Partially Adaptive Regularized Multiple Regression Analysis for Estimating Linear Causal Effects

Hisayoshi Nanmo, manabu kuroki

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.