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Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation

Tom Loeys (UGent) , Wouter Talloen (UGent) , Liesbet Goubert (UGent) , Beatrijs Moerkerke (UGent) and Stijn Vansteelandt (UGent)
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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 2years after the break-up.
Keywords
confounding, mediation, moderation, moderated mediation, CAUSAL, DECOMPOSITION, TESTS

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Chicago
Loeys, Tom, Wouter Talloen, Liesbet Goubert, Beatrijs Moerkerke, and Stijn Vansteelandt. 2016. “Assessing Moderated Mediation in Linear Models Requires Fewer Confounding Assumptions Than Assessing Mediation.” British Journal of Mathematical & Statistical Psychology 69 (3): 352–374.
APA
Loeys, T., Talloen, W., Goubert, L., Moerkerke, B., & Vansteelandt, S. (2016). Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation. BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY, 69(3), 352–374.
Vancouver
1.
Loeys T, Talloen W, Goubert L, Moerkerke B, Vansteelandt S. Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation. BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY. 2016;69(3):352–74.
MLA
Loeys, Tom, Wouter Talloen, Liesbet Goubert, et al. “Assessing Moderated Mediation in Linear Models Requires Fewer Confounding Assumptions Than Assessing Mediation.” BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 69.3 (2016): 352–374. Print.
@article{8507229,
  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 2years after the break-up.},
  author       = {Loeys, Tom and Talloen, Wouter and Goubert, Liesbet and Moerkerke, Beatrijs and Vansteelandt, Stijn},
  issn         = {0007-1102},
  journal      = {BRITISH JOURNAL OF MATHEMATICAL \& STATISTICAL PSYCHOLOGY},
  keyword      = {confounding,mediation,moderation,moderated mediation,CAUSAL,DECOMPOSITION,TESTS},
  language     = {eng},
  number       = {3},
  pages        = {352--374},
  title        = {Assessing moderated mediation in linear models requires fewer confounding assumptions than assessing mediation},
  url          = {http://dx.doi.org/10.1111/bmsp.12077},
  volume       = {69},
  year         = {2016},
}

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