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Total-effect Test May Erroneously Reject So-called "Full" or "Complete" Mediation

Author

Listed:
  • Tingxuan Han

    (Tsinghua University)

  • Luxi Zhang

    (University of Macau)

  • Xinshu Zhao

    (University of Macau)

  • Ke Deng

    (Tsinghua University)

Abstract

The procedure for establishing mediation, i.e., determining that an independent variable X affects a dependent variable Y through some mediator M, has been under debate. The classic causal steps require that a "total effect" be significant, now also known as statistically acknowledged. It has been shown that the total-effect test can erroneously reject competitive mediation and is superfluous for establishing complementary mediation. Little is known about the last type, indirect-only mediation, aka "full" or "complete" mediation, in which the indirect (ab) path passes the statistical partition test while the direct-and-remainder (d) path fails. This study 1) provides proof that the total-effect test can erroneously reject indirect-only mediation, including both sub-types, assuming least square estimation (LSE) F-test or Sobel test; 2) provides a simulation to duplicate the mathematical proofs and extend the conclusion to LAD-Z test; 3) provides two real-data examples, one for each sub-type, to illustrate the mathematical conclusion; 4) in view of the mathematical findings, proposes to revisit concepts, theories, and techniques of mediation analysis and other causal dissection analyses, and showcase a more comprehensive alternative, process-and-product analysis (PAPA).

Suggested Citation

  • Tingxuan Han & Luxi Zhang & Xinshu Zhao & Ke Deng, 2023. "Total-effect Test May Erroneously Reject So-called "Full" or "Complete" Mediation," Papers 2309.08910, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2309.08910
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    References listed on IDEAS

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    1. Gopalakrishnan, Shanthi & Zhang, Haisu, 2019. "Client dependence: A boon or bane for vendor innovation? A competitive mediation framework in IT outsourcing," Journal of Business Research, Elsevier, vol. 103(C), pages 407-416.
    2. Xinshu Zhao & John G. Lynch & Qimei Chen, 2010. "Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 37(2), pages 197-206, August.
    3. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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