We study identification of parametric and semiparametric models with missing covariate data. When covariate data are missing not at random, identification is not guaranteed even under fairly restrictive parametric assumptions, a fact that is illustrated with several examples. We propose a general approach to establish identification of parametric and semiparametric models when a covariate is missing not at random. Without auxiliary information about the missingness process, identification of parametric models is strongly dependent on model specification. However, in the presence of a fully observed shadow variable, which is correlated with the missing covariate but otherwise independent of its missingness, identification is more broadly achievable, including in fairly large semiparametric models. With a shadow variable, special consideration is given to the generalized linear models with the missingness process unrestricted. Under such a setting, the outcome model is identified for familiar generalized linear models, and we provide counterexamples when identification fails. For estimation, we describe an inverse probability weighted estimator that incorporates the shadow variable to estimate the missingness process, and we evaluate its performance via simulations.

中文翻译：

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使用不可忽略的缺失协变量数据进行识别和推断

我们研究了具有缺失协变量数据的参数和半参数模型的识别。当协变量数据不是随机丢失时，即使在相当严格的参数假设下也不能保证识别，几个例子说明了这一事实。我们提出了一种通用方法来在协变量不是随机丢失时建立参数和半参数模型的识别。如果没有关于缺失过程的辅助信息，参数模型的识别强烈依赖于模型规范。然而，在存在完全观察到的阴影变量的情况下，该变量与缺失的协变量相关但与其缺失无关，识别更广泛地实现，包括在相当大的半参数模型中。使用阴影变量，特别考虑了缺失过程不受限制的广义线性模型。在这样的设置下，结果模型被识别为熟悉的广义线性模型，当识别失败时我们提供反例。对于估计，我们描述了一个逆概率加权估计器，它结合了影子变量来估计缺失过程，并通过模拟评估其性能。