3.2 Reading

Reference

Baron, R. M. & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical Considerations. Journal of Personality and Individual Differences, 51(6), 1173–1182. https://doi.org/10.1037//0022-3514.51.6.1173

Questions

  1. What is mediation? Give an example of mediation.
  2. According to the authors, we must satisfy four criteria to infer mediation. What are these criteria?
  3. What is “moderation”, and how is it different from “mediation”?
  4. Give an example of moderation.
  5. What are the four methods given by Baron and Kenny as suitable ways to to study interaction effects?
  6. How can you determine whether a variable is a mediator or moderator?

Answers

  1. Mediation is a way of describing the relations among three, or more, variables. Specifically, mediation entails a causal process wherein X affects Y indirectly through M. With a hypothesis of mediation, we ask how or why does X affect Y?

    • Amount of study (X) affects exam score (Y) through mastery of the course material (M).
    • Physical exercise (X) affects mood (Y) through neurotransmitter levels (M).
    • Political events (X) affect stock prices (Y) through investor hopes/fears (M).

  2. According to the authors, we can only infer mediation after satisfying the following criteria.

    1. X significantly predicts Y.
    2. X significantly predicts M.
    3. M significantly predicts Y.
    4. The size of the effect of X on Y decreases after controlling for M.

  3. A moderator is a variable that affects the relation between two other variables. Moderation is about context: when does X affect Y (where we define when in terms of the level of some moderator variable). Mediation, on the other hand, is concerned with explaining how X transmits its effect to Y (in terms of intermediary variables).

  4. A few possibilities:

    • Quality of recovery moderates the relation between training intensity and strength gains for power lifters.
    • Amount of income moderates the relation between length of employment and level of job satisfaction.
    • Level of fatalistic thinking moderates the efficacy of a new therapy for treating depression.

  5. The different recommendations are broken down according to the measurement levels of the IV and moderator.

    • Case 1: Discrete IV, Discrete Moderator \(\rightarrow\) Factorial ANOVA
    • Case 2: Continuous IV, Discrete Moderator \(\rightarrow\) Test the focal effect within each level of the moderator.
    • Case 3: Discrete IV, Continuous Moderator \(\rightarrow\) Include (an) interaction effect(s) in your model.
    • Case 4: Continuous IV, Continuous Moderator \(\rightarrow\) Include an interaction effect in your model.

  6. The data cannot tell us if some variable, say Z, should be a moderator or a mediator; we must base this decision on theory and substantive expertise. We must think about the process by which X affects Y and ask:

    • Is Z an intermediary step in the causal chain linking X and Y?
      • If so, we should include Z as a mediator.
    • Does Z stand apart from the causal chain linking X and Y but affect the nature of that linkage via contextual influences?
      • If so, we should include Z as a moderator.

    Statistically speaking, we would prefer our moderators to be unrelated to X and Y, while we want mediators to relate strongly with both X and Y.

Questions

  1. What is an indirect or mediated effect?
  2. What is the difference between the total and direct effect?
  3. What is the main problem with the Barron & Kenny “Causal Steps Approach”?
  4. What is bootstrapping, and why is it a better way to test mediation than Sobel’s test?
  5. Explain how it is possible that “effects that don’t exist can be mediated”.

Answers

  1. The indirect effect (IE) is the part of the effect of X on Y that is transmitted through M. We compute the IE by multiplying the effect of X on M (a) and the effect of M on Y (b): \(IE = ab\).

  2. The total effect is the effect of X on Y without accounting for M. The direct effect is the effect of X on Y after controlling for M.

  3. The B&K approach infers mediation based on a sequence of significance tests, and this repeated testing lowers power. Moreover, if no significant total effect is found between X and Y, researchers applying B&K logic must infer the absence of any indirect effect, but a nonsignificant total effect does not imply a lack of mediation.

  4. Bootstrapping constructs an empirical sampling distribution for a parameter by resampling rows from the original data many (e.g., 1000) times, and conducting the same analysis on each of these samples. The distribution of these parameter estimates represents an empirical sampling distribution for the parameter. This sampling distribution is then used to support inference (e.g., by deriving confidence intervals or standard errors). Sobel’s test assumes the IE is normally distributed, which cannot be true in finite samples. Bootstrapping is a nonparametric technique that directly estimates the sampling distribution of the IE rather than assuming some parametric form.

  5. The following passage from the reading (p. 414) explains:

    That X can exert an indirect effect on Y through M in the absence of an association between X and Y becomes explicable once you consider that a total effect is the sum of many different paths of influence, direct and indirect, not all of which may be a part of the formal model. For example, it could be that two or more indirect paths carry the effect from X through Y, and those paths operate in opposite directions (cf., MacKinnon, Krull, & Lockwood, 2000). Much as a main effect in 2 \(\times\) 2 ANOVA might be nonsignificant if the simple effects are opposite in sign (i.e., a crossover interaction), two or more indirect effects with opposite signs can cancel each other out, producing a total effect and perhaps even a total indirect effect that is not detectably different from zero, in spite of the existence of specific indirect effects that are not zero.