HBEH 761 (Module 2): Mediation and Moderation

What are some problems with the Normal Theory approach (Sobel test) to test the significance of the indirect effect?

- Assumes the sampling distribution of A*B is normal - Low power (increased likelihood of Type 2 error) and generates confidence intervals that tend to be less accurate

What are common moderation patterns?

- Exacerbating (enhancing): the relationship between X & Y gets stronger as W increases - Buffering (dampening): the relationship between X & Y gets weaker as W increases. - Antagonistic: the relationship between X & Y reverses direction (i.e., sign) as W increases. - Can also hypothesize that the relationship between X & Y will change in significance as W increases (i.e., go from nonsignificant to significant or vice versa)

What can mediation analyses tell us?

- How/why contextual factors have effects on subsequent developmental processes - The processes through which an intervention works to influence health behavior - Which components of an intervention are essential for behavior change - The processes that explain why some demographic groups are more at risk for negative health outcomes than others.

What are some critiques of Baron & Kenny's "Causal Steps" approach to assessing mediation?

- It neither formally quantifies the indirect effect nor requires any kind of inferential test about it - Hypothesis tests based on assumptions that may not be met, the more tests that are conducted the more likely a mistake will be made. Better to minimize # of tests - Indirect effect may be significant even if c isn't significant and even if path(s) a and/or b are not significant.

What are different approaches for testing the significance of the indirect effect (path A*B)?

- Normal theory approach (Sobel test) - Bootstrapping - Monte Carlo confidence intervals - Distribution of product approach *We only cover the first two approaches in HBEH 761

Mediation hypotheses imply a causal relationship between X & M and M & Y. However, establishing causality is complex. What are some ways to improve causal inference?

- Randomized designs (experiments) to establish non-spuriousness - Inclusion of statistical controls to establish non-spuriousness - Longitudinal designs to establish temporality

A moderation hypothesis is supported if:

- The parameter estimate for the interaction term (X*W) is statistically significant - Post-hoc probing of the interaction determines that moderation pattern is as specified in the hypothesis.

What are examples of health behavior theories that involve mediation?

- Theory of planned behavior - Social norms theory

What can moderation analyses tell us?

- Whether contextual characteristics affect relations between individual level variables and behaviors - Whether a particular policy/program is more or less effective for certain subgroups

What are the steps for assessing moderation (in regression) with a single moderator?

0) Mean-center continuous predictors 1) Estimate a regression model including X, W, and X*W 2) If regression coefficient for X*W is. significant, probe the interaction to determine the predicted value of Y at different levels of X & W 3) Obtain parameter estimates, standard errors, and tests of significance for the effect of X on Y at different levels of W.

What are the steps for assessing moderation (in regression) with multiple moderators?

0) Mean-center continuous predictors 1) Estimate a regression model including X, Ws, and NO interaction terms (reduced model) -----Estimate a model including X, Ws, and all interaction terms (full model) -----Test significance of set of interaction terms using incremental f-test -----If f-test is not statistically significant, moderation is not supported 2) If f-test is significant, probe interaction terms 3) For each significant interaction, obtain parameter estimates, standard errors, and tests of significance for the effect of X on Y at different levels of W.

What are the steps for assessing simple mediation?

1) Examine association between X & Y (path C) 2) Examine association between X & M (path A) 3) Examine association between X & Y and between M & Y in a model where X & M are both predictors of Y (paths B and C') 4) Test the statistical significance of the indirect effect (path A*B).

How is a confounder different from a mediating variable?

A confounder is not on the causal pathway between X and Y, while a mediating variable is.

What is a confounder?

A variable related to X and Y that falsely accentuates or obscures relations between them.

What is a moderator?

A variable that alters the direction or strength of the relation between X & Y. Moderation hypotheses specify the conditions under which a particular causal effect occurs and/or is altered.

What are the mediation pathways?

A: Effect of X on the proposed mediator (M) B: Effect of M on Y C': Direct effect of X on Y, controlling for M C: Total effect of X on Y A*B: Indirect effect of X on Y through M

Statistical adjustments for third variables that are mediators or confounders will typically _________ relations between X & Y. a) increase b) decrease c) the relations will not be affected

B

What is bootstrapping?

Computationally intensive method that involves repeatedly sampling from the data set with replacement and estimating the indirect effect in each bootstrap sample. An empirical approximation of the sampling distribution of A*B is built and used to construct a confidence interval for the indirect effect.

For the estimate of the indirect effect to be interpreted causally, we must there is no confounding of: a) the X-Y association b) the X-M association c) the M-Y association d) all of the above e) none of the above

D

True or False: Significance of the indirect effect is all that matters for determining whether or not a mediation hypothesis is supported.

False. Even if an indirect effect is significant, it doesn't automatically mean that a mediation hypothesis is supported. The mediation hypothesis could say that increases in X are associated with increases in M, which in turn lead to increases in Y. However, in the initial steps of mediation analyses (where you're testing the association between X & M, and M& Y), it could be found that the relationships work differently For example, increases in X could be associated with decreases in M, which could in turn be associated with decreases in Y. This is why the initial steps in mediation analysis are important and why you don't go straight to analyzing the indirect effect.

Let's say you are modeling the relationship between depression and alcohol use, and you are interested in learning whether race moderates the relationship. If in your analyses you found that race does not significantly moderate the relationship, how would you expect the relationship between X & Y to look graphically for each level of your race variable?

I would expect to see parallel lines, wherein the effect of depression on alcohol use was the same for each race. This is known as an "unconditional effect."

Mediation is present if the ____________ is statistically significant.

Indirect effect

What is Baron & Kenny's "Causal Steps" approach to assessing mediation?

Mediation is present if: - Path C is statistically significant - Path A is statistically significant - Path B is statistically significant - If these criteria are met, then C and C' are compared. If C' pathway is not statistically significant, then "full mediation" is supported. If the C' pathway is smaller in magnitude than C but still statistically significant then "partial mediation" is said to have occurred.

What is simple mediation?

Mediation that only involves one mediator

______________ can pit competing theories of mechanisms against one another.

Multiple mediator models

What is mediation?

The process by which independent variables (X) exert influences on dependent variables (Y) through intervening variables (M: mediators).

True or False: Mediation is concerned with how or by what means a causal effect occurs.

True

True or False: The bootstrapping approach is a non-parametric approach that does not impose the assumption of normality in the sampling distribution of A*B.

True

True or False: Statistical testing cannot determine whether a third variable is a mediator or confounder.

True. Instead, you would rely on theory and accumulated knowledge to determine this.

True or False: Mediated moderation analysis is the same thing as moderated mediation analysis with product of X & W serving as causal agent of focus.

True. The models are the same. The difference is how they are interpreted and on what part of the model your attention is focused.

When probing a significant interaction, how do you determine the different levels of X & W to probe on?

Use +1 SD/ -1 SD