Comparing Two Proxy Methods for Causal Identification

TL;DR

This paper compares two proxy variable methods for causal inference, analyzing their assumptions, scope, and differences to guide their application in unmeasured variable scenarios.

Contribution

It provides a detailed comparison of bridge equation and array decomposition approaches, clarifying their assumptions and applicability in causal effect identification.

Findings

Analyzes model restrictions of both methods

Clarifies scope of applicability for each approach

Provides insights into assumptions underlying proxy methods

Abstract

Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors used to identify counterfactual quantities via eigendecomposition tasks. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.