Solutions to Assumption Violation David A. Kenny davidakenny.net
Jan 04, 2016
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