Statistics and Its Interface

Volume 15 (2022)

Number 1

Pathway Lasso: pathway estimation and selection with high-dimensional mediators

Pages: 39 – 50



Yi Zhao (Department of Biostatistics and Health Data Science, Indiana University School of Medicine, Indianapolis, In., U.S.A.)

Xi Luo (Department of Biostatistics and Data Science, University of Texas Health Science Center, Houston, Tx., U.S.A.)


In many scientific studies, it becomes increasingly important to delineate the pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as the product of coefficients. However, it becomes unstable and computationally challenging to fit such models with high-dimensional mediators. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity means that a small number of mediators have a nonzero mediation effect between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function for the mediation effects, and it enables a computationally tractable optimization criterion to estimate and select pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. We also prove the asymptotic consistency of our Pathway Lasso estimator for the mediation effect. On both simulated data and an fMRI data set, the proposed approach yields higher pathway selection accuracy and lower estimation bias than competing methods.


convex optimization, mediation analysis, structural equation modeling, path analysis

R code is available on GitHub at

Luo was partially supported by National Institutes of Health grants R01EB022911 and R01MH110449 and National Science Foundation grant DMS 1557467.

Received 15 July 2020

Accepted 27 March 2021

Published 11 August 2021