PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects
This addresses challenges in causal inference for researchers dealing with observational data and high-dimensional settings, offering a novel method to enhance estimation reliability.
The paper tackles the problem of estimating linear causal effects when covariates satisfying the back-door criterion are unobserved or when multicollinearity/high-dimensional issues prevent standard methods, proposing the PCM Selector as a two-stage penalized regression approach that provides consistent or less biased estimators and improves estimation accuracy through variable selection for intermediate variables.
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.