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Abstract:
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In many scientific studies, it becomes important to delineate causal pathways through a large number of mediators. Structural equation modeling (SEM) is a popular technique to estimate pathway effects expressed as products of coefficients. However, it becomes unstable to fit such models with high dimensional mediators as predictors, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown.This paper proposes a sparse mediation model using regularized SEM approach, where sparsity means a small number of mediators have nonzero mediation effect. To address model selection challenge, we introduce a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function. It enables a computationally tractable optimization criterion to estimate and select pathway effects. We develop a fast ADMM-type algorithm to compute model parameters, and show that the interative updates can be expressed in closed form. On both simulated data and an fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than competing methods.
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