Ordinal variables, such as on the Likert scale, are common in applied research. Yet, existing methods for causal inference tend to target nominal or continuous data. When applied to ordinal data, this fails to account for the inherent ordering or imposes well-defined relative magnitudes. Hence, there is a need for specialised methods to compute interventional effects between ordinal variables while accounting for their ordinality. One potential framework is to presume a latent Gaussian Directed Acyclic Graph (DAG) model: that the ordinal variables originate from marginally discretising a set of Gaussian variables whose latent covariance matrix is constrained to satisfy the conditional independencies inherent in a DAG. Conditioned on a given latent covariance matrix and discretisation thresholds, we derive a closed-form function for ordinal causal effects in terms of interventional distributions in the latent space. Our causal estimation combines naturally with algorithms to learn the latent DAG and its parameters, like the Ordinal Structural EM algorithm. Simulations demonstrate the applicability of the proposed approach in estimating ordinal causal effects both for known and unknown structures of the latent graph. As an illustration of a real-world use case, the method is applied to survey data of 408 patients from a study on the functional relationships between symptoms of obsessive-compulsive disorder and depression.

翻译：序数变量（如李克特量表）在应用研究中十分常见。然而，现有的因果推断方法主要针对名义变量或连续数据。当应用于序数数据时，这些方法要么未能考虑其固有的顺序性，要么强加了明确的相对量级。因此，需要专门的方法来计算序数变量间的干预效应，同时考虑其序数特性。一个潜在的框架是假设一个潜在高斯有向无环图模型：即序数变量源于对一组高斯变量的边缘离散化，这些高斯变量的潜在协方差矩阵被约束以满足DAG中固有的条件独立性。在给定潜在协方差矩阵和离散化阈值的条件下，我们推导出一个关于潜在空间中干预分布的序数因果效应的闭式函数。我们的因果估计方法与学习潜在DAG及其参数的算法（如序数结构EM算法）自然结合。仿真实验证明了所提方法在估计序数因果效应方面的适用性，无论潜在图的结构已知或未知。作为现实世界用例的示例，该方法被应用于一项关于强迫症与抑郁症状功能关系的研究中408名患者的调查数据。