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.