Robust analysis of mixed models with missing data

点击翻译按钮获取中文摘要

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.