Title: Robust Mediation Analysis in R Using Package robmed

Authors: Andreas Alfons, Nufer Y. Ates, Patrick J.F. Groenen

Affiliation: Erasmus Universiteit Rotterdam; Sabanci University

Abstract:
Mediation analysis is one of the most widely used statistical techniques in
the social and behavioral sciences. The mediation model in its simplest form
allows to study how an independent variable (X) affects a dependent variable
(Y) through an intervening variable that is called a mediator (M). More
complex mediation models may consist of multiple hypothesized mediators, as
well as additional control variables. Such an analysis is often carried out
via a collection of regression models, in which case the indirect effects of X
on Y through the mediators can be computed as products of coefficients from
those regression models. The standard test for the indirect effects is a
bootstrap test based on ordinary least squares (OLS) regressions. However,
this test is very sensitive, e.g., to outliers or heavy tails, which poses a
serious threat to empirical testing of theory about mediation mechanisms.

The R package robmed implements a robust test for mediation analysis based on
the fast and robust bootstrap methodology for robust regression estimators.
This procedure yields reliable results for estimating the effect size and
assessing its significance, even when the data deviate from the usual
normality assumptions. Furthermore, the standard bootstrap test and other
proposals are included in the package. We will demonstrate the use of package
robmed in an example from management research.