Bayesian structured additive quantile regression for inflated bounded data

TL;DR

This paper introduces Bayesian structured additive quantile regression models for inflated bounded data, allowing flexible modeling of boundary inflation and continuous outcomes with complex predictor effects.

Contribution

It develops a novel Bayesian framework for modeling inflated bounded data with structured additive predictors, including nonlinear and spatial effects, using MCMC in Liesel.

Findings

Effective in simulation studies

Applied successfully to traffic fatality data

Evaluated speech intelligibility in cochlear implant users

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.