Bayesian structured additive quantile regression for inflated bounded data

Francisco F. Queiroz; Johannes Brachem; Paul F. V. Wiemann; Thomas Kneib

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arXiv · 2603.03987

Bayesian structured additive quantile regression for inflated bounded data

Francisco F. Queiroz·Johannes Brachem·Paul F. V. Wiemann·Thomas Kneib

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Abstract

Bounded continuous data on the unit interval frequently arise in applied fields and often exhibit a non-negligible proportion of observations at the boundaries. Inflated regression models address this feature by combining a continuous distribution on the unit interval with a discrete component to account for zero- and/or one-inflation. In this paper, we propose a class of Bayesian structured additive quantile regression models for inflated bounded continuous data that accommodates zero- and/or one-inflation. The proposed approach enables direct modeling of both the conditional quantiles of the continuous component and the probabilities of observing zeros and/or ones, with structured additive predictors incorporated in both parts, including nonlinear effects, spatial effects, random effects, and varying-coefficient terms. Posterior inference is carried out using Markov chain Monte Carlo algorithms implemented through the software Liesel, a probabilistic programming framework for semiparametric regression. The practical performance of the proposed models is illustrated through simulation studies and two real-data applications: one analyzing the proportion of traffic-related fatalities across Brazilian municipal districts, and another evaluating speech intelligibility in cochlear implant recipients under different experimental conditions.

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BibTeX RIS

Francisco F. Queiroz, Johannes Brachem, Paul F. V. Wiemann, Thomas Kneib. 2026-03-04. Bayesian structured additive quantile regression for inflated bounded data. https://arxiv.org/abs/2603.03987

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