On the implied weights of linear regression for causal inference

Understand

A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances.

• Now, linear regression models are commonly used to analyze observational data and estimate causal effects.
• How do linear regression adjustments in observational studies emulate key features of randomized experiments, such as covariate balance, self-weighted sampling, and study representativeness? In this paper, we provide answers to this and related questions by analyzing the implied (individual-level data) weights of linear regression methods.
• We derive new closed-form expressions of the weights and examine their properties in both finite and asymptotic regimes.