On Testability of the Front-Door Model via Verma Constraints
This addresses the challenge of validating causal models with unmeasured confounders for researchers in statistics and causal inference, representing an incremental advance.
The paper tackles the problem of testing the often-implausible assumptions of the front-door model for causal inference, showing that under mild conditions with an auxiliary variable, these assumptions can be tested via Verma constraints, and proposes two goodness-of-fit tests evaluated on real and synthetic data.
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.