{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15323",
  "author_total": 3,
  "authors": [
    {
      "name": "Mahmud Hasan"
    },
    {
      "name": "Niloofar Ramezani"
    },
    {
      "name": "Hrishikesh Chakraborty"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1es506g7fajzs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15323",
  "fulltext_url": null,
  "id": "1es506g7fajzs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15323",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Bayesian Inference"
    ]
  ],
  "openalex": "W7221776789",
  "pdf_url": "https://arxiv.org/pdf/2610.15323",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1es506g7fajzs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.15323",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15323"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Deep Neural Mixed Models for Nonlinear Longitudinal Prediction with Subject-Specific Heterogeneity",
  "title_text": "Deep Neural Mixed Models for Nonlinear Longitudinal Prediction with Subject-Specific Heterogeneity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/1es506g7fajzs",
  "venue": "arXiv",
  "versions": []
}