Equivalence of two least-squares estimators for indirect effects

Wen Wu Wang*, Ping Yu, Yuejin Zhou, Tiejun Tong, Zhonghua Liu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


In social and behavioral sciences, the mediation test based on the indirect effect is an important topic. There are many methods to assess intervening variable effects. In this paper, we focus on the difference method and the product method in mediation models. Firstly, we analyze the regression functions in the simple mediation model, and provide an expectation-consistent condition. We further show that the difference estimator and the product estimator are numerically equivalent based on the least-squares regression regardless of the error distribution. Secondly, we generalize the equivalence result to the three-path model and the multiple mediators model, and prove a general equivalence result in a class of restricted linear mediation models. Thirdly, we investigate the empirical distributions of the indirect effect estimators in the simple mediation model by simulations, and show that the indirect effect estimators are normally distributed as long as one multiplicand of the product estimator is large. Finally, we introduce some popular R packages for mediation analysis and also provide some useful suggestions on how to correctly conduct mediation analysis.

Original languageEnglish
Pages (from-to)7364–7375
Number of pages12
JournalCurrent Psychology
Issue number9
Early online date10 Jul 2021
Publication statusPublished - Mar 2023

Scopus Subject Areas

  • Psychology(all)

User-Defined Keywords

  • Bootstrap
  • Difference in coefficients
  • Indirect effects
  • Least-squares regression
  • Mediation analysis
  • Product of coefficients


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