On the implied weights of linear regression for causal inference

by   Ambarish Chattopadhyay, et al.

In this paper, we derive and analyze the implied weights of linear regression methods for causal inference. We obtain new closed-form, finite-sample expressions of the weights for various types of estimators based on multivariate linear regression models. In finite samples, we show that the implied weights have minimum variance, exactly balance the means of the covariates (or transformations thereof) included in the model, and produce estimators that may not be sample bounded. Furthermore, depending on the specification of the regression model, we show that the implied weights may distort the structure of the sample in such a way that the resulting estimator is biased for the average treatment effect for a given target population. In large samples, we demonstrate that, under certain functional form assumptions, the implied weights are consistent estimators of the true inverse probability weights. We examine doubly robust properties of regression estimators from the perspective of their implied weights. We also derive and analyze the implied weights of weighted least squares regression. The equivalence between minimizing regression residuals and optimizing for certain weights allows us to bridge ideas from the regression modeling and causal inference literatures. As a result, we propose a set of regression diagnostics for causal inference. We discuss the connection of the implied weights to existing matching and weighting approaches. As special cases, we analyze the implied weights in common settings such as multi-valued treatments, regression after matching, and two-stage least squares regression with instrumental variables.



There are no comments yet.


page 1

page 2

page 3

page 4


Propensity Score Weighting for Causal Inference with Multi-valued Treatments

This article proposes a unified framework, the balancing weights, for es...

Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression

We study the benign overfitting theory in the prediction of the conditio...

A framework for causal inference in the presence of extreme inverse probability weights: the role of overlap weights

In this paper, we consider recent progress in estimating the average tre...

Distributional Robustness of K-class Estimators and the PULSE

In causal settings, such as instrumental variable settings, it is well k...

Note on the Delta Method for Finite Population Inference with Applications to Causal Inference

This work derives a finite population delta method. The delta method cre...

Adaptive normalization for IPW estimation

Inverse probability weighting (IPW) is a general tool in survey sampling...

Linear Regression with Shuffled Labels

Is it possible to perform linear regression on datasets whose labels are...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.