PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910859010244608 |
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| author | Nanmo, Hisayoshi Kuroki, Manabu |
| author_facet | Nanmo, Hisayoshi Kuroki, Manabu |
| contents | For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_18180 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects Nanmo, Hisayoshi Kuroki, Manabu Methodology Machine Learning For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion. |
| title | PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2412.18180 |