Exploring the Application of Logistic Mixed Models in Binary and Longitudinal Data with Random Effects

Posted: Aug 17, 1986

• Evelyn Wilson
• Evelyn Young
• Maria King

Abstract

Longitudinal binary data analysis presents unique challenges in statistical modeling, particularly when dealing with clustered or hierarchical data structures. The logistic mixed model, also known as the generalized linear mixed model for binary outcomes, has emerged as a powerful framework for addressing these challenges. However, traditional implementations often rely on restrictive assumptions about the random effects structure and employ approximation methods that may be inadequate for complex dependency patterns. This research addresses these limitations by developing and evaluating innovative extensions to the logistic mixed model framework. The motivation for this work stems from the increasing complexity of longitudinal studies in various scientific domains. In clinical trials, for instance, patients may exhibit heterogeneous treatment responses that evolve over time, requiring flexible modeling of both between-subject and within-subject variations. Similarly, in educational research, students' binary outcomes (such as passing examinations) may depend on both individual characteristics and classroom-level effects that interact with time. Existing methods often struggle to adequately capture these complex dependency structures while maintaining computational feasibility. Our research makes several key contributions to the field. First, we introduce a novel parameterization of the random effects covariance matrix that explicitly models temporal dependencies while accommodating cross-sectional clustering. Second, we develop an adaptive quadrature algorithm that improves upon existing numerical integration methods for high-dimensional random effects. Third, we propose a Bayesian regularization approach for sparse random effects selection, addressing the challenge of model complexity in high-dimensional settings.