AbstractMediation analysis attempts to determine whether the relationship between an independent variable (e.g., exposure) and an outcome variable can be explained, at least partially, by an intermediate variable, called a mediator. Most methods for mediation analysis focus on one mediator at a time, although multiple mediators can be jointly analyzed by structural equation models (SEMs) that account for correlations among the mediators. We extend the use of SEMs for the analysis of multiple mediators by creating a sparse group lasso penalized model such that the penalty considers the natural groupings of parameters that determine mediation, as well as encourages sparseness of the model parameters. This provides a way to simultaneously evaluate many mediators and select those that have the most impact, a feature of modern penalized models. Simulations are used to illustrate the benefits and limitations of our approach, and application to a study of DNA methylation and reactive cortisol stress following childhood trauma discovered two novel methylation loci that mediate the association of childhood trauma scores with reactive cortisol stress levels. Our new methods are incorporated into R software called regmed.