Recursive linear structural equation models are widely used to postulate causal mechanisms underlying observational data. In these models, each variable equals a linear combination of a subset of the remaining variables plus an error term. When there is no unobserved confounding or selection bias, the error terms are assumed to be independent. We consider estimating a total causal effect in this setting. The causal structure is assumed to be known only up to a maximally oriented partially directed acyclic graph (MPDAG), a general class of graphs that can represent a Markov equivalence class of directed acyclic graphs (DAGs) with added background knowledge. We propose a simple estimator based on recursive least squares, which can consistently estimate any identified total causal effect, under point or joint intervention. We show that this estimator is the most efficient among all regular estimators that are based on the sample covariance, which includes covariate adjustment and the estimators employed by the joint-IDA algorithm. Notably, our result holds without assuming Gaussian errors.
翻译:精确的线性结构方程式模型被广泛用于假设观测数据背后的因果关系机制。在这些模型中,每个变量等于剩余变量子子子的线性组合加上一个错误术语。当没有未观察到的混淆或选择偏差时,错误术语被假定为独立。我们考虑估计这一设置中的总因果关系。根据假设,因果关系结构仅被理解为指向最大方向的局部单向单向圆形图(MPDAG),这是一个一般的图表类别,可以代表具有附加背景知识的定向单向图(DAGs)的马克夫等值类。我们基于递归性最小方块的简单估算器,它可以在点干预或联合干预下一致估计任何已确定的总因果关系效应。我们表明,这一估算器是所有基于样本共变法的常规估测器中最有效的,其中包括共变式调整和联合开发算法使用的估测器。值得注意的是,我们得出的结果没有假定标值错误。