Marginalized Random Effects Models for Multivariate Longitudinal Binary Data

Keunbaik Lee, Yongsung Joo, Jae Keun Yoo, and JungBok Lee

Generalized linear models with random effects are often used to explain the serial dependence of longitudinal
categorical data. Marginalized random effects models (MREMs) permit likelihood-based estimations of
marginal mean parameters and also explain the serial dependence of longitudinal data. In this paper, we
extend the MREM to accommodate multivariate longitudinal binary data. A maximum marginal likelihood
estimation is proposed utilizing a Quasi-Newton algorithm with Quasi-Monte Carlo integration of the random
effects. Our approach is applied to analyze metabolic syndrome data from the Korean Genomic Epidemiology
Study (KGES) for Korean adults