Inference for multiple treatment effects using confounder importance learning
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| author | Papaspiliopoulos, Omiros Rossell, David Torrens-i-Dinarès, Miquel |
| author_facet | Papaspiliopoulos, Omiros Rossell, David Torrens-i-Dinarès, Miquel |
| contents | We address modelling and computational issues for multiple treatment effect inference under many potential confounders. Our main contribution is providing a trade-off between preventing the omission of relevant confounders, while not running into an over-selection of instruments that significantly inflates variance. We propose a novel empirical Bayes framework for Bayesian model averaging that learns from data the prior inclusion probabilities of key covariates. Our framework sets a data-dependent prior that asymptotically matches the true amount of confounding in the data, as measured by a novel confounding coefficient. A key challenge is computational. We develop fast algorithms, using an exact gradient of the marginal likelihood that has linear cost in the number of covariates, and a variational counterpart. Our framework uses widely-used ingredients and largely existing software, and it is implemented within the R package mombf. We illustrate our work with two applications. The first is the association between salary variation and discriminatory factors. The second, that has been debated in previous works, is the association between abortion policies and crime. Our approach provides insights that differ from previous analyses especially in situations with weaker treatment effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_00314 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Inference for multiple treatment effects using confounder importance learning Papaspiliopoulos, Omiros Rossell, David Torrens-i-Dinarès, Miquel Methodology Applications Computation 62J12 (Primary), 62P20 (Secondary) We address modelling and computational issues for multiple treatment effect inference under many potential confounders. Our main contribution is providing a trade-off between preventing the omission of relevant confounders, while not running into an over-selection of instruments that significantly inflates variance. We propose a novel empirical Bayes framework for Bayesian model averaging that learns from data the prior inclusion probabilities of key covariates. Our framework sets a data-dependent prior that asymptotically matches the true amount of confounding in the data, as measured by a novel confounding coefficient. A key challenge is computational. We develop fast algorithms, using an exact gradient of the marginal likelihood that has linear cost in the number of covariates, and a variational counterpart. Our framework uses widely-used ingredients and largely existing software, and it is implemented within the R package mombf. We illustrate our work with two applications. The first is the association between salary variation and discriminatory factors. The second, that has been debated in previous works, is the association between abortion policies and crime. Our approach provides insights that differ from previous analyses especially in situations with weaker treatment effects. |
| title | Inference for multiple treatment effects using confounder importance learning |
| topic | Methodology Applications Computation 62J12 (Primary), 62P20 (Secondary) |
| url | https://arxiv.org/abs/2110.00314 |