The variance of causal effect estimators for binary v-structures
Adjusting for covariates is a well-established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study, there may be different adjustment sets, equally valid from a theoretical perspective, leading t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-05-01
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| Series: | Journal of Causal Inference |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jci-2021-0025 |
| _version_ | 1797998372873830400 |
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| author | Kuipers Jack Moffa Giusi |
| author_facet | Kuipers Jack Moffa Giusi |
| author_sort | Kuipers Jack |
| collection | DOAJ |
| description | Adjusting for covariates is a well-established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study, there may be different adjustment sets, equally valid from a theoretical perspective, leading to identical causal effects. However, in practice, with finite data, estimators built on different sets may display different precisions. To investigate the extent of this variability, we consider the simplest non-trivial non-linear model of a v-structure on three nodes for binary data. We explicitly compute and compare the variance of the two possible different causal estimators. Further, by going beyond leading-order asymptotics, we show that there are parameter regimes where the set with the asymptotically optimal variance does depend on the edge coefficients, a result that is not captured by the recent leading-order developments for general causal models. As a practical consequence, the adjustment set selection needs to account for the relative magnitude of the relationships between variables with respect to the sample size and cannot rely on purely graphical criteria. |
| first_indexed | 2024-04-11T10:47:40Z |
| format | Article |
| id | doaj.art-75e4fda807ad4b67a9b93123ff2601bd |
| institution | Directory Open Access Journal |
| issn | 2193-3685 |
| language | English |
| last_indexed | 2024-04-11T10:47:40Z |
| publishDate | 2022-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj.art-75e4fda807ad4b67a9b93123ff2601bd2022-12-22T04:29:00ZengDe GruyterJournal of Causal Inference2193-36852022-05-011019010510.1515/jci-2021-0025The variance of causal effect estimators for binary v-structuresKuipers Jack0Moffa Giusi1Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, SwitzerlandDepartment of Mathematics and Computer Science, University of Basel, Basel, SwitzerlandAdjusting for covariates is a well-established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study, there may be different adjustment sets, equally valid from a theoretical perspective, leading to identical causal effects. However, in practice, with finite data, estimators built on different sets may display different precisions. To investigate the extent of this variability, we consider the simplest non-trivial non-linear model of a v-structure on three nodes for binary data. We explicitly compute and compare the variance of the two possible different causal estimators. Further, by going beyond leading-order asymptotics, we show that there are parameter regimes where the set with the asymptotically optimal variance does depend on the edge coefficients, a result that is not captured by the recent leading-order developments for general causal models. As a practical consequence, the adjustment set selection needs to account for the relative magnitude of the relationships between variables with respect to the sample size and cannot rely on purely graphical criteria.https://doi.org/10.1515/jci-2021-0025causalitycovariate adjustmentstructure learningbayesian networksprobability theory62h22 |
| spellingShingle | Kuipers Jack Moffa Giusi The variance of causal effect estimators for binary v-structures Journal of Causal Inference causality covariate adjustment structure learning bayesian networks probability theory 62h22 |
| title | The variance of causal effect estimators for binary v-structures |
| title_full | The variance of causal effect estimators for binary v-structures |
| title_fullStr | The variance of causal effect estimators for binary v-structures |
| title_full_unstemmed | The variance of causal effect estimators for binary v-structures |
| title_short | The variance of causal effect estimators for binary v-structures |
| title_sort | variance of causal effect estimators for binary v structures |
| topic | causality covariate adjustment structure learning bayesian networks probability theory 62h22 |
| url | https://doi.org/10.1515/jci-2021-0025 |
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