Cited by 7,806Psychometric Methodologies and TestingAdvanced Causal Inference TechniquesStatistical Methods and Bayesian Inference

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Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods

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MacKinnon, David P., Lockwood, Chondra M., Williams, Jason·2004·Multivariate Behavioral Research

DOI 10.1207/s15327906mbr3901_4PMC PMC2821115

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Abstract

The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

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Self-citation

Authors: MacKinnon, D. P., Lockwood, C. M., & Williams, J.
Affiliations: Arizona State University (US)
ORCID: MacKinnon, David P.
Williams, Jason
Venue: Multivariate Behavioral Research
Publisher: Informa UK Limited
Published: 2004-01
Volume: 39
Issue: 1
Pages: 99-128
ISSN: 0027-3171 (ISSN-L)
1532-7906
DOI: 10.1207/s15327906mbr3901_4
PMC: PMC2821115
OpenAlex: W2113168655
Cited by: 7,806
References: 63
Citations by year: 2026: 497 · 2025: 503 · 2024: 486 · 2023: 526 · 2022: 580 · 2021: 571 · 2020: 549 · 2019: 507 · 2018: 458 · 2017: 437 · 2016: 446 · 2015: 430 · 2014: 413 · 2013: 376 · 2012: 297
FWCI: 56.41
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: Multivariate Behavioral Research (publishedVersion)
PubMed (publishedVersion)
PubMed Central (acceptedVersion)
Funders: National Institute on Drug Abuse (R01DA009757)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: indirect effects, confidence limits, bias-corrected bootstrap, resampling, confidence interval coverage, mediation analysis, standard error estimation

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Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods

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