On testability of the front-door model via Verma constraints

Rohit Bhattacharya, Razieh Nabi
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:202-212, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-bhattacharya22a, title = {On testability of the front-door model via {V}erma constraints}, author = {Bhattacharya, Rohit and Nabi, Razieh}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {202--212}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/bhattacharya22a/bhattacharya22a.pdf}, url = {https://proceedings.mlr.press/v180/bhattacharya22a.html}, 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.} }
Endnote
%0 Conference Paper %T On testability of the front-door model via Verma constraints %A Rohit Bhattacharya %A Razieh Nabi %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-bhattacharya22a %I PMLR %P 202--212 %U https://proceedings.mlr.press/v180/bhattacharya22a.html %V 180 %X 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.
APA
Bhattacharya, R. & Nabi, R.. (2022). On testability of the front-door model via Verma constraints. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:202-212 Available from https://proceedings.mlr.press/v180/bhattacharya22a.html.

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