Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data
研究了在不可忽略缺失机制下，正态分布、正态混合模型和t混合模型的可识别性，给出了Logistic缺失机制下模型可识别的充要条件，并通过模拟和实际数据验证。
Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values themselves even conditional on the observed data. With a nonignorable missing mechanism, the model of interest is often not identifiable without imposing further assumptions. We find that even if the missing mechanism has a known parametric form, the model is not identifiable without specifying a parametric outcome distribution. Although it is fundamental for valid statistical inference, identifiability under nonignorable missing mechanisms is not established for many commonly used models. In this article, we first demonstrate identifiability of the normal distribution under monotone missing mechanisms. We then extend it to the normal mixture and t mixture models with nonmonotone missing mechanisms. We discover that models under the Logistic missing mechanism are less identifiable than those under the Probit missing mechanism. We give necessary and sufficient conditions for identifiability of models under the Logistic missing mechanism, which sometimes can be checked in real data analysis. We illustrate our methods using a series of simulations, and apply them to a real-life dataset. Supplementary materials for this article are available online.