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

Abstract

This paper 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.

Keywords:

• B-splines
• indirect effect
• mediation analysis
• varying coefficient models

Acknowledgement:

The authors would like to thank the AE and reviewers for their constructive comments, which lead to a significant improvement of this work. All authors equally contribute to the paper, and the authors are listed according to seniority. Jingyuan Liu is corresponding author. Liao and Li’s research was supported by National Science Foundation (NSF) grants DMS 1820702, DMS 1953196 and DMS 2015539, and National Institutes of Health (NIH) grant R01CA229542 funded by the National Cancer Institute (NCI). Liu’s research was supported by National Natural Science Foundation of China 11771361 and 11871409. Coffman’s research was supported by the NIH grant R01CA229542. The content is solely the responsibility of the authors and does not necessarily represent the official views of NSF, NCI or NIH.

Additional information

Funding

Liao and Li’s research was supported by National Science Foundation (NSF) grants DMS 1820702, DMS 1953196 and DMS 2015539, and National Institutes of Health (NIH) grant R01CA229542 funded by the National Cancer Institute (NCI). Liu’s research was supported by National Natural Science Foundation of China 11771361 and 11871409. Coffman’s research was supported by the NIH grant R01CA229542.