Mediation: Solutions to Assumption Violation

David A. Kennydavidakenny.net

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You Need to Know

• Assumptions of Mediation

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Causal Assumptions(Guaranteed if X is manipulated.)

• Perfect Reliability–for M and X • No Reverse Causal Effects–Y may not cause M– M and Y not cause X• No Omitted Variables (Confounders)–all common causes of M and Y, X and M, and X and Y measured and controlled

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General Strategies• Design

– Randomization– More measures– More time points

• Statistical Analysis– Instrumental Variable Estimation– Structural Equation Modeling– New methods being developed

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Randomization• If it all possible, X should be

randomized.

• Randomizing M is more difficult because M is caused by X (hopefully).

– Three possibilities

• Second study to determine if M Y

• Manipulate something that causes M

• “Compensatory” manipulation

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Timing of the Measurement

• In principle, M should be measured after X but before Y.

• X might be measured at the same time as M (e.g., number of treatment sessions), but it must be assumed that X has not changed since when it affected M.

• M might be measured at the same time as Y, but it must be assumed that M has not changed since when it affected Y.

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Measure Baseline Values

• Obtain baseline measures of M and Y or M0 and Y0.

• If X is not manipulated, measure a baseline value or X0.

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Unreliability in Causal Variable

• Focus on measurement error in M.

• Measurement error in X also matters but if X is manipulated, it is reasonable to assume no measurement error.

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Increase Reliability• Strategies

–Have more items

–Have better measures

• Does not solve the problem but reduces it.

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Using SEM to Adjust for Unreliability

• Multiple Indicators

• Known Reliability

• Instrumental Variable Estimation

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Multiple Indicators

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Known Reliability

X

U1

U2

MLatent

M e1 1

a

1

Yc'

b

1

Fix error variance to V(M)(1 – )

Instrumental Variable

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Reverse Causation

• Focus on Y causing M.

• Also issues of M and Y causing X. If X is manipulated, neither of these possibilities are plausible.

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What to Do about Reverse Causation?

• Longitudinal designs

• Instrumental variable method

–Will discuss with omitted variables

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Longitudinal Design

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Issues• Proper time lag?

–Are the lags the same for all pairs of variables?

• Can we just have two waves?

• Right model of change?

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Omitted Variables• A variable that causes M and Y

but is not measured.

• Also a variable that causes X and Y or X and M but is not measured. If X is manipulated, neither of these possibilities are plausible.

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What to Do about Omitted Variables?

• Include them.

• Instrumental variable estimation.

• Shared method variance.

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Include Them in the Analysis• Think of what they are, measure

them, and use them as covariates.

• If many such variables, perhaps create propensity scores.

• Use of baseline measures (works only if these mediate the effect of the omitted variable).

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Instrumental Variables• Criteria

– Must cause M

– Must not cause Y

• Types

– X as an instrument.

– A covariate as an instrument.

– Manipulation of M as an instrument.

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Effect of Vitamin A Supplements in Northern Sumatra

22Sommer et al. (1986) in Lancet (N = 25,939)

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“Standard” Results

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Instrumental Variable Estimation

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Instrumental Variable Estimation

X

U1

U2

MLatent

YLatent

M1

e1

1

1

M2

e21

M3

e31

Y1

e4

1

1

Y2

e51

Y3

e61

a b

c' 1

1

Shared Method

Effects

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Additional Webinars

• Sensitivity Analyses

• Causal Inference Approach