global_rq {GET}

Global quantile regression

Description

Global tests of significance for the effect of covariates in quantile regression

Usage

global_rq(
  nsim,
  formula.full,
  formula.reduced,
  taus,
  data,
  contrasts = NULL,
  permutationstrategy = c("Freedman-Lane", "Freedman-Lane+remove zeros",
    "within nuisance", "remove location", "remove location scale", "remove quantile"),
  savefuns = FALSE,
  rq.args = NULL,
  lm.args = NULL,
  GET.args = NULL,
  mc.cores = 1L,
  mc.args = NULL,
  cl = NULL
)

Arguments

nsim

The number of random permutations.

formula.full

The formula specifying the general linear model, see formula in lm.

formula.reduced

The formula of the reduced model with nuisance factors only. This model should be nested within the full model.

taus

The quantiles to be used.

data

data.frame where to look for variables.

contrasts

Passed directly to rq.

permutationstrategy

The permutation strategy to be used. See details.

savefuns

Logical. If TRUE, then the functions from permutations are saved to the attribute simfuns.

rq.args

Additional arguments passed to rq.

lm.args

A named list of additional arguments to be passed to lm. See details.

GET.args

A named list of additional arguments to be passed to global_envelope_test, e.g. typeone specifies the type of multiple testing control, FWER or FDR. See global_envelope_test for the defaults and available options.

mc.cores

The number of cores to use, i.e. at most how many child processes will be run simultaneously. Must be at least one, and parallelization requires at least two cores. On a Windows computer mc.cores must be 1 (no parallelization). For details, see mclapply, for which the argument is passed. Parallelization can be used in generating simulations and in calculating the second stage tests.

mc.args

A named list of additional arguments to be passed to mclapply. Only relevant if mc.cores is more than 1.

cl

Allows parallelization through the use of parLapply (works also in Windows), see the argument cl there, and examples.

Details

The possible permutation strategies include "Freedman-Lane" (FL), "Freedman-Lane+remove zeros" (FL+), "within nuisance" (WN), "remove location" (RL), "remove location scale" (RLS), "remove quantile" (RQ), which correspond to those in Mrkvička et al. (Section 4.1-4.6 and Table 1).

Value

A global_envelope or combined_global_envelope object, which can be printed and plotted directly.

References

Mrkvička, T., Konstantinou, K., Kuronen, M. and Myllymäki, M. (2023) Global quantile regression. arXiv:2309.04746 [stat.ME]. https://doi.org/10.48550/arXiv.2309.04746

Myllymäki, M and Mrkvička, T. (2023). GET: Global envelopes in R. arXiv:1911.06583 [stat.ME]. https://doi.org/10.48550/arXiv.1911.06583

Freedman, D., & Lane, D. (1983) A nonstochastic interpretation of reported significance levels. Journal of Business & Economic Statistics, 1(4), 292-298. doi:10.2307/1391660

Examples

if(require("quantreg", quietly=TRUE)) {
  data("stackloss")
  res <- global_rq(nsim = 19, # Increase nsim for serious analysis!
    formula.full = stack.loss ~ Air.Flow + Water.Temp + Acid.Conc.,
    formula.reduced = stack.loss ~ Water.Temp,
    taus = seq(0.1, 0.9, length=10), permutationstrategy = "remove quantile",
    data = stackloss, GET.args = list(typeone = "fwer"))
  plot(res)
}