Generalized Linear Mixed Models for Longitudinal Data with Missing Values: A Monte Carlo EM Approach

摘要

Longitudinal data have vast applications in medicine, epidemiology, agriculture and education. Longitudinal data analysis is usually characterized by its complexity due to inter-correlation between repeated measurements within each subject. One way to incorporate this inter-correlation is to extend the generalized linear model (GLM) to the generalized linear mixed model (GLMM) via including the random effects component. When the distribution of the random effects is far from the usual features of the Gaussian density, such as the student's t-distribution, this increases the complexity of the analysis as well as introducing critical features of subject heterogeneity. Thus, statistical techniques based on relaxing normality assumption for the random effects distribution are of interest. This paper aims to find the maximum likelihood estimates of the parameters of the GLMM when the normality assumption for the random effects is relaxed. Estimation is done in the presence of missing data. We assume a selection model for longitudinal data with a dropout pattern. The proposed estimation method is applied to both simulated and real data sets.