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Four applications of permutation methods to testing a single-mediator model.

Aaron B Taylor1, David P MacKinnon

  • 1Department of Psychology, Texas A&M University, 4235 TAMU, College Station, TX 77843-4235, USA. aaron.taylor@tamu.edu

Behavior Research Methods
|February 8, 2012
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Summary

Permutation tests offer new ways to analyze single-mediator models. The noniterative permutation confidence interval for ab showed excellent error control, power, and coverage, making it a recommended method for mediation analysis.

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Mediation analysis is crucial for understanding indirect effects in statistical models.
  • Existing methods for mediation analysis, including bootstrap and product of coefficients tests, have limitations.
  • Permutation tests offer a computationally intensive yet robust alternative for estimating sampling distributions.

Purpose of the Study:

  • To evaluate four novel applications of permutation tests for the single-mediator model.
  • To compare the performance of these new permutation tests against established mediation analysis methods.
  • To assess Type I error rates, statistical power, and confidence interval coverage for each method.

Main Methods:

  • Employed a Monte Carlo simulation study to rigorously compare statistical methods.
  • Evaluated permutation tests including the test of ab, joint significance test, and noniterative/iterative confidence intervals.
  • Compared these with existing methods: joint significance, distribution of the product, and bootstrap tests (percentile and bias-corrected).

Main Results:

  • The noniterative permutation confidence interval for ab demonstrated superior performance.
  • This method effectively controlled Type I error, offered high statistical power, and provided excellent confidence interval coverage.
  • The iterative permutation confidence interval excelled in coverage, though with slightly lower power than some existing methods.

Conclusions:

  • Permutation confidence interval methods are highly recommended, particularly when precise confidence interval estimation is a priority in mediation analysis.
  • The noniterative permutation confidence interval for ab is a strong candidate for practical application due to its balanced performance.
  • SPSS and SAS macros are provided to facilitate the implementation of these recommended permutation confidence interval methods.