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

Abstract

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.

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BibTeX RIS

BibTeX

@misc{hasan2026deep,
  title = {{Deep Neural Mixed Models for Nonlinear Longitudinal Prediction with Subject-Specific Heterogeneity}},
  author = {Mahmud Hasan and Niloofar Ramezani and Hrishikesh Chakraborty},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15323},
  eprint = {2610.15323},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15323},
}

RIS

TY  - UNPB
TI  - Deep Neural Mixed Models for Nonlinear Longitudinal Prediction with Subject-Specific Heterogeneity
AU  - Mahmud Hasan
AU  - Niloofar Ramezani
AU  - Hrishikesh Chakraborty
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15323
UR  - https://arxiv.org/abs/2610.15323
AB  - 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.
ER  -

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