Quantile regression heteroscedasticity test¶

Source: R/quantile_regression_joint.R · Help: ?performQuantileRegressionTest

Tests equality of regression slopes across two or more conditional quantiles using the joint Wald-type test implemented by quantreg::anova.rqs(). The procedure accounts for dependence among quantile-specific estimates from the same sample rather than treating their covariance matrices as independent.

Usage¶

performQuantileRegressionTest(
  model,
  data = NULL,
  taus = c(0.25, 0.75),
  se_type = c("nid", "ker"),
  iid = TRUE
)

Arguments¶

model: A fitted stats::lm object describing the mean structure whose conditional quantile slopes are to be compared.
data: A base::data.frame containing the variables referenced in model. When NULL, the default, the model frame of model is used. It holds the terms of the model rather than its variables (log(x) rather than x), so a model that transforms a variable needs data, as does a model with an offset() term, and so may a fit whose weights or offset argument is a column of the data, which the model frame holds as (weights) or (offset).
taus: Numeric vector containing at least two distinct quantiles strictly between zero and one.
se_type: Standard-error method used by quantreg::anova.rqs(); supported values are "nid" and "ker".
iid: Logical indicating whether identical conditional densities are assumed when computing the joint test.

Value¶

An htest object containing the F-like joint statistic, numerator and denominator degrees of freedom, p-value, fitted quantiles, and quantile-specific slope estimates.

Details¶

Under a pure location-shift model with homoskedastic errors, regression slopes are equal across quantiles. Rejection therefore provides evidence against that location-shift/homoskedastic specification. The result should not be interpreted as a universal test for every possible form of heteroscedasticity.

Weighted fits are refused, although the resampling tests accept them. On a fit with weights \(w_i\) the null hypothesis is that the Pearson residuals \(\sqrt{w_i}\, e_i\) have constant variance, which is a statement about the regression of \(\sqrt{w_i}\, y_i\) on \(\sqrt{w_i}\, x_i\). The quantile regressions this test fits are of \(y\) on \(x\), where the errors have variance \(\sigma^2 / w_i\) by assumption, so their slopes differ across quantiles even when the weights are right. Fitting them on the weighted scale does not by itself repair that: there the conditional quantiles are the regression plus a constant, and the constant is not a column of the weighted regressors. Adding a column of ones would restore the location-shift form, but that version of the test needs its own derivation and its own size study, and has neither.

References¶

Koenker, R., & Bassett, G. (1982). Robust tests for heteroscedasticity based on regression quantiles. Econometrica, 50(1), 43–61.

Koenker, R. (2005). Quantile Regression. Cambridge University Press.

Examples¶

if (requireNamespace("quantreg", quietly = TRUE)) {
  # The test needs at least 40 observations, so mtcars (32) is too small.
  model <- lm(stations ~ mag + depth, data = quakes)
  performQuantileRegressionTest(model, quakes)
}