Approximation, Consistency, and Prediction in Generalized Neural Network Mixed Models for Longitudinal and Clustered Data
Abstract
Generalized neural network mixed models (GNMMs) combine neural networks and mixed-effects models to analyze longitudinal and clustered data. Although GNMMs have shown good predictive performance in practice, their statistical properties are not well understood. Therefore, this paper studies several important properties of GNMM and provides theoretical support for its use. First, we show that the neural-network component can approximate an unknown nonlinear fixed-effect function arbitrarily well and establish consistency of the fitted neural- network function for its population target within a given network class. Next, we establish consistency of random-effect estimation under increasing within-subject information and show that the GNMM predictor converges to the true predictor. We then prove consistency of the conditional mean function and show that the excess mean squared prediction error (MSPE) relative to the oracle prediction error converges to zero. We conduct simulation studies to examine nonlinear fixed-effect recovery, random-effect estimation, predictor and conditional mean estimation, and excess prediction error under different numbers of subjects and repeated observations. We also apply GNMM to a longitudinal schizophrenia dataset to predict continuous and binary depression outcomes using smartphone- based behavioral measurements and compare its predictive performance with generalized linear mixed models and conventional artificial neural networks. Both the theoretical and empirical results demonstrate that GNMM provides a flexible framework for modeling nonlinear longitudinal and clustered data. These findings provide a statistical foundation for GNMM prediction and support future methodological developments.
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BibTeX
@misc{hasan2026approximation,
title = {{Approximation, Consistency, and Prediction in Generalized Neural Network Mixed Models for Longitudinal and Clustered Data}},
author = {Mahmud Hasan and Md Moinul Ahsan and Mathias Nthiani Muia and Mous-Abou Hamadou and Chathurika S Abeykoon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15270},
eprint = {2610.15270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15270},
}
RIS
TY - UNPB
TI - Approximation, Consistency, and Prediction in Generalized Neural Network Mixed Models for Longitudinal and Clustered Data
AU - Mahmud Hasan
AU - Md Moinul Ahsan
AU - Mathias Nthiani Muia
AU - Mous-Abou Hamadou
AU - Chathurika S Abeykoon
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15270
UR - https://arxiv.org/abs/2610.15270
AB - Generalized neural network mixed models (GNMMs) combine neural networks and mixed-effects models to analyze longitudinal and clustered data. Although GNMMs have shown good predictive performance in practice, their statistical properties are not well understood. Therefore, this paper studies several important properties of GNMM and provides theoretical support for its use. First, we show that the neural-network component can approximate an unknown nonlinear fixed-effect function arbitrarily well and establish consistency of the fitted neural- network function for its population target within a given network class. Next, we establish consistency of random-effect estimation under increasing within-subject information and show that the GNMM predictor converges to the true predictor. We then prove consistency of the conditional mean function and show that the excess mean squared prediction error (MSPE) relative to the oracle prediction error converges to zero. We conduct simulation studies to examine nonlinear fixed-effect recovery, random-effect estimation, predictor and conditional mean estimation, and excess prediction error under different numbers of subjects and repeated observations. We also apply GNMM to a longitudinal schizophrenia dataset to predict continuous and binary depression outcomes using smartphone- based behavioral measurements and compare its predictive performance with generalized linear mixed models and conventional artificial neural networks. Both the theoretical and empirical results demonstrate that GNMM provides a flexible framework for modeling nonlinear longitudinal and clustered data. These findings provide a statistical foundation for GNMM prediction and support future methodological developments.
ER -