Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a limited-information maximum likelihood (LIML) estimator can obtain an unbiased estimate for causal effects despite there being nonlinear outcomes such as binary outcomes; however, it requires that we specify not only a correct outcome model but also a correct treatment model. Therefore, detecting correct models is an important process. In this paper, we propose two model selection procedures: AIC-type and BIC-type, and confirm their properties. The proposed model selection procedures are based on a LIML estimator. We prove that a proposed BIC-type model selection procedure has model selection consistency, and confirm their properties of the proposed model selection procedures through simulation datasets.

翻译：不可计量的共变构成因果关系推论的重要问题之一。即使有一些未计量的共变,一些工具性可变方法,如两阶段的剩余包容(2SRI)估测器,或有限信息最大可能性(LIML)估测器,尽管存在非线性结果,如二元结果,仍可获得对因果关系的公正估计;然而,它要求我们不仅指定一个正确的结果模型,而且指定一个正确的处理模型。因此,发现正确的模型是一个重要过程。在本文件中,我们提出两个示范选择程序:AIC类型和BIC类型,并确认其特性。拟议的示范选择程序以LIML的估测器为基础。我们证明,拟议的BIC类型模型选择程序具有模式性选择的一致性,并通过模拟数据集确认拟议模型选择程序的性质。