Tree-Based Statistical Modeling for Longitudinal Data

Tree-based statistical models offer a flexible, data-driven approach to analysing repeated measurements collected over time. By partitioning subjects into subgroups with distinct trajectories or response patterns, these methods naturally accommodate non-linear effects and complex interactions among predictors. Incorporation of random effects and dependence structures enables the models to account for within-subject correlation and heterogeneous variance. Recent methodological advances have focused on blending traditional mixed-effect frameworks with recursive partitioning techniques, yielding interpretable, yet powerful, tools for personalised risk profiling, treatment-subgroup detection and forecasting in disciplines as diverse as medicine, psychology and education. Practical implementations often exploit ensemble strategies—such as boosting or random forests—to enhance predictive accuracy while maintaining coherence with longitudinal study designs. Overall, tree-based modelling has become central to addressing challenges of high-dimensional covariates, time-varying effects and nested data structures in modern longitudinal research.

Research from Nature Portfolio

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Research from all publishers

Recent extensions of model-based recursive partitioning have adapted generalized linear mixed-effects model (GLMM) trees for growth-curve analysis, enabling automatic detection of subgroups with distinct linear trajectories. In simulated and empirical studies, these extended GLMM trees demonstrated improved accuracy in recovering true population heterogeneity and greater computational efficiency than earlier partitioning methods. Complementary work has introduced mixed-effect models with integrated tree components that jointly estimate a parametric linear part and multiple non-parametric trees to capture interactions at both individual and cluster levels. This approach affords direct interpretability of main effects alongside flexible modelling of non-linearities, with valid post-selection inference and robust performance in Monte Carlo evaluations. Another strand of research has produced extended mixed-effect location-scale (E-MELS) tree models, which include random effects not only for subject-level means but also for residual variance and temporal autocorrelation. Empirical applications illustrate how E-MELS trees can improve individual-level forecasting in intensive longitudinal studies, supported by open-source software for practical deployment.

Tree-Based Statistical Modeling for Longitudinal Data publication trend

The graph below shows the total number of articles in tree-based statistical modeling for longitudinal data across all publications each year (not limited to Nature Index journals).

Technical terms

Longitudinal data: Repeated observations of the same subjects over time, often exhibiting within-subject correlation.

Mixed-effects model: A regression framework combining fixed effects (population-level parameters) with random effects (subject or cluster-specific deviations).

Recursive partitioning: An algorithmic process that splits data into subgroups according to predictor values, forming a decision tree structure.

Generalized linear mixed-effects model tree (GLMM tree): A model-based recursive partitioning technique that embeds a mixed-effects structure within each tree node to account for clustering or longitudinal correlation.

Mixed-effect location-scale tree model (E-MELS tree): A tree-based extension of mixed-effects models that incorporates random effects for both the mean (location) and variance/autocorrelation (scale) components.

References

1. Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees. Behavior Research Methods (2017).
2. Subgroup detection in linear growth curve models with generalized linear mixed model (GLMM) trees. Behavior Research Methods (2024).
3. Mixed-effect models with trees. Advances in Data Analysis and Classification (2022).
4. A Lasso and a Regression Tree Mixed-Effect Model with Random Effects for the Level, the Residual Variance, and the Autocorrelation. Psychometrika (2022).