Robust mediation analysis: What we talk about when we talk about robustness

Mediation analysis allows empirical researchers to study how an exposure variable affects an outcome variable through one or more intervening variables. Over the years, mediation analysis has become one of the most widely used statistical techniques in the social, behavioral, and medical sciences. Yet the most popular techniques for mediation analysis rely strongly on normality assumptions and are therefore susceptible to the influence of outliers or nonnormal distributions. We review common mediation models and discuss various approaches for estimation and inference, including their implementation in software packages. Moreover, we present robust alternatives, thereby clarifying different notions of robustness. We further consider a setting where the mediation model holds in a latent space but where measurement issues create deviations from normality assumptions in the observed variable space, which is a setting not commonly considered in the literature on robust mediation analysis, and we obtain preliminary results via a simulation study. Finally, we highlight the mechanics and relevance of robust methods in an an illustrative empirical application.