Fit a joint multi-tau mixture of quantile regressions (non-crossing, shared labels)

Estimates a finite mixture of quantile regressions at a vector of quantile levels tau jointly, with one latent classification shared across all levels (a coupled E-step that pools the per-level component likelihoods) and guaranteed non-crossing of the within-component quantile curves. This closes the two problems Wu & Yao (2016, sec.5) leave open: within-component crossing and cross-tau classification ambiguity.

Usage

mixqr_nc(
  formula,
  data,
  m = 2L,
  tau = c(0.25, 0.5, 0.75),
  noncrossing = c("rearrange", "none"),
  class_coupling = c("pool", "median"),
  nstart = 10L,
  control = mixqr_control(),
  weights = NULL
)

Arguments

formula, data, m, nstart, control, weights

As in mixqr().

tau

Increasing vector of quantile levels (length >= 2).

noncrossing

"rearrange" (default; monotone-rearrange the fitted per-tau quantiles within each component, Chernozhukov et al. 2010) or "none" (legacy per-tau fits, which may cross – for diagnosis/comparison).

class_coupling

How the shared E-step pools over tau: "pool" (default; geometric mean, weights 1/L) or "median" (classify on the median level only).

Value

An object of class c("mixqr_multitau", "mixqr") with a coefficient array coefficients ([p+1, m, L]), the shared posterior/classification, mix_prop, the tau grid, and a crossing diagnostic (raw crossings, 0 after rearrangement).

References

Wu, Q. and Yao, W. (2016). Mixtures of quantile regressions. CSDA 93, 162–176. Chernozhukov, V., Fernandez-Val, I. and Galichon, A. (2010). Quantile and probability curves without crossing. Econometrica 78, 1093–1125.

Examples

# \donttest{
d <- sim_mixqr_cross(n = 160, seed = 1)
fit <- mixqr_nc(y ~ x, data = d, m = 2, tau = c(0.1, 0.25, 0.5, 0.75, 0.9))
fit$crossing      # raw crossings -> 0 after rearrangement
#> $raw
#> [1] 4
#> 
#> $after
#> [1] 0
#> 
#> $method
#> [1] "rearrange"
#> 
predict(fit)[1, , ]   # non-crossing quantiles for observation 1
#>          tau0.1    tau0.25     tau0.5     tau0.75    tau0.9
#> [1,] -4.2533230 -3.4859573 -1.9496616 -0.04859789 1.3461069
#> [2,] -0.9219902 -0.6912938 -0.2959845  0.09807378 0.3183975
# }