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mixqrgate

Location-varying gating for mixtures of quantile regressions

mixqrgate extends mixqr so that the mixing probabilities of a finite mixture of quantile regressions can depend on covariates — and on the quantile level. The mixing weights follow a multinomial-logit gate; with a quantile-indexed gate, latent-class membership can change across the conditional distribution. An observation may belong to one regime near the median and another in the tail.

This is the location-varying mixing of Furno (2025), turned from a Stata reweighting heuristic into a likelihood/EM object — with standard errors on the gate, which the original method does not provide.

Installation

# install.packages("remotes")
remotes::install_github("kvenkita/mixqr")       # required
remotes::install_github("kvenkita/mixqrgate")

Quick start

library(mixqrgate)

d <- sim_gate2(n = 600, gamma = c(0, 1.5))      # gate depends on z

# concomitant gate at the median
fit <- mixqrgate(y ~ x, data = d, gating = ~ z, G = 2, tau = 0.5)
summary(fit)          # component coefficients + gate coefficients WITH SEs

# location-varying gate: refit the gate at each quantile
fitv <- mixqrgate(y ~ x, data = d, gating = ~ z, G = 2,
                  tau = c(0.1, 0.5, 0.9), vary_gating = "discrete")
plot(fitv, which = "gating")                    # gate-vs-tau picture

Key features

• Concomitant gate. gating = ~ z1 + z2 puts a multinomial logit on the mixing probabilities; the gating covariates may differ from the component-regression covariates.
• Quantile-indexed gate. A vector tau with vary_gating = "discrete" refits the gate at each quantile, so membership can vary across the distribution (Furno’s location-varying mixing).
• Inference on the gate. Sandwich standard errors, z- and p-values per quantile — answer whether and how membership changes with the covariates and with tau.
• Reduces to mixqr. gating = ~1 gives a constant gate and the ordinary mixture-of-quantile-regressions fit.
• Two engines. Parametric asymmetric-Laplace (method = "ald") or the Wu & Yao nonparametric kernel-density path (method = "kde").

Relationship to mixqr

mixqrgate reuses mixqr’s component and constrained-error-density machinery through its extension API (weighted_rq(), constrained_kde()); only the gate is new. The component estimates, diagnostics, and quantile semantics are those of mixqr.

Citation

Venkitasubramanian, K. (2026). mixqrgate: Location-Varying Gating for Mixtures of Quantile Regressions. R package version 0.1.0.

Please also cite Furno (2025) for the location-varying mixing idea and Wu & Yao (2016) for the mixture-of-quantile-regressions estimator.

Author and license

Created and maintained by Kailas Venkitasubramanian, University of North Carolina at Charlotte. MIT licensed.

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.