Longitudinal quantile-based regression models using multivariate asymmetric heavy-tailed distributions and leapfrog HMC algorithm

Abstract

Modeling longitudinal quantile regression in a multivariate framework poses particular computational and conceptual challenges due to the inherent complexity of multivariate dependencies. While univariate quantile-based models can be extended to higher dimensions via Gram-Schmidt orthogonalization, such extensions often have practical limitations. To address these challenges, this paper introduces a flexible family of multivariate asymmetric distributions using the probabilistic Rosenblatt transformation. This framework preserves conditional coherence across longitudinal quantile processes via a sequential likelihood factorization, provides an explicit characterization of quantiles shaped by distributional asymmetry and covariate effects, controls for the influence of outliers, and improves computational efficiency in the estimation process. For Bayesian inference, we implement a leapfrog Hamiltonian Monte Carlo algorithm with the No-U-Turn Sampler to estimate longitudinal quantile-based regression parameters. Simulation studies over various quantile levels demonstrate the method’s theoretical properties, while two empirical applications highlight its practical utility and superior performance.