How to test the missing data mechanism in a hidden Markov model
针对结果变量有缺失的隐马尔可夫模型，提出了检验可忽略缺失和完全随机缺失机制的方法，无需按缺失模式分组，基于给定潜在状态和协变量时缺失数据的条件概率估计，并通过模拟和养猪实例验证。
A Hidden Markov Model with missing data in the outcome variable is considered. The initial and transition probabilities of the Markov chain and the emission probability of the HMM are allowed to depend on fully observed covariables. Tests for the ignorable and for the MCAR mechanisms are proposed. These tests do not require grouping the individuals by their missing pattern, making them easier to apply in practice. They are based on the estimates of the conditional probabilities of emitting a missing data given the latent state of the Markov chain and some observed covariables. When the ignorable mechanism holds, the conditional probabilities of emitting a missing value are the same for a given value of the observed variables. On the contrary, when the MCAR mechanism holds, these probabilities are all the same. A practical implementation of these tests based on simulations is proposed, along with a presentation of their performances. A real example from piglet farming illustrates their use.