Shrinkage-Based Regressions with Many Related Treatments

TL;DR

This paper introduces a lightweight ridge regression model for observational causal analysis that effectively estimates effects of multiple related treatments, reducing noise and enabling targeted decision-making.

Contribution

It proposes a novel shrinkage-based regression method that balances heterogeneity and homogeneity in treatment effect estimation, improving accuracy over traditional approaches.

Findings

Reduces mean squared error in treatment effect estimates

Allows easy reconstruction of aggregated treatment effects

Demonstrates practical utility at Wayfair

Abstract

When using observational causal models, practitioners often want to disentangle the effects of many related, partially-overlapping treatments. Examples include estimating treatment effects of different marketing touchpoints, ordering different types of products, or signing up for different services. Common approaches that estimate separate treatment coefficients are too noisy for practical decision-making. We propose a computationally light model that uses a customized ridge regression to move between a heterogeneous and a homogenous model: it substantially reduces MSE for the effects of each individual sub-treatment while allowing us to easily reconstruct the effects of an aggregated treatment. We demonstrate the properties of this estimator in theory and simulation, and illustrate how it has unlocked targeted decision-making at Wayfair.