Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor type I error control) and additive noise models are not suitable for applications in which the response is not measured on a continuous scale, but reflects categories or counts. Here, we develop transformation-model (TRAM) based ICP, allowing for continuous, categorical, count-type, and uninformatively censored responses (these model classes, generally, do not allow for identifiability when there is no exogenous heterogeneity). As an invariance test, we propose TRAM-GCM based on the expected conditional covariance between environments and score residuals with uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we also consider TRAM-Wald, which tests invariance based on the Wald statistic. We provide an open-source R package 'tramicp' and evaluate our approach on simulated data and in a case study investigating causal features of survival in critically ill patients.

翻译：从观测数据中发现因果关系是一项基础但具有挑战性的任务。不变因果预测（ICP, Peters 等, 2016）是一种因果特征选择方法，它需要来自异质环境的数据，并利用因果模型的不变性。ICP 已被推广到一般加性噪声模型，并通过条件独立性检验扩展到非参数设置。然而，后者通常存在检验功效低（或一类错误控制差）的问题，而加性噪声模型不适用于响应变量并非连续尺度测量，而是反映类别或计数的应用场景。在此，我们开发了基于变换模型（TRAM）的 ICP，允许处理连续型、类别型、计数型以及无信息删失响应变量（这些模型类别通常在没有外生异质性时无法识别）。作为不变性检验，我们提出了基于环境与得分残差之间期望条件协方差的 TRAM-GCM，并具有一致的渐近水平保证。对于线性移位 TRAM 的特殊情况，我们还考虑了 TRAM-Wald，它基于 Wald 统计量检验不变性。我们提供了开源 R 包 'tramicp'，并在模拟数据以及一项关于危重患者生存因果特征的案例研究中评估了我们的方法。