Abstract
Mediation analysis has many applications in psychology and the social sciences. The most prevalent methods typically assume that the error distribution is normal and homoscedastic. However, this assumption may rarely be met in practice, which can affect the validity of the mediation analysis. To address this problem, we propose robust mediation analysis based on median regression. Our approach is robust to various departures from the assumption of homoscedasticity and normality, including heavy-tailed, skewed, contaminated, and heteroscedastic distributions. Simulation studies show that under these circumstances, the proposed method is more efficient and powerful than standard mediation analysis. We further extend the proposed robust method to multilevel mediation analysis, and demonstrate through simulation studies that the new approach outperforms the standard multilevel mediation analysis. We illustrate the proposed method using data from a program designed to increase reemployment and enhance mental health of job seekers.