Equivalence between direct and indirect effects with different sets of intermediate variables and covariates

TL;DR

This paper establishes criteria to determine when different sets of variables can estimate the same direct and indirect effects, aiding variable selection and improving estimation accuracy in causal effect analysis.

Contribution

It provides novel criteria for testing equivalence of effects across variable sets and discusses variable selection impacts on estimation accuracy beyond linear regression assumptions.

Findings

Criteria for testing equivalence of effects across variable sets

Selecting variables with a direct effect does not always improve estimation accuracy

Enables judgment of variable sets for cost-effective and accurate effect estimation

Abstract

This paper deals with the concept of equivalence between direct and indirect effects of a treatment on a response using two sets of intermediate variables and covariates. First, we provide criteria for testing whether two sets of variables can estimate the same direct and indirect effects. Next, based on the proposed criteria, we discuss the variable selection problem from the viewpoint of estimation accuracy of direct and indirect effects, and show that selecting a set of variables that has a direct effect on a response cannot always improve estimation accuracy, which is contrary to the situation found in linear regression models. These results enable us to judge whether different sets of variables can yield the same direct and indirect effects and thus help us select appropriate variables to estimate direct and indirect effects with cost reduction or estimation accuracy.