title: Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation.
abstract: It is well known from the mediation analysis literature that the identification of direct and indirect effects relies on strong no unmeasured confounding assumptions of no unmeasured confounding. Even in randomized studies the mediator may still be correlated with unobserved prognostic variables that affect the outcome, in which case the mediator's role in the causal process may not be inferred without bias. In the behavioural and social science literature very little attention has been given so far to the causal assumptions required for moderated mediation analysis. In this paper we focus on the index for moderated mediation, which measures by how much the mediated effect is larger or smaller for varying levels of the moderator. We show that in linear models this index can be estimated without bias in the presence of unmeasured common causes of the moderator, mediator and outcome under certain conditions. Importantly, one can thus use the test for moderated mediation to support evidence for mediation under less stringent confounding conditions. We illustrate our findings with data from a randomized experiment assessing the impact of being primed with social deception upon observer responses to others' pain, and from an observational study of individuals who ended a romantic relationship assessing the effect of attachment anxiety during the relationship on mental distress 2 years after the break-up.
authors.affiliation: Department of Data Analysis, Ghent University, Belgium. tom.loeys@ugent.be.
authors.forename: Tom
authors.initials: T
authors.lastname: Loeys
authors.affiliation: Department of Data Analysis, Ghent University, Belgium.
authors.forename: Wouter
authors.initials: W
authors.lastname: Talloen
authors.affiliation: Department of Experimental-Clinical and Health Psychology, Ghent University, Belgium.
authors.forename: Liesbet
authors.initials: L
authors.lastname: Goubert
authors.affiliation: Department of Data Analysis, Ghent University, Belgium.
authors.forename: Beatrijs
authors.initials: B
authors.lastname: Moerkerke
authors.affiliation: Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium.
authors.forename: Stijn
authors.initials: S
authors.lastname: Vansteelandt
mesh_terms: D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D006801:Humans; D016014:Linear Models; D012044:Regression Analysis
keywords: confounding; mediation; moderated mediation; moderation