{"title":"An unbiased estimator of the causal effect on the variance based on the back-door criterion in Gaussian linear structural equation models","authors":"Taiki Tezuka, Manabu Kuroki","doi":"10.1016/j.jmva.2023.105201","DOIUrl":null,"url":null,"abstract":"<div><p>This paper assumes a context in which cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model<span> and the corresponding directed acyclic graph. We consider the situation where we observe a set of random variables satisfying the so-called back-door criterion. When the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator<span> of the causal effect (the estimated causal effect) on the variance of the outcome variable with external intervention in which a treatment variable is set to a specified constant value. In addition, we provide the variance formula for the estimated causal effect on the variance. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating causal effects.</span></span></p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000477","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
This paper assumes a context in which cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model and the corresponding directed acyclic graph. We consider the situation where we observe a set of random variables satisfying the so-called back-door criterion. When the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator of the causal effect (the estimated causal effect) on the variance of the outcome variable with external intervention in which a treatment variable is set to a specified constant value. In addition, we provide the variance formula for the estimated causal effect on the variance. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating causal effects.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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