Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models

• 成果类型: Article
• 署名作者: Schultheiss, Christoph; Buhlmann, Peter; Yuan, Ming
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2157728
• 发表日期: 2024
• 页码: 1019-1031
• 关键词: inference; identification; DISCOVERY; tests

摘要

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. for this article are available online.