On Fitting Generalized Linear Mixed Effects Models for Longitudinal Binary Data Using Different Correlation Structures

Abstract

The generalized linear mixed effects model (GLMM) approach is widely used to analyze longitudinal binary data when the goal of the study is a subject-specific interpretation because it allows missing values on the response, provided they are missing at random (MAR), and accounts the correlation among the repeated observations of the same subject by the inclusion of random effects in the linear predictor. However, in GLMM it is assumed that the observations of the same subject are independent conditional to the random effects and covariates which may be not true. To overcome this problem [9] extended this model using binary Markov chains as the basic stochastic mechanism. The aim of this paper is to give a statistical assessment of both approaches in terms of properties such as efficiency and coverage probability, as well as, to give some guidelines for the choice of the statistical approach to an applied researcher. Both procedures are described and a simulation study is carried out to compare their performance. An analysis of a longitudinal binary data set illustrates the performance of both procedures in a practical example. The R packages lme4 and bild are used.