Estimations and Tests for Generalized Mediation Models with High-Dimensional Potential Mediators

Abstract

Motivated by an empirical analysis of stock reaction to COVID-19 pandemic, we propose a generalized mediation model with high-dimensional potential mediators to study the mediation effects of financial metrics that bridge company’s sector and stock value. We propose an estimation procedure for the direct effect via a partial penalized maximum likelihood method and establish its theoretical properties. We develop a Wald test for the indirect effect and show that the proposed test has a ${\chi }^2$ limiting null distribution. We also develop a partial penalized likelihood ratio test for the direct effect and show that the proposed test asymptotically follows a ${\chi }^2$-distribution under null hypothesis. A more efficient estimator of indirect effect under complete mediation model is also developed. Simulation studies are conducted to examine the finite sample performance of the proposed procedures and compare with some existing methods. We further illustrate the proposed methodology with an empirical analysis of stock reaction to COVID-19 pandemic via exploring the underlying mechanism of the relationship between companies’ sectors and their stock values.

Keywords:

• Lasso
• Mediation analysis
• Penalized Likelihood
• SCAD penalty
• Sparsity

Acknowledgments

The authors thank the editors and referees for their constructive comments and suggestions. All the authors contribute equally to the article, and are listed in the alphabetical order. Jingyuan Liu is corresponding author.

Disclosure Statement

There are no competing interests to declare.

Additional information

Funding

Guo’s research was supported by Beijing Natural Science Foundation (BNSF) 1212004 and National Natural Science Foundation of China grants (NNSFC) 12071038. Liu’s research was supported by NNSFC 12271456, 71988101 and the Ministry of Education Research in the Humanities and Social Sciences 22YJA910002. Li’s research was supported by National Science Foundation (NSF) DMS-1820702, and NIH grants R01AI136664 and R01AI170249. The content is solely the responsibility of the authors and does not necessarily represent the official views of NSF, NIH, NNSFC or BNSF.