presentation on

Mediator Designs

# Studies with Mediator Designs

Knowledge of Mediation Designs

Norms Regarding Conducting Mediation Studies

Strong desire to help find design examples.

Beliefs About the Importance of Theory Testing

Thank YouReferences

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