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

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 cri...

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Bibliographic Details
Published in:Multivariate behavioral research 2004-01, Vol.39 (1), p.99-128
Main Authors: MacKinnon, David P., Lockwood, Chondra M., Williams, Jason
Format: Article
Language:English
Subjects:
Bootstrap method
Data Analysis
Evaluation Methods
Multivariate analysis
Regression (Statistics)
Research Methodology
Sampling
Simulation
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Summary: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.
ISSN:0027-3171
1532-7906
DOI:10.1207/s15327906mbr3901_4