Generalized Varying Coefficient Mediation Models

Abstract

Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a two-layer generalized varying coefficient mediation model. This model captures the bridging effects of mediators that may vary with another variable, by treating them as smooth functions of this variable. It also allows various response types by introducing the generalized varying coefficient model in the first layer. The varying direct and indirect effects are estimated through spline expansion. The theoretical properties of the estimated direct and indirect coefficient functions including estimation biases, asymptotic distributions and so forth, are explored. Simulation studies validate the finite-sample performance of the proposed estimation method. A real data analysis based on the proposed model discovers some interesting behavioral economic phenomenon, that self-efficacy influences the deleterious impact of economic stress, both directly and indirectly through depressed affect, on business owners’ withdrawal intentions.