What assumptions about the data-generating process are required to permit a causal interpretation of partial regression coefficients? To answer this question, this paper generalizes Pearl's single-door and back-door criteria and proposes a new criterion, which enables the identification of total or partial causal effects. In addition, this paper elucidates the mechanism of post-treatment bias, showing that a repeated sequence of nodes can be a potential source of this bias. The results apply to linear data-generating processes represented by directed acyclic graphs with distribution-free error terms.

翻译：要使偏回归系数具有因果解释，需要对数据生成过程做出何种假设？为回答此问题，本文推广了Pearl的单门准则与后门准则，提出了一种新准则，该准则能够识别总因果效应或部分因果效应。此外，本文阐明了处理后偏误的机制，表明节点重复序列可能是此类偏误的潜在来源。研究结果适用于由具有无分布误差项的有向无环图表示的线性数据生成过程。