Causal Inference Using Mediation Analysis or Instrumental Variables - Full Mediation in the Absence of Conditional Independence

Thomas Otter; Max J. Pachali; Stefan Mayer; Jan R. Landwehr

doi:10.15358/0344-1369-2018-2-41

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- 2–2 Editorial Bernhard Swoboda Bernhard Swoboda 2–2
- 3–94 Research Articles 3–94
  - 3–25 A User's Guide to the Galaxy of Conjoint Analysis and Compositional Preference Measurement Michael Steiner, Martin Meißner Michael Steiner, Martin Meißner 3–25
  - 26–40 Control Variables in Marketing Research Martin Klarmann, Sven Feurer Martin Klarmann, Sven Feurer 26–40
  - 41–57 Causal Inference Using Mediation Analysis or Instrumental Variables - Full Mediation in the Absence of Conditional Independence Thomas Otter, Max J. Pachali, Stefan Mayer, Jan R. Landwehr Thomas Otter, Max J. Pachali, Stefan Mayer, Jan R. Landwehr 41–57
  - 58–94 Avoiding Pitfalls in Experimental Research in Marketing Anja Spilski, Andrea Gröppel-Klein, Heribert Gierl Anja Spilski, Andrea Gröppel-Klein, Heribert Gierl 58–94
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Marketing ZFP , page 41 - 57

Causal Inference Using Mediation Analysis or Instrumental Variables - Full Mediation in the Absence of Conditional Independence

Autoren

Thomas Otter Max J. Pachali Stefan Mayer Jan R. Landwehr

DOI
- doi.org/10.15358/0344-1369-2018-2-41
- ISSN: 0344-1369
- ISSN online: 0344-1369
Zusammenfassung

This paper re-emphasizes the topic of model specification in the context of mediation analysis and highlights the ambiguous nature of results that are consistent with partial mediation, both with respect to the existence of a direct causal effect, and with respect to correct inference about the indirect effect. While none of our individual results are genuinely new, they are often only discussed on the side or as “special topics” in application oriented discussions, or in the newer, more technical literature on causal inference in mediation analysis. With this paper, we hope to contribute to the acute awareness of model specification issues in the wider community of researchers that rely on mediation analysis for their substantive research. We clarify the differences between mediation analysis and IV-estimation as a starting point for the discussion of model specification in the context of mediation analysis. Specifically, we highlight the connection between full mediation and conditional independence and show that conditional independence may be violated even though full mediation holds at a causal theory level. When this is the case, standard mediation analysis yields biased inference both with respect to the direct and the indirect effect. We emphasize that this is a problem separate from, and prior to the problem of reliably assessing the statistical significance of estimates suggestive of an indirect effect. We discuss how Bayes factors usefully improve on p-values in the context of testing for the absence of effects and suggest the development of additional testable hypotheses and of the corresponding testing routines. Finally, we suggest that researcher relying on mediation analysis should investigate alternative model specifications, notably a specification that allows for unobserved common causes of the mediator and the dependent variable, and a specification that allows for measurement error in the mediator. This can be easily accomplished using covariance algebra or structural equation modeling software. Finally, our results imply that full mediation at a causal theory level could be more common than currently believed.

Abstract

This paper re-emphasizes the topic of model specification in the context of mediation analysis and highlights the ambiguous nature of results that are consistent with partial mediation, both with respect to the existence of a direct causal effect, and with respect to correct inference about the indirect effect. While none of our individual results are genuinely new, they are often only discussed on the side or as “special topics” in application oriented discussions, or in the newer, more technical literature on causal inference in mediation analysis. With this paper, we hope to contribute to the acute awareness of model specification issues in the wider community of researchers that rely on mediation analysis for their substantive research. We clarify the differences between mediation analysis and IV-estimation as a starting point for the discussion of model specification in the context of mediation analysis. Specifically, we highlight the connection between full mediation and conditional independence and show that conditional independence may be violated even though full mediation holds at a causal theory level. When this is the case, standard mediation analysis yields biased inference both with respect to the direct and the indirect effect. We emphasize that this is a problem separate from, and prior to the problem of reliably assessing the statistical significance of estimates suggestive of an indirect effect. We discuss how Bayes factors usefully improve on p-values in the context of testing for the absence of effects and suggest the development of additional testable hypotheses and of the corresponding testing routines. Finally, we suggest that researcher relying on mediation analysis should investigate alternative model specifications, notably a specification that allows for unobserved common causes of the mediator and the dependent variable, and a specification that allows for measurement error in the mediator. This can be easily accomplished using covariance algebra or structural equation modeling software. Finally, our results imply that full mediation at a causal theory level could be more common than currently believed.
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