Exploratory Mediation Analysis with Many Potential Mediators

Abstract: Social and behavioral scientists are increasingly employing technologies such as fMRI, smartphones, and gene sequencing, which yield 'high-dimensional' datasets with more columns than rows. There is increasing interest, but little substantive theory, in the role the variables in these data play in known processes. This necessitates exploratory mediation analysis, for which structural equation modeling is the benchmark method. However, this method cannot perform mediation analysis with more variables than observations. One option is to run a series of univariate mediation models, which incorrectly assumes independence of the mediators. Another option is regularization, but the available implementations may lead to high false positive rates. In this paper, we develop a hybrid approach which uses components of both filter and regularization: the 'Coordinate-wise Mediation Filter'. It performs filtering conditional on the other selected mediators. We show through simulation that it improves performance over existing methods. Finally, we provide an empirical example, showing how our method may be used for epigenetic research.