[Paper Review] Robust Mediation Analysis: The R Package robmed

Andreas Alfons, Ateş, Nüfer Y.+1 more|EUR Research Repository (Erasmus University Rotterdam)|Feb 24, 2022

Conflict Management and Negotiation4 citations

TL;DR

This paper introduces the R package robmed, which provides robust mediation analysis using fast-and-robust bootstrap methods based on MM-estimators, offering reliable inference under non-normality and outlier contamination. It outperforms traditional OLS-based bootstrap methods in terms of Type I error control and power across various distributions and outlier scenarios.

ABSTRACT

Mediation analysis is one of the most widely used statistical techniques in the social, behavioral, and medical sciences. Mediation models allow to study how an independent variable affects a dependent variable indirectly through one or more intervening variables, which are called mediators. The analysis is often carried out via a series of linear regressions, in which case the indirect effects can be computed as products of coefficients from those regressions. Statistical significance of the indirect effects is typically assessed via a bootstrap test based on ordinary least-squares estimates. However, this test is sensitive to outliers or other deviations from normality assumptions, which poses a serious threat to empirical testing of theory about mediation mechanisms. The R package robmed implements a robust procedure for mediation analysis based on the fast-and-robust bootstrap methodology for robust regression estimators, which yields reliable results even when the data deviate from the usual normality assumptions. Various other procedures for mediation analysis are included in package robmed as well. Moreover, robmed introduces a new formula interface that allows to specify mediation models with a single formula, and provides various plots for diagnostics or visual representation of the results.

Motivation & Objective

• To address the sensitivity of conventional mediation analysis to outliers and deviations from normality assumptions.
• To develop a robust alternative to ordinary least-squares (OLS)-based bootstrap methods in mediation analysis.
• To implement a fast-and-robust bootstrap procedure using MM-estimators for improved reliability under heavy-tailed and skewed error distributions.
• To provide a user-friendly formula interface and diagnostic plots for model interpretation and validation.
• To ensure compatibility with existing tools like the PROCESS macro by offering similar output structures and options for confidence intervals or p-values.

Proposed method

• Employs MM-estimators for robust regression to minimize the influence of outliers in the estimation of mediation model parameters.
• Applies the fast-and-robust bootstrap methodology to generate stable sampling distributions for indirect effects.
• Uses a single formula interface to specify full mediation models, simplifying model specification compared to sequential regression calls.
• Implements diagnostic plots to detect influential observations and assess model assumptions.
• Provides both bootstrap-based confidence intervals and normal-theory intervals via the `type` argument in `confint()` and `coef()` functions.
• Supports estimation of total, direct, and indirect effects with robust standard errors and significance testing via bootstrap resampling.

Experimental results

Research questions

• RQ1 How does the performance of robust mediation analysis compare to OLS-based bootstrap methods under non-normal error distributions?
• RQ2 To what extent does the robust bootstrap procedure maintain Type I error control when data contain outliers or heavy-tailed errors?
• RQ3 Can the fast-and-robust bootstrap with MM-estimators improve power and accuracy in detecting indirect effects compared to existing robust alternatives?
• RQ4 How does the robust method perform in comparison to data-cleaning-based approaches (e.g., Zu et al., 2010) in terms of reliability and efficiency?
• RQ5 To what extent can the package interface emulate the widely used PROCESS macro in SPSS/SAS for ease of adoption by researchers?

Key findings

• The robust bootstrap method based on MM-estimators maintains appropriate Type I error rates across a wide range of distributions, including those with high kurtosis and skewness.
• In the presence of outliers, the robust method correctly failed to reject the null hypothesis of no indirect effect (95% CI: -0.294 to -0.009), while the OLS-based method incorrectly failed to detect significance (95% CI: -0.214 to 0.025).
• The robust method demonstrated superior performance in controlling the family-wise error rate and maintaining statistical power under contamination and non-normality.
• Diagnostic plots revealed a heavy-tailed distribution in the data, which explained the discrepancy between OLS and robust results, supporting the use of robust methods in such cases.
• The package's output structure closely mirrors that of the PROCESS macro, facilitating adoption by researchers familiar with SPSS/SAS-based workflows.
• The `confint()` and `coef()` functions allow flexible extraction of bootstrap or normal-theory intervals, enabling researchers to report confidence intervals or p-values as needed.