A Bayesian quantile mixed model for bounded discrete outcomes
Abstract
Quantile regression for longitudinal bounded integer outcomes must accommodate discreteness, finite support, and dependence within participants. We develop a Bayesian quantile mixed model using a discrete Kumaraswamy distribution parameterized through a smooth quantile anchor whose ceiling gives the corresponding integer quantile. Covariates and correlated Gaussian participant effects enter a logit predictor for the scaled anchor, while a separate regression models distributional shape. Posterior computation combines a conjugate Gaussian coefficient update, available for compatible fixed and random effect designs, with slice sampling and covariance interweaving. Simulations showed small biases in regression coefficients and generally near-nominal coverage of 95% credible intervals. An application to repeated cognitive scores illustrates covariate associations across separately fitted quantile levels. Posterior predictive checks captured broad distributional patterns.
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BibTeX
@misc{burger2026bayesian,
title = {{A Bayesian quantile mixed model for bounded discrete outcomes}},
author = {Divan Aristo Burger},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02713},
eprint = {2611.02713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02713},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bayesian quantile mixed model for bounded discrete outcomes
AU - Divan Aristo Burger
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02713
UR - https://arxiv.org/abs/2611.02713
AB - Quantile regression for longitudinal bounded integer outcomes must accommodate discreteness, finite support, and dependence within participants. We develop a Bayesian quantile mixed model using a discrete Kumaraswamy distribution parameterized through a smooth quantile anchor whose ceiling gives the corresponding integer quantile. Covariates and correlated Gaussian participant effects enter a logit predictor for the scaled anchor, while a separate regression models distributional shape. Posterior computation combines a conjugate Gaussian coefficient update, available for compatible fixed and random effect designs, with slice sampling and covariance interweaving. Simulations showed small biases in regression coefficients and generally near-nominal coverage of 95% credible intervals. An application to repeated cognitive scores illustrates covariate associations across separately fitted quantile levels. Posterior predictive checks captured broad distributional patterns.
ER -