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bqmm: Bayesian Multilevel Quantile Regression in R

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  • Venkitasubramanian, Kailas

    (University of North Carolina at Charlotte)

Abstract

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.

Suggested Citation

  • Venkitasubramanian, Kailas, 2026. "bqmm: Bayesian Multilevel Quantile Regression in R," SocArXiv 7d5xb_v1, Center for Open Science.
    • Handle: RePEc:osf:socarx:7d5xb_v1
    DOI: 10.31235/osf.io/7d5xb_v1
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    References listed on IDEAS

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    1. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    2. Geraci, Marco, 2014. "Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i13).
    3. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
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