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Mediation: Solutions to Assumption Violation

Mediation: Solutions to Assumption Violation. David A. Kenny davidakenny.net. You Need to Know. Assumptions of Mediation. 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

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Mediation: Solutions to Assumption Violation

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  1. Mediation: Solutions to Assumption Violation David A. Kenny davidakenny.net

  2. You Need to Know • Assumptions of Mediation

  3. 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 3

  4. General Strategies Design Randomization More measures More time points Statistical Analysis Instrumental Variable Estimation Structural Equation Modeling New methods being developed 4

  5. 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

  6. 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.

  7. 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.

  8. 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. 8

  9. Increase Reliability • Strategies • Have more items • Have better measures • Does not solve the problem but reduces it.

  10. Using SEM to Adjust for Unreliability • Multiple Indicators • Known Reliability • Instrumental Variable Estimation

  11. Multiple Indicators

  12. Known Reliability Fix error variance to V(M)(1 – a)

  13. Instrumental Variable

  14. 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.

  15. What to Do about Reverse Causation? • Longitudinal designs • Instrumental variable method • Will discuss with omitted variables

  16. Longitudinal Design

  17. Issues • Proper time lag? • Are the lags the same for all pairs of variables? • Can we just have two waves? • Right model of change?

  18. 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.

  19. What to Do about Omitted Variables? Include them. Instrumental variable estimation. Shared method variance. 19

  20. 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). 20

  21. 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. 21

  22. Effect of Vitamin A Supplements in Northern Sumatra Sommer et al. (1986) in Lancet (N = 25,939) 22

  23. “Standard” Results 23

  24. Instrumental Variable Estimation 24

  25. Instrumental Variable Estimation

  26. Shared Method Effects

  27. Additional Webinars • Sensitivity Analyses • Causal Inference Approach

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