Statistics, Measurement, and Evaluation in Education, Department of Educational, School, and Counseling Psychology, College of Education, University of Missouri.
Educational Leadership and Policy Analysis, College of Education, University of Missouri.
Multivariate Behav Res. 2020 Jul-Aug;55(4):495-515. doi: 10.1080/00273171.2018.1528542. Epub 2019 Apr 12.
Statistical methods to identify mis-specifications of linear regression models with respect to the direction of dependence (i.e. whether or better approximates the data-generating mechanism) have received considerable attention. Direction dependence analysis (DDA) constitutes such a statistical tool and makes use of higher-moment information of variables to derive statements concerning directional model mis-specifications in observational data. Previous studies on direction of dependence mainly focused on statistical inference and guidelines for the selection from the two directionally competing candidate models ( versus ) while assuming the absence of unobserved common causes. The present study describes properties of DDA when confounders are present and extends existing DDA methodology by incorporating the confounder model as a possible explanation. We show that all three explanatory models can be uniquely identified under standard DDA assumptions. Further, we discuss the proposed approach in the context of testing competing mediation models and evaluate an organizational model proposing a mediational relation between school leadership and student achievement via school safety using observational data from an urban school district. Overall, DDA provides strong empirical support that school safety has indeed a causal effect on student achievement but suggests that important confounders are present in the school leadership-safety relation.
统计方法可以识别线性回归模型在依存方向上的误设定（即 或 更好地逼近数据生成机制），这些方法受到了广泛关注。方向依存分析（DDA）就是这样一种统计工具，它利用变量的高阶矩信息来得出关于观测数据中方向性模型误设定的结论。先前关于方向依存的研究主要集中在统计推断和从两个竞争的方向性候选模型（ 与 ）中进行选择的指导方针上，同时假设不存在未观察到的共同原因。本研究描述了存在混杂因素时 DDA 的性质，并通过将混杂因素模型纳入可能的解释，扩展了现有的 DDA 方法。我们证明，在标准 DDA 假设下，可以唯一地识别所有三个解释模型。此外，我们还在测试竞争中介模型的背景下讨论了所提出的方法，并使用城市学区的观测数据评估了一个组织模型，该模型提出学校领导与学生成绩之间存在中介关系，其通过学校安全来实现。总的来说，DDA 提供了强有力的经验支持，表明学校安全确实对学生成绩有因果影响，但也表明学校领导与安全之间存在重要的混杂因素。
