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

arXiv: https://arxiv.org/abs/2412.18180 · HTML: https://mlsanity.com/paper/2412.18180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 33 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Estimating Treatment Effects with Observed Confounders and Mediators](https://mlsanity.com/paper/2003.11991/) (2020)

## Abstract (arXiv)

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.