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bqmm

Bayesian Multilevel Quantile Regression

bqmm fits Bayesian mixed-effects (multilevel) quantile regression models in R using the asymmetric Laplace working likelihood and Stan. It lets you ask how a predictor relates to any quantile of an outcome — the median, the tails, or a whole grid — while accounting for clustered or repeated-measures data through random effects, and it returns full Bayesian uncertainty.

The package fills a genuine gap in the R ecosystem. Existing tools are either frequentist (lqmm, qrLMM), Bayesian but single-level (bayesQR, Brq), or able to fit multilevel quantile models only awkwardly and with statistically invalid uncertainty (brms’s asym_laplace()). bqmm provides a clean, quantile-first interface and valid fixed-effect inference via the Yang, Wang & He (2016) correction.

📖 Full documentation, primer, and articles: https://kvenkita.github.io/bqmm/

Installation

# install.packages("remotes")
remotes::install_github("kvenkita/bqmm")

bqmm compiles Stan models on installation, so a working C++ toolchain is required (Rtools on Windows, the standard compiler chain on macOS/Linux).

Quick start

library(bqmm)
data(Orthodont, package = "nlme")

# Conditional median of growth, with a random intercept per child
fit <- bqmm(distance ~ age + (1 | Subject), data = Orthodont, tau = 0.5)

summary(fit)              # fixed effects with valid (adjusted) intervals
VarCorr(fit)             # random-effect standard deviations

# Several quantiles in one call
fit_q <- bqmm(distance ~ age + (1 | Subject), data = Orthodont,
              tau = c(0.1, 0.5, 0.9))
plot(fit_q)              # coefficient-versus-quantile paths
predict(fit_q, noncrossing = "rearrange")   # non-crossing quantiles

Key features

Familiar lme4 formula interface — y ~ x + (1 + x | group); nested and crossed random effects work out of the box.
One or many quantiles in a single call (a scalar or vector tau).
Valid inference — the Yang, Wang & He (2016) posterior-variance correction is applied by default, fixing the well-known invalidity of naive asymmetric-Laplace credible intervals. Verified by simulation to cover at or above the nominal level.
Correlated random effects — cov = "unstructured" adds an LKJ-correlated random intercept and slope, with the correlation reported by VarCorr().
Non-crossing — optional post-hoc rearrangement so fitted quantiles never cross.
Ecosystem citizen — works with the posterior and bayesplot stacks via as_draws(), and ships the usual lme4/rstanarm-style methods.

Key functions

Function	Purpose
`bqmm()`	Fit a Bayesian multilevel quantile regression model
`bqmm_prior()`	Specify priors (fixed effects, scale, random-effect SDs, LKJ)
`ald()`	The asymmetric Laplace family object
`summary()`, `fixef()`, `coef()`	Fixed-effect estimates and intervals
`ranef()`, `VarCorr()`	Random effects and their (co)variances
`vcov(fit, adjusted = TRUE)`	Yang–Wang–He–corrected covariance
`predict()`, `fitted()`	Fitted / predicted conditional quantiles
`posterior_predict()`, `posterior_epred()`	Posterior predictive draws
`as_draws()`	Hand the fit to `posterior` / `bayesplot`
`rearrange_quantiles()`	Remove quantile crossing

Documentation

Primer — a thorough, accessible guide for applied researchers: the method, fitting, priors, inference, diagnostics, and visualization.
Get started — a short tour.
Multilevel structure — random intercepts/slopes, correlated and crossed effects.
Valid inference — why naive intervals fail and how the correction works.
Review & testing report — the validation evidence behind the package.
Function reference.

Citation

If you use bqmm, please cite it:

Venkitasubramanian, K. (2026). bqmm: Bayesian Multilevel Quantile Regression. R package version 0.1.0. https://github.com/kvenkita/bqmm

citation("bqmm")

Please also cite the underlying methodology where appropriate — Yu & Moyeed (2001) for the asymmetric Laplace approach and Yang, Wang & He (2016) for the inference correction.

Author and license

Created and maintained by Kailas Venkitasubramanian. Released under the MIT License.

References

Yu, K. & Moyeed, R. A. (2001). Bayesian quantile regression. Statistics & Probability Letters, 54(3), 437–447.
Kozumi, H. & Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. J. Stat. Comput. Simul., 81(11), 1565–1578.
Geraci, M. & Bottai, M. (2014). Linear quantile mixed models. Statistics and Computing, 24(3), 461–479.
Yang, Y., Wang, H. J. & He, X. (2016). Posterior inference in Bayesian quantile regression with asymmetric Laplace likelihood. International Statistical Review, 84(3), 327–344.
Chernozhukov, V., Fernández-Val, I. & Galichon, A. (2010). Quantile and probability curves without crossing. Econometrica, 78(3), 1093–1125.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.