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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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Correcting the Bias Correction for the Bootstrap Confidence Interval in Mediation Analysis.

Tristan D Tibbe1, Amanda K Montoya1

  • 1Department of Psychology, University of California, Los Angeles, Los Angeles, CA, United States.

Frontiers in Psychology
|June 17, 2022
PubMed
Summary

New bias-corrected bootstrap methods for indirect effects in mediation analysis were evaluated. While offering potential power gains, their inflated type I error rates mean the percentile bootstrap confidence interval remains recommended for controlled error rates.

Keywords:
bias correctionbias-corrected bootstrap confidence intervalbootstrappingindirect effectmediationpowertype I error rate

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • The bias-corrected bootstrap confidence interval (BCBCI) was previously favored for indirect effect inference in mediation analysis due to its power in small samples.
  • Methodologists now criticize BCBCI for inflated Type I error rates, leading to the percentile bootstrap confidence interval (PBCI) being the recommended alternative.
  • There is a need for robust inferential methods that balance power and Type I error control for indirect effects.

Purpose of the Study:

  • To propose and evaluate two novel bias-corrected bootstrap methods for confidence intervals of indirect effects in mediation analysis.
  • To compare the performance of these new methods against existing BCBCI and PBCI using Monte Carlo simulations.
  • To assess the trade-offs between statistical power and Type I error rates for different bias-corrected bootstrap approaches.

Main Methods:

  • A Monte Carlo simulation study was conducted to compare five confidence interval methods: BCBCI, PBCI, Stine's (1989) bias-corrected method, a novel reduced BCBCI, and Chen and Fritz's (2021) Winsorized BCBCI.
  • Performance criteria included balance (CI coverage symmetry), power, and Type I error rates.
  • An extension of the simulation controlled for Type I error inflation to re-evaluate the power of the bias-corrected methods.

Main Results:

  • Methods formed a performance continuum: BCBCI showed the best balance, highest power, and highest Type I error; PBCI showed the worst balance, lowest power, and lowest Type I error.
  • The proposed alternative bias-corrected methods fell between BCBCI and PBCI on all performance metrics.
  • After controlling for Type I error inflation, the enhanced power of the alternative bias-corrected methods was primarily attributed to their higher Type I error rates.

Conclusions:

  • The percentile bootstrap confidence interval (PBCI) remains the recommended method for indirect effects when controlling Type I error rates is paramount.
  • While alternative bias-corrected methods may offer higher power, this comes at the cost of increased Type I error rates.
  • Future research should investigate the generalizability of these findings under conditions such as missing data and confounding variables.