mixqr: An Extensible Framework for Finite Mixtures of Quantile and Expectile Regressions in R

Finite mixtures of quantile regressions recover latent regimes that differ in how a predictor shapes the whole conditional distribution of an outcome, not just its mean. We present mixqr, an extensible R framework built on a single expectation-maximization (EM) substrate and an engine/extension contract. On that platform sit five capabilities, four of which we believe to be absent from R: the core free-weight mixture of Wu and Yao (2016); a concomitant, quantile-indexed gate (companion mixqrgate) that turns the location-varying mixing of Furno (2025) into a likelihood/EM object with a Louis observed-information variance; expectile and M-quantile component families (Newey and Powell 1987; Breckling and Chambers 1988); component-specific penalized selection, the quantile analogue of Khalili and Chen (2007); and a joint multi-quantile estimator that shares one latent classification across quantile levels and removes within-component crossing by monotone rearrangement (Chernozhukov, Fernandez-Val and Galichon 2010). The last directly addresses both problems Wu and Yao (2016, sec. 5) leave open-supplying a single cross-quantile-coherent classification and order-respecting reported quantiles. We anchor the paper on a Dutch language-achievement study, where combination classes are significantly more likely to show a steep socioeconomic gradient, add real-data and simulation demonstrations of the new capabilities, and validate coverage, selection accuracy, and crossing elimination by simulation.