Practical problems with missing data are common, and many methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. In this paper, we present a new hypothesis testing approach for deciding between the conventional notions of missing at random and missing not at random in generalized linear models in the presence of instrumental variables. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our testing approach achieves an objective data-oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis.

中文翻译：

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在存在工具变量的情况下测试广义线性模型中的随机缺失假设

缺失数据的实际问题很常见，并且已经开发了许多关于统计程序的有效性和/或效率的方法。一个中心焦点是，长期以来人们对数据缺失的治理机制一直很感兴趣，正确地决定适当的机制对于进行适当的实际调查至关重要。在本文中，我们提出了一种新的假设检验方法，用于在存在工具变量的情况下在广义线性模型中决定随机缺失和非随机缺失的传统概念。基本思想是在估计量之间制定适当的差异度量，仅当随机缺失不成立时，其属性才会显着差异。我们表明，我们的测试方法实现了随机丢失与否之间客观的面向数据的选择。我们通过理论分析、模拟研究和真实数据分析证明了新测试的可行性、有效性和功效。