A Bayesian Copula Dirichlet Process GLM for Longitudinal Data

Abstract

We introduce a semiparametric Bayesian generalized linear model (GLM) for longitudinal continuous outcomes that preserves the usual interpretation of the GLM regression structure while leaving the baseline distribution nonparametric. The proposed copula Dirichlet process generalized linear model (CDPGLM) combines a Dirichlet process prior for the baseline distribution, a parametric GLM regression structure for covariate effects, and a copula for longitudinal within--subject dependence. This construction separates modeling the marginal distribution of an individual repeated measurement from modeling the association: the Dirichlet process GLM component defines the marginal density and regression mean, whereas the copula captures dependence among repeated measurements. Compared with a parametric beta mixed--effects model, the CDPGLM provides similarly efficient estimation of regression effects while being substantially more robust to estimate marginal distributions and lower-tail probabilities (the complement of exceedance probability). In an application to data from the National Heart, Lung, and Blood Institute (NHLBI) Lung Health Study, the CDPGLM and a parametric mixed beta model gave comparable inference on regression coefficients, but the CDPGLM more closely matched the empirical marginal distribution and reported more realistic and detailed lower--tail risk summaries.

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BibTeX RIS

BibTeX

@misc{yuan2026bayesian,
  title = {{A Bayesian Copula Dirichlet Process GLM for Longitudinal Data}},
  author = {Shijie Yuan and Entejar Alam and Asmit Chakraborty and Paul Rathouz and Jonathan Schildcrout and Peter Müller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30467},
  eprint = {2610.30467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30467},
}

RIS

TY  - UNPB
TI  - A Bayesian Copula Dirichlet Process GLM for Longitudinal Data
AU  - Shijie Yuan
AU  - Entejar Alam
AU  - Asmit Chakraborty
AU  - Paul Rathouz
AU  - Jonathan Schildcrout
AU  - Peter Müller
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30467
UR  - https://arxiv.org/abs/2610.30467
AB  - We introduce a semiparametric Bayesian generalized linear model (GLM) for longitudinal continuous outcomes that preserves the usual interpretation of the GLM regression structure while leaving the baseline distribution nonparametric. The proposed copula Dirichlet process generalized linear model (CDPGLM) combines a Dirichlet process prior for the baseline distribution, a parametric GLM regression structure for covariate effects, and a copula for longitudinal within--subject dependence. This construction separates modeling the marginal distribution of an individual repeated measurement from modeling the association: the Dirichlet process GLM component defines the marginal density and regression mean, whereas the copula captures dependence among repeated measurements. Compared with a parametric beta mixed--effects model, the CDPGLM provides similarly efficient estimation of regression effects while being substantially more robust to estimate marginal distributions and lower-tail probabilities (the complement of exceedance probability). In an application to data from the National Heart, Lung, and Blood Institute (NHLBI) Lung Health Study, the CDPGLM and a parametric mixed beta model gave comparable inference on regression coefficients, but the CDPGLM more closely matched the empirical marginal distribution and reported more realistic and detailed lower--tail risk summaries.
ER  -

Abstract

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