Keywords: Causal effect, Back-door criterion, Collapsibility, High-dimensional data
TL;DR: This paper propose a novel regularized multiple regression analysis for estimating linear causal effects.
Abstract: This paper assumes that cause-effect relationships among variables can be described with a linear structural equation model. Then, a situation is considered where a set of observed covariates satisfies the back-door criterion but the ordinary least squares method cannot be applied to estimate linear causal effects because of multicollinearity/high-dimensional data problems. In this situation, we propose a novel regression approach, the ``partially adaptive Lp-regularized multiple regression analysis'' (PALpMA) method for estimating the total effects. Different from standard regularized regression analysis, PALpMA provides a consistent or less-biased estimator of the linear causal effect. PALpMA is also applicable to evaluating direct effects through the single-door criterion. Given space constraints, the proofs, some numerical experiments, and an industrial case study on setting up painting conditions of car bodies are provided in the Supplementary Material.
Supplementary Material: zip