Estimation and selection in linear mixed models with missing data under compound symmetric structure

It is quite appealing to extend existing theories in classical linear models to correlated responses where linear mixed-effects models are utilized and the dependency in the data is modeled by random effects. In the mixed modeling framework, missing values occur naturally due to dropouts or non-responses, which is frequently encountered when dealing with real data. Motivated by such problems, we aim to investigate the estimation and model selection performance in linear mixed models when missing data are present. Inspired by the property of the indicator function for missingness and its relation to missing rates, we propose an approach that records missingness in an indicator-based matrix and derive the likelihood-based estimators for all parameters involved in the linear mixed-effects models. Based on the proposed method for estimation, we explore the relationship between estimation and selection behavior over missing rates. Simulations and a real data application are conducted for illustrating the effectiveness of the proposed method in selecting the most appropriate model and in estimating parameters.