Partial, conditional, and moderated moderated mediation: Quantification, inference, and interpretation

ABSTRACT

Mediation of X’s effect on Y through a mediator M is moderated if the indirect effect of X depends on a fourth variable. Hayes [(2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50, 1–22. doi:10.1080/00273171.2014.962683] introduced an approach to testing a moderated mediation hypothesis based on an index of moderated mediation. Here, I extend this approach to models with more than one moderator. I describe how to test if X’s indirect effect on Y is moderated by one variable when a second moderator is held constant (partial moderated mediation), conditioned on (conditional moderated mediation), or dependent on a second moderator (moderated moderated mediation). Examples are provided, as is a discussion of the visualization of indirect effects and an illustration of implementation in the PROCESS macro for SPSS and SAS.

KEYWORDS:

• Conditional process analysis
• moderated mediation
• regression analysis
• indirect effect
• PROCESS macro

Notes

1. Preacher et al. (2007) discuss moderation of an indirect effect when two variables moderate separate paths in the causal system, and Hayes and Preacher (2013) illustrate conditional process analysis in a model with three moderators. But neither of these directly address the kinds of questions that are the focus of this paper.

2. To simplify the discussion, I do not distinguish between parameters and estimates of those parameters in my notation. Thus, symbols such as a, b, or c' could refer to an unknown parameter or estimate of that parameter based on data available. When the distinction is important, I will verbally rather than symbolically distinguish between them.

3. Of course, more than just news content is “manipulated” in this natural experiment. For example, perhaps those interviewed after his death were talking more about terrorism with neighbors and friends than those interviewed before his death.

4. When conditioning on “average sex,” these indirect effects conditioned on age are sex-weighted average conditional indirect effects, with the estimates weighted more heavily toward the conditional indirect effect among men because there are more men in the sample. One could condition at Z = 0.50, which would generate sex-unweighted average conditional indirect effects.