Title: Variable selection for mediation analysis with latent factors via group-wise penalization
Authors: Qing Wang - Wellesley College (United States) [presenting]
Yeying Zhu - University of Waterloo (Canada)
Xizhen Cai - Williams College (United States)
Abstract: A mediation analysis model is considered where the outcome depends on exposure and a number of latent factors that are related to a set of observable mediators. In addition, we assume that there exist some redundant mediators that do not relate to the factors or outcome. We first apply a penalized factor analysis model with group-wise regularization to uncover the relationship between the mediators and latent factors so as to filter out irrelevant mediators. An expectation-maximization algorithm is employed to fit the penalized factor analysis model. Then, we utilize the attained latent factors to understand their relationship with both the exposure and the outcome through a two-step procedure. Simulations in both low and high-dimensional settings are considered. The results suggest that our proposed model yields a more accurate identification of the true mediators and produces a smaller bias for the mediation model compared to existing methods. Ongoing work is to incorporate simultaneous mediator and factor selection in contrast to the two-stage process.