Robust analysis of mixed models with missing data

缺失数据是许多实验研究的共同特征，包括调查和临床试验。对不完整或缺失数据的估计方法通常基于某些建模假设下的似然函数。EM算法是一种常用的迭代算法，用于非完全数据问题的最大似然估计。EM的M步执行ML估计，就像没有丢失数据一样，也就是说，就像它们已经被填充一样。E步在给定观测数据和当前参数估计的情况下计算缺失数据的条件期望，然后将这些期望替换为缺失数据或缺失数据的某些函数。在这个项目中，我将解决经典ML方法的非鲁棒性，用于将广义线性混合模型拟合到具有不可忽略的缺失响应的聚类相关数据。众所周知，机器学习估计对数据中的潜在异常值或偏离基本假设非常敏感。换句话说，异常值对ML估计的影响是无界的。为了获得具有缺失数据的广义线性混合模型的有界影响估计，将考虑ML方法的鲁棒替代方法。我们将详细研究稳健估计的渐近性质。将进行仿真以探索鲁棒方法的性能，并将其与经典方法进行比较。鲁棒方法将在机器学习估计的框架内开发，并期望在数据中没有异常值时几乎与机器学习方法一样有效。但是，当数据中存在异常值时，与经典方法相比，鲁棒方法的精度增益预期要大得多。

Missing data are a common feature in many experimental studies, including surveys and clinical trials. Methods of estimation for incomplete or missing data are often based on the likelihood function under certain modeling assumptions. The EM algorithm is a commonly used iterative procedure for maximum likelihood (ML) estimation in incomplete-data problems. The M step of EM performs ML estimation just as if there were no missing data, that is, as if they had been filled in. The E step calculates the conditional expectation of the missing data given the observed data and current estimates of the parameters, and then substitutes these expectations for the missing data or some functions of the missing data. In this project, I will address the nonrobust properties of the classical ML method for fitting generalized linear mixed models to clustered correlated data with nonignorable missing responses. It is well-known that ML estimates are sensitive to potential outliers in the data or departures from underlying assumptions. In other words, the influence of outliers on the ML estimates is unbounded. To obtain bounded influence estimates of generalized linear mixed models with missing data, a robust alternative to the ML method will be considered. The asymptotic properties of the robust estimates will be investigated in some detail. Simulations will be carried out to explore the performance of the robust method and to compare it to its classical counterpart. The robust method will be developed in the framework of ML estimation and is expected to be almost as efficient as the ML method when there is no outliers in the data. But the gain in precision from the robust method is expected to be significantly large as compared to the classical method when there are outliers in the data.