Examining the Application of Mixed Effects Models in Analyzing Repeated Measures and Longitudinal Data Structures

Posted: Oct 16, 2019

• Logan Hill
• Jack Roberts
• Luna Baker

Abstract

Longitudinal data analysis represents a cornerstone of modern statistical methodology, with applications spanning clinical trials, educational research, economic studies, and psychological assessment. The fundamental challenge in analyzing such data lies in properly accounting for the inherent correlation structure among repeated measurements from the same subject or unit. Mixed effects models, also known as multilevel or hierarchical models, have emerged as the predominant framework for addressing this challenge due to their ability to simultaneously model both fixed population-level effects and random subject-specific variations. However, despite their widespread adoption, conventional mixed effects models often impose restrictive assumptions that may not adequately capture the complexity of real-world longitudinal processes. This research addresses several critical limitations in current mixed effects modeling approaches. First, traditional models typically assume stationary covariance structures, meaning that the within-subject correlation pattern remains constant over time. In many practical applications, this assumption is violated as the strength and pattern of correlation may evolve throughout the study period. Second, existing methods often struggle with irregular measurement times and informative missing data, particularly when the missingness mechanism depends on unobserved outcomes. Third, the specification of random effects structure in high-dimensional settings remains challenging, with conventional approaches either oversimplifying the complexity or risking overparameterization. Our work introduces a novel methodological framework that integrates functional data analysis principles with mixed effects modeling. This hybrid approach preserves the interpretability and computational efficiency of parametric mixed models while incorporating the flexibility of nonparametric methods to capture complex temporal patterns. We develop a dynamic covariance estimation technique that adapts to evolving correlation structures and propose a Bayesian regularization approach for high-dimensional random effects that balances model complexity with predictive accuracy.