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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Confidence intervals for indirect effects in mediation models are crucial for statistical inference.
  • Likelihood-based confidence intervals (LBCI) using maximum likelihood estimation assume multivariate normality, limiting their application with non-normal data.
  • The robustness of LBCI under non-normality, particularly when predictor variables deviate from normality while error terms remain conditionally normal, requires investigation.

Purpose of the Study:

  • To compare the performance of LBCI with other methods for estimating confidence intervals of indirect effects in mediation models when predictor variables are not normally distributed.
  • To evaluate the robustness of LBCI under conditions of non-normal predictor distributions, specifically when error terms are conditionally normal.
  • To assess the effectiveness of alternative methods, including nonparametric bootstrapping, LBCI-ADF, LBCI-Fixed-X, and Monte Carlo simulations, under these specific distributional assumptions.

Main Methods:

  • A simulation study was employed using both simple and serial mediation models.
  • The distribution of the predictor variable was manipulated to simulate non-normal conditions.
  • The performance of LBCI was compared against nonparametric bootstrapping, LBCI-ADF, LBCI-Fixed-X, and Monte Carlo methods, focusing on coverage probabilities.

Main Results:

  • Monte Carlo simulations performed worst in estimating confidence intervals for indirect effects.
  • LBCI and LBCI-Fixed-X demonstrated suboptimal performance with high kurtosis and large indirect effects, even with large sample sizes.
  • LBCI-ADF and nonparametric bootstrapping generally yielded coverage probabilities close to the nominal level, with minor issues in serial mediation models with small sample sizes.

Conclusions:

  • Standard LBCI methods are not robust to non-normal predictor distributions in mediation analysis.
  • Nonparametric bootstrapping and LBCI-ADF are recommended as more reliable methods for constructing confidence intervals for indirect effects when normality assumptions are violated.
  • Researchers should carefully consider the distributional properties of their data when selecting a method for estimating confidence intervals in mediation models.