Quantile regression heteroscedasticity test

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,
  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.

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.

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)
}
#> 
#> 	Quantile regression joint test of equality of slopes
#> 
#> data:  stations ~ mag + depth
#> F = 26.909, df1 = 2, df2 = 1998, p-value = 2.938e-12
#> alternative hypothesis: at least one slope differs across quantiles
#> sample estimates:
#>          tau_0.25    tau_0.75
#> mag   38.60737066 49.11654471
#> depth  0.01311127  0.01088702
#>