rqmlr

rqmlr is a statistical framework and R package for robust quantile regression in linear mixed-effects models. It is designed to estimate conditional quantiles of a response variable when data exhibit grouped structure, non-normal errors, or outliers. By combining the ideas of quantile regression with robust loss functions and a random-effects specification, rqmlr yields quantile-specific estimates of fixed effects and variance components for random effects.

Key features include support for multiple quantile levels (tau), flexible random-effects structures (random intercepts and slopes), a formula interface compatible with lme4, and inference via bootstrap-based standard errors or asymptotic approximations. The package provides methods to summarize results, produce fitted values and residuals, perform predictions, and generate diagnostic plots. It aims to be usable with standard data frames and familiar modeling syntax.

Typical workflow involves specifying a model with a formula such as y ~ fixed + (1|group) and choosing one or more quantile levels. After fitting, users inspect parameter estimates, check convergence diagnostics, and compare models across quantiles. Example usage might include fitting a model with multiple taus to explore how covariate effects vary across the outcome distribution.

Applications and relation: rqmlr is applicable in fields where effects differ across the outcome distribution and where outliers or heteroscedasticity bias mean-based models. It relates to quantile regression and linear mixed models, building on robust statistics literature. See also: quantile regression, linear mixed models, robust statistics, lme4.