Mediation analysis with latent factors using simultaneous group‐wise and parameter‐wise penalization

Abstract

Mediation analysis aims to uncover the underlying mechanism of how an exposure variable affects the outcome of interest through one or more than one mediating variables. In the event that the number of candidate mediators is large, variable selection or dimension reduction techniques are often utilized to reduce the dimension of the initial set of mediators. In this paper, we propose a latent variable approach using sparse factor analysis with both group‐wise and parameter‐wise penalization to remove irrelevant candidate mediators and estimate the latent factors simultaneously. After the low‐dimensional latent mediating factors are obtained, the direct and indirect effects can be estimated and tested from a multivariate mediation model. To demonstrate the practical applications of the proposed methodology, we apply it to a weight behaviour dataset and an environmental dataset, separately.