Package {mixqrgate}

mixqrgate: Location-Varying Gating for Mixtures of Quantile Regressions

Description

A companion to the mixqr package that adds a concomitant-covariate, quantile-indexed mixing gate to finite mixtures of quantile regressions. The mixing probabilities follow a multinomial-logit model whose coefficients can depend on gating covariates and on the quantile level, so latent-class membership may change across the conditional distribution – the location-varying mixing idea of Furno (2025), turned into a likelihood/EM object with standard errors on the gate.

Main entry point

• mixqrgate() – fit a gated mixture of quantile regressions.

• sim_gate2() – a two-component design with a location-varying gate.

Author(s)

Maintainer: Kailas Venkitasubramanian kailasv@gmail.com [copyright holder]

References

Furno, M. (2025). Finite Mixture at Quantiles and Expectiles. Journal of Risk and Financial Management 18(4), 177.

Wu, Q. and Yao, W. (2016). Mixtures of quantile regressions. Computational Statistics & Data Analysis 93, 162–176.

Grün, B. and Leisch, F. (2008). FlexMix version 2: finite mixtures with concomitant variables and varying and constant parameters. Journal of Statistical Software 28(4), 1–35.

See Also

Useful links:

• https://github.com/kvenkita/mixqrgate

• Report bugs at https://github.com/kvenkita/mixqrgate/issues

Minimal pseudo-inverse (avoids a MASS dependency).

Description

Minimal pseudo-inverse (avoids a MASS dependency).

Usage

MASS_ginv(A, tol = 1e-10)

Confidence intervals for the gate coefficients

Description

Confidence intervals for the gate coefficients

Usage

## S3 method for class 'mixqrgate'
confint(object, parm, level = 0.95, tau = NULL, ...)

Arguments

Value

A matrix of lower/upper limits for the gate coefficients.

Gate probabilities pi_ik from gate coefficients and gating design.

Description

Gate probabilities pi_ik from gate coefficients and gating design.

Usage

gate_predict(gamma, Z)

Arguments

Value

An ⁠n x G⁠ matrix of mixing probabilities.

Sandwich covariance for the gate coefficients (the inference Furno lacks). ⁠V = A^{-1} B A^{-1}⁠, A = -Hessian of Q, B = sum_i s_i s_i'.

Description

Sandwich covariance for the gate coefficients (the inference Furno lacks). ⁠V = A^{-1} B A^{-1}⁠, A = -Hessian of Q, B = sum_i s_i s_i'.

Usage

gate_sandwich_vcov(Z, P, fit)

Louis observed-information gate covariance (analytic, classification-aware).

Description

Applies Louis's (1982) identity to the gate block: the observed information is the complete-data information minus the missing information induced by the latent class labels, ⁠I_obs = A - sum_i ( E[S_i S_i' | y] - s_i s_i' )⁠, where A is the complete-data gate information (the gate Newton information at the fitted probabilities), ⁠s_i = sum_k p_ik g_ik⁠ is the conditional score and g_ik the gate score were observation i in class k. The cross-information with the component coefficients is O(1/n) and omitted (DESIGN sec. 2.4), so this is the gate-block marginal. Cheaper than the multiple-imputation variance and a useful cross-check. Returns solve(I_obs).

Usage

gate_vcov_louis(Z, posterior, prior)

Multiple-imputation gate covariance (propagates classification uncertainty).

Description

Draws hard labels from the posterior, refits the gate, and combines the within- and between-imputation variance: ⁠V = V_W + (1 + 1/B) V_B⁠.

Usage

gate_vcov_mi(Z, posterior, ridge, B = 200L, maxit = 50L, tol = 1e-08)

One gated-EM fit from a single initial responsibility matrix.

Description

One gated-EM fit from a single initial responsibility matrix.

Usage

gated_em_fit(y, X, Z, G, tau, method, p_init, control)

Arguments

Value

A list with the fitted state (beta, gate, prior, posterior, loglik...).

Fit a weighted multinomial logit by ridge-penalised Newton/IRLS.

Description

Fit a weighted multinomial logit by ridge-penalised Newton/IRLS.

Usage

irls_multinom_fit(Z, P, lambda = 0.001, maxit = 50L, tol = 1e-08)

Arguments

Value

A list with gamma (⁠(q+1) x (G-1)⁠), hessian, pi, converged.

Fit a gated mixture of quantile regressions

Description

Fits a finite mixture of tau-quantile regressions whose mixing probabilities follow a multinomial-logit gate on concomitant covariates, optionally indexed by the quantile level. The gate turns the location-varying mixing of Furno (2025) into a likelihood/EM object with standard errors.

Usage

mixqrgate(
  formula,
  data,
  gating = ~1,
  G = 2L,
  tau = 0.5,
  vary_gating = c("none", "discrete"),
  method = c("ald", "kde"),
  variance = c("sandwich", "louis", "stochEM"),
  gate_B = 200L,
  control = mixqrgate_control()
)

Arguments

Value

An object of class "mixqrgate".

References

Furno, M. (2025). Finite Mixture at Quantiles and Expectiles. JRFM 18(4), 177.

Examples

set.seed(1)
d <- sim_gate2(n = 300)
fit <- mixqrgate(y ~ x, data = d, gating = ~ z, G = 2, tau = 0.5)
fit

Control parameters for mixqrgate()

Description

Control parameters for mixqrgate()

Usage

mixqrgate_control(
  nstart = 10L,
  maxit = 500L,
  tol = 1e-06,
  gate_ridge = 0.001,
  gate_maxit = 50L,
  gate_tol = 1e-08,
  label_order = "slope",
  bandwidth = NULL,
  kde_grid = 512L,
  trace = FALSE,
  seed = NULL
)

Arguments

Value

A list of class "mixqrgate_control".

Permutation that orders components by slope (default) or intercept.

Description

Permutation that orders components by slope (default) or intercept.

Usage

order_components(beta, label_order = "slope")

Plot a gated mixture fit

Description

which = "gating" draws the class-average gate probability against the quantile level – the location-varying mixing picture that is Furno's headline finding. which = "fit" draws the data coloured by class with the component quantile lines at the first grid point.

Usage

## S3 method for class 'mixqrgate'
plot(x, which = c("gating", "fit"), ...)

Arguments

Value

Invisibly x.

Predict gate probabilities or class membership

Description

Predict gate probabilities or class membership

Usage

## S3 method for class 'mixqrgate'
predict(object, newdata = NULL, type = c("prob", "class"), tau = NULL, ...)

Arguments

Value

A matrix of gate probabilities (type = "prob") or an integer vector of class labels (type = "class").

Simulate a two-component mixture with a concomitant gate

Description

Membership depends on a gating covariate z through a logit ⁠Pr(class 2 | z) = plogis(gamma[1] + gamma[2] z)⁠; the two components are quantile regressions of y on x with distinct slopes. Errors are median-zero.

Usage

sim_gate2(
  n = 400L,
  gamma = c(0, 1.5),
  b1 = c(2, -3),
  b2 = c(-2, 3),
  sigma = c(1, 1.5),
  loc_vary = 0,
  het = FALSE
)

Arguments

Details

With loc_vary > 0 the gate becomes genuinely location-varying in the sense of Furno (2025): membership also depends on the latent quantile rank, so class 2 is over-represented in the upper tail and the class composition – hence the fitted gate – shifts across the quantile level. With het = TRUE the second component's spread grows with x.

Value

A data frame with y, x, z, and the true class.

References

Furno, M. (2025). Finite Mixture at Quantiles and Expectiles. JRFM 18(4), 177.

Row-wise softmax over (G-1) linear predictors plus a zero reference column.

Description

Row-wise softmax over (G-1) linear predictors plus a zero reference column.

Usage

softmax_rows(eta)

Summarize a gated mixture fit

Description

Reports, per quantile level, the component coefficients and the gate coefficients with standard errors, z- and p-values – the inference on how membership depends on the gating covariates (and, across the grid, on tau).

Usage

## S3 method for class 'mixqrgate'
summary(object, ...)

Arguments

Value

An object of class "summary.mixqrgate".