Optimal testing in linear models with implications for causal inference
线性模型中的最优检验及其因果推断含义AI 解读 ↓
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线性模型中的最优检验及其因果推断含义
- 研究问题
- 在具有严格时间因果顺序的线性模型中，如何检验总效应和间接效应，并判断其检验功效何时优于回归系数检验？
- 方法与思路
- 作者在严格排序的时间因果图中使用 Gram–Schmidt 分解，将直接效应转换为总效应，并分析中介比例与下游传播。
- 材料陈述的贡献
- 摘要称，论文推导间接效应与中介比例的精确分布，给出总效应检验功效更高的条件，并应用于反馈系统的滞后检测。
- 阅读关注点
- 应核对因果图、混杂控制和误差分布条件，区分正交变换与因果识别，并检查非平稳稳健性及功效比较的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未核实；摘要未列明完整识别条件，时间先后与正交化本身不能保证因果解释。
原文摘要
Despite its widespread use in practice, multiple regression suffers from two important limitations due to ignoring the structure between predictors. First, reported coefficients are, in fact, direct effects in a causal context. These are often less meaningful than total effects when accounting for a factor's contribution, however, estimating the latter typically requires a causal diagram to be specified among predictors. The second limitation is multicollinearity, which causes a number of issues for inference, in particular loss of power. While any orthogonal transformation resolves multicollinearity, only the Gram-Schmidt decomposition resolves both limitations by transforming direct effects into total effects, in a strictly-ordered temporal causal diagram. This directed acyclic graph (DAG) is of notable importance in practice, where causal precedence often comes from temporal separation. Identifying total effects with vector directions leads to exact distributions for the indirect effect and fraction mediated for each predictor, with equal or better powered tests compared to existing mediation software. We establish conditions under which testing for total effects is more powerful than coefficient tests in regression, which is a compelling reason for the use of temporal DAGs in general practice. The paper further develops the theory of indirect effects decomposition and quantifies how effects originating from a variable or set propagate via arbitrary downstream mediators or sets. This is applied to lag detection in causal discovery, by testing the flow of indirect effects between variables at specific lags in a feedback loop. Unlike standard time series methods, this approach is robust to lack of stationarity.