Questions: Mediation and Indirect Effects Analysis

Question 1

A researcher uses observational data to show that college attendance (X) increases lifetime earnings (Y), and that college-developed skills (M) mediate this relationship. She concludes that M causally explains the income gap. What is the most important methodological problem?

• A. She should have used structural equation modeling rather than regression to compute the indirect effect
• B. Sequential ignorability is unlikely to hold — unmeasured confounders of M→Y (e.g., unobserved ability) could bias the indirect effect estimate and make it non-causal
• C. Mediation analysis cannot be applied to observational data under any circumstances
• D. The product-of-coefficients method always overestimates indirect effects compared to counterfactual approaches

Answer: (B)

Causal mediation requires sequential ignorability: no unmeasured confounders of X→Y, AND no unmeasured confounders of M→Y conditional on X. In observational research, this second assumption is almost never satisfied. Unobserved variables (like underlying ability or motivation) may jointly cause both M (skills acquired) and Y (earnings), producing a spurious indirect effect. Demonstrating a statistically significant indirect effect in observational data does not establish that M causally mediates — it establishes that the data are consistent with mediation, conditional on strong untestable assumptions.

Question 2

A researcher finds that the indirect effect of X on Y through M is statistically significant, but the direct effect of X on Y is zero (complete mediation). What can she most accurately conclude?

• A. X causes Y entirely through M, and M is the causal mechanism
• B. Full mediation is established, eliminating the need to consider other mediators
• C. The data are consistent with complete mediation, but causal claims require sequential ignorability assumptions that must be stated explicitly and probed with sensitivity analyses
• D. A zero direct effect means the model is misspecified — direct effects can never truly be zero

Answer: (C)

Statistical significance of the indirect effect and a zero direct effect are consistent with complete mediation — but 'consistent with' is not the same as 'establishes.' Causal language requires the sequential ignorability assumptions to hold. In observational data, the pattern could also result from unmeasured confounding. The correct posture is to report the finding, state the assumptions, and probe their plausibility with sensitivity analyses rather than asserting causal mediation. Options A and B use causal language ('causes,' 'established') that is not warranted by observational evidence alone.

Question 3

When the effect of M on Y differs depending on the level of X (an X×M interaction exists), the simple product-of-coefficients formula for the indirect effect can give misleading results.

• T. True
• F. False

Answer: True

The product-of-coefficients formula (indirect effect = a×b, where a is the X→M effect and b is the M→Y effect) assumes these paths are independent of X's value. When X moderates the M→Y relationship, this formula is incorrect. The counterfactual definitions of the natural indirect effect (NIE) and natural direct effect (NDE) correctly handle this case by integrating over the distribution of X, but they require more complex estimation (bootstrapping for confidence intervals, testing interaction terms). Ignoring X×M interactions when they exist produces biased decompositions.

Question 4

Demonstrating a statistically significant indirect effect (X→M→Y) in a well-powered observational study is sufficient to conclude that M causally mediates the relationship between X and Y.

• T. True
• F. False

Answer: False

Statistical significance addresses sampling error, not confounding. A significant indirect effect means the estimated indirect path is unlikely to be zero by chance — but it says nothing about whether unmeasured confounders are producing a spurious pattern. Causal mediation requires sequential ignorability: effective randomization of both X and M (conditional on X). In observational data, neither condition is easily satisfied, which is why mediation claims should be accompanied by explicit assumption statements and sensitivity analyses, not asserted as established mechanisms.

Question 5

What is sequential ignorability in mediation analysis, and why does its violation mean that mediation findings from observational data should be interpreted cautiously?

Model answer: Sequential ignorability requires two conditions: (1) no unmeasured confounders of the X→Y relationship (X is effectively randomized), and (2) no unmeasured confounders of the M→Y relationship conditional on X (M is effectively randomized given X). If either condition fails, the estimated indirect effect may be biased by variables that jointly cause M and Y or X and Y. In observational research, unmeasured factors like ability, motivation, or socioeconomic background routinely violate these assumptions, making it impossible to distinguish a true causal indirect effect from spurious correlation through a third variable.

This is why mediation claims from purely observational data are often overstated. The statistical machinery of mediation analysis runs correctly and produces a significant indirect effect — but the causal interpretation requires assumptions the data cannot verify. Sensitivity analyses (e.g., how strong would an unmeasured confounder need to be to explain away the indirect effect?) are the responsible way to probe these assumptions. When possible, experimental manipulation of X or M provides much stronger grounds for causal mediation claims.