Varying Coefficient Mediation Model and Application to Analysis of Behavioral Economics Data

This article is concerned with causal mediation analysis with varying indirect and direct effects. We propose a varying coefficient mediation model, which can also be viewed as an extension of moderation analysis on a causal diagram. We develop a new estimation procedure for the direct and indirect effects based on B-splines. Under mild conditions, rates of convergence and asymptotic distributions of the resulting estimates are established. We further propose a F-type test for the direct effect. We conduct simulation study to examine the finite sample performance of the proposed methodology, and apply the new procedures for empirical analysis of behavioral economics data.