# Deep Neural Mixed Models for Nonlinear Longitudinal Prediction with Subject-Specific Heterogeneity

arXiv: https://arxiv.org/abs/2610.15323 · HTML: https://mlsanity.com/paper/2610.15323/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 11 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Doctor AI: Predicting Clinical Events via Recurrent Neural Networks](https://mlsanity.com/paper/1511.05942/) (2015)
- [Neural Mixed Effects for Nonlinear Personalized Predictions](https://mlsanity.com/paper/2306.08149/) (2023)
- [Deep mixture of linear mixed models for complex longitudinal data](https://mlsanity.com/paper/2311.07156/) (2023)

## Abstract (arXiv)

Longitudinal health data often exhibit within-subject correlation, subject-specific heterogeneity, and complex nonlinear predictor--response relationships that may not be adequately captured by conventional mixed models. We propose a Deep Generalized Neural Network Mixed Model (DGNMM) that extends the GLMM framework by using a deep neural network to learn nonlinear population-level relationships while incorporating directly trainable, regularized subject-specific effects to capture individual heterogeneity. The model is estimated using prediction-oriented stochastic optimization with separate regularization of the neural-network parameters and subject-specific effects. This formulation allows us to investigate when increased nonlinear representation capacity provides additional predictive benefit in the presence of subject-specific heterogeneity. A simulation study varies population-level nonlinearity and subject-specific heterogeneity and compares DGNMM with GLMM, artificial neural network (ANN), Maity--Pal (MP), and GNMM alternatives for continuous and binary longitudinal outcomes. In the real-data application, DGNMM achieved the lowest MSPE for continuous depression and anxiety prediction, while alternative models remained competitive for binary outcomes. Exploratory subject-level analyses showed heterogeneous predictive gains across individuals, but the magnitude of the estimated subject-specific effects was not significantly associated with predictive gain. Overall, increased nonlinear representation capacity was most beneficial for continuous prediction under nonlinear response structures, while greater subject-specific heterogeneity did not systematically yield larger predictive gains.