PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects

TL;DR

This paper introduces PCM Selector, a novel two-stage penalized regression method designed to accurately estimate causal effects in high-dimensional or unobservable covariate scenarios, improving upon existing methods.

Contribution

The paper proposes PCM Selector, a new approach that consistently estimates causal effects and performs variable selection for mediators in complex linear structural models.

Findings

PCM Selector provides less biased causal effect estimates.

It outperforms standard methods in high-dimensional settings.

The approach effectively selects relevant mediators.

Abstract

For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.