On Testability of the Front-Door Model via Verma Constraints

TL;DR

This paper investigates the testability of the front-door causal model assumptions using Verma constraints, proposing new goodness-of-fit tests and comparing them to instrumental variable methods.

Contribution

It introduces methods to test front-door assumptions via generalized equality constraints and evaluates their effectiveness on real and synthetic data.

Findings

Proposed two goodness-of-fit tests for front-door assumptions.

Validated tests on real and synthetic datasets.

Compared front-door testability with instrumental variable approaches.

Abstract

The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of variables) that fully mediates the effect of the treatment on the outcome, and (ii) which simultaneously does not suffer from similar issues of confounding as the treatment-outcome pair -- are often deemed implausible. This paper explores the testability of these assumptions. We show that under mild conditions involving an auxiliary variable, the assumptions encoded in the front-door model (and simple extensions of it) may be tested via generalized equality constraints a.k.a Verma constraints. We propose two goodness-of-fit tests based on this observation, and evaluate the efficacy of our proposal on real and synthetic data. We also provide theoretical and empirical comparisons to instrumental variable approaches to handling unmeasured confounding.