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A Unification of Mediator, Confounder, and Collider Effects

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Third-variable effects, such as mediation and confounding, are core concepts in prevention science, providing the theoretical basis for investigating how risk factors affect behavior and how interventions change behavior. Another third variable, the collider, is not commonly considered but is also important for prevention science. This paper describes the importance of the collider effect as well as the similarities and differences between these three third-variable effects. The single mediator model in which the third variable (T) is a mediator of the independent variable (X) to dependent variable (Y) effect is used to demonstrate how to estimate each third-variable effect. We provide difference in coefficients and product of coefficients estimators of the effects and demonstrate how to calculate these values with real data. Suppression effects are defined for each type of third-variable effect. Future directions and implications of these results are discussed.

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  • 12 July 2021

    Springer Nature’s version of this paper was updated to reflect the removal of the redundant sentence: "The correct causal model is an exacting qualification,requiring a program of research with precise definition of causal effects, specification of assumptions, and sensitivity analysis for how violatingassumptions affects results.", which was inadvertently added in the last paragraph of Discussion section.


  1. This paper describes adjustment as including an additional predictor in a regression model. Adjustment comes in other forms and names including conditioning on a variable, controlling for a variable, stratifying by a variable, and selection into a study by a variable (see Elwert & Winship, 2014 and Morgan & Winship, 2015 for more on these topics).


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We thank Adam Cohen, Matthew Fritz, Linda Luecken, June Tangney, Jenn Tein, Matthew Valente, members of the Research in Prevention Laboratory, and reviewers for helpful comments.


A grant from the National Institute on Drug Abuse (R37DA09757) supported this research in part. Some of this research was presented at the 2019 conference of the American Psychological Association.

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Correspondence to David P. MacKinnon.

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All analyses in the article were secondary data analyses. All procedures, including the informed consent process, were conducted in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000 and the Arizona State University Human Subjects Internal Review Board.

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Data were collected via Informed Consent in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000.

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The authors declare that they have no conflict of interest.

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MacKinnon, D.P., Lamp, S.J. A Unification of Mediator, Confounder, and Collider Effects. Prev Sci 22, 1185–1193 (2021).

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