Post-Hoc Mixture Models to eBLUPs from Linear Mixed-Effects Models: A Tractable Approach for Clustering Irregular Longitudinal Data

Abstract

Clustering longitudinal data with irregular and sparse measurement schedules has become important in analyzing many medical data and associated decision-making. These datasets often involve observation times that vary across individuals, making trajectory-based analysis essential for uncovering meaningful patterns. Mixture-based linear mixed-effects models, such as heterogeneous linear mixed-effects models and growth mixture modeling, are commonly used for this purpose. While theoretically powerful, these methods often suffer from convergence issues and computational inefficiency in large-scale applications. This study introduces a computationally efficient two-step approach that applies a post-hoc mixture model to empirical Best Linear Unbiased Predictors (eBLUPs), derived from a fitted (piecewise) linear mixed-effects model under homogeneity assumptions. The method is then demonstrated with real clinical data, in which it effectively identified distinct growth trajectories in early childhood data involving 3,365 children across 51,711 clinic visits. The optimal number of clusters is then selected using the BIC, likelihood ratio tests, and model-based validation, achieving the best balance of model fit, classification stability, and interpretability. Simulation studies have shown that eBLUPs preserve individual-level heterogeneity and that post-hoc mixture modeling outperforms HLME across varying separability. Overall, this approach offers a robust, interpretable, and scalable alternative to traditional clustering methods for irregular longitudinal data.