Exploratory Mediation Analysis via Regularization

Abstract

Exploratory mediation analysis refers to a class of methods used to identify a set of potential mediators of a process of interest. Despite its exploratory nature, conventional approaches are rooted in confirmatory traditions, and as such have limitations in exploratory contexts. We propose a two-stage approach called exploratory mediation analysis via regularization (XMed) to better address these concerns. We demonstrate that this approach is able to correctly identify mediators more often than conventional approaches and that its estimates are unbiased. Finally, this approach is illustrated through an empirical example examining the relationship between college acceptance and enrollment.

Keywords: exploratory mediation analysis; lasso; mediation; regularization.

FIGURE 1

The single mediator model.

FIGURE 2

The multiple mediator model.

FIGURE 3

Population model for Study 1: Mediator selection.

FIGURE 4

Plot of Bayesian information criterion (BIC) values associated with corresponding values of lambda for Study 3: Empirical example. Jumps in the BIC result from setting a parameter to 0, thus changing the degrees of freedom.

FIGURE 5

Final model for Study 3: Empirical example. (a) Total effect. (b) The direct effect as well as the effects associated with the selected mediators.