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

2. You Need to Know
Assumptions of Mediation

3. (Guaranteed if X is manipulated.)
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. Fix error variance to V(M)(1 – a)
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 Estimation24

25. Instrumental Variable Estimation

26. Shared Method
Effects

27. Additional Webinars
Sensitivity Analyses
Causal Inference Approach