Friday, April 22, 2022, 1:30pm to 3:00pm
Science Center, Room 316
Please save the date for the 2021 Dempster Prize seminar which will be presented by our award winner Ambarish Chattopadhyay for his paper (with Jose Zubizarreta) "On the implied weights of linear regression for causal inference". The talk will be on 22 April, 1.30pm, in room 316, Science Center. The talk will be followed by the Dempster Prize presentation and a reception for Ambarish.
Title: On the implied weights of linear regression for causal inference
Abstract: 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 talk, 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-sample and asymptotic regimes. We show that the implied weights of general regression problems can be equivalently obtained by solving a convex optimization problem. This equivalence allows us to bridge ideas from the regression modeling and causal inference literature. As a result, we propose novel regression diagnostics for causal inference that are part of the design stage of an observational study. As special cases, we analyze the implied weights in common settings such as multi-valued treatments, regression adjustment after matching, and two-stage least squares regression with instrumental variables.