Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables
Identification and Model Testing in Linear Structural Equation Models using Auxiliary Variables
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发表时间：
2016-12
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通讯作者：
Bryant Chen;D. Kumor;E. Bareinboim
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作者：
Bryant Chen;D. Kumor;E. Bareinboim
我们开发了一种新的方法来识别和模型测试的线性结构方程模型（SEMs）的基础上辅助变量（AV），它概括了广泛使用的家庭被称为工具变量的方法。识别问题涉及的条件下，因果参数可以唯一地估计从一个观察，非因果协方差矩阵。在本文中，我们提供了一个算法的因果参数的线性结构模型，包括以前的国家的最先进的方法识别。换句话说，我们的算法比文献中先前已知的方法识别更多的系数和模型。我们的算法建立在辅助变量和模型变量之间的条件独立关系的图论表征，这是本文开发的。此外，我们利用这种新的特性，允许识别时，有限的实验数据或新的实质性知识的域。最后，我们开发了一个新的程序，使用AV模型测试。
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification problem is concerned with the conditions under which causal parameters can be uniquely estimated from an observational, non-causal covariance matrix. In this paper, we provide an algorithm for the identification of causal parameters in linear structural models that subsumes previous state-of-the-art methods. In other words, our algorithm identifies strictly more coefficients and models than methods previously known in the literature. Our algorithm builds on a graph-theoretic characterization of conditional independence relations between auxiliary and model variables, which is developed in this paper. Further, we leverage this new characterization for allowing identification when limited experimental data or new substantive knowledge about the domain is available. Lastly, we develop a new procedure for model testing using AVs.