bqmm: Bayesian Multilevel Quantile Regression in R

Quantile regression describes how covariates shift the conditional quantiles of an outcome, not merely its mean, and is indispensable when effects are heterogeneous across the response distribution. When data are clustered or longitudinal, a mixed-effects formulation is needed. I present bqmm, an R package for Bayesian multilevel quantile regression built on the asymmetric Laplace working likelihood and Stan. The package offers an lme4-style formula interface with nested and crossed random effects, optional LKJ-correlated random effects, estimation of one or several quantiles in a single call, post-hoc non-crossing rearrangement, and a transparent menu of fixed-effect interval methods — the naive posterior, the Yang–Wang–He (2016) sandwich correction, and the infinitesimal jackknife — because the asymmetric Laplace likelihood is misspecified and naive credible intervals can be invalid. The paper describes the model and software design, illustrates usage on longitudinal growth data, summarises a validation study (parameter recovery, simulation-based calibration, and a coverage study), and compares bqmm with related software.