Traditional statistical approaches primarily aim to model associations between variables, but many scientific and practical questions require causal methods instead. These approaches rely on assumptions about an underlying structure, often represented by a directed acyclic graph (DAG). When all variables are measured at the same level, causal structures can be learned using existing techniques. However, no suitable methods exist when data are organized hierarchically or across multiple levels. This paper addresses such cases, where both unit-level and group-level variables are present. These multi-level structures frequently arise in fields such as agriculture, where plants (units) grow within different environments (groups). Building on nonlinear structural causal models, or additive noise models, we propose a method that accommodates unobserved confounders as well as group-specific causal functions. The approach is implemented in the R package HSCM, available at https://CRAN.R-project.org/package=HSCM.

翻译：传统统计方法主要旨在建模变量间的关联关系，但许多科学与实际问题需要采用因果方法。这些方法依赖于对底层结构的假设，通常以有向无环图（DAG）表示。当所有变量在同一层级被测量时，可利用现有技术学习因果结构。然而，当数据以层次化或多层级形式组织时，尚无适用方法。本文针对同时存在单元层级与组层级变量的场景展开研究。此类多层级结构常见于农业等领域，例如植物（单元）生长于不同环境（组）中。基于非线性结构因果模型（即加性噪声模型），我们提出一种能同时处理未观测混杂因子与组特异性因果函数的方法。该方法的实现已集成于R软件包HSCM中，可通过https://CRAN.R-project.org/package=HSCM获取。