Calculate quantile regression goodness of fit using residuals and non-conditional residuals
goodfit(resid, resid_nl, tau)numeric vector of residuals from the conditional quantile model
numeric vector of residuals from the non-conditional (null) quantile model
numeric value from zero to one for the estimated quantile
A numeric value from 0 to 1 indicating goodness of fit
The goodness of fit measure for quantile regression is estimated as 1 minus the ratio between the sum of absolute deviations in the fully parameterized models and the sum of absolute deviations in the null (non-conditional) quantile model. The values are useful for comparisons between quantile models, but they are not comparable to standard coefficients of determination. The latter is based on the variance of squared deviations, whereas goodness of fit values for quantile regression are based on absolute deviations. Goodness of fit values will always be smaller than R2 values.
Koenker, R., Machado, J.A.F. 1999. Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association. 94(448):1296-1310.
wrtdsrsd for residuals
library(quantreg)
#> Loading required package: SparseM
#>
#> Attaching package: ‘SparseM’
#> The following object is masked from ‘package:base’:
#>
#> backsolve
## random variables
x <- runif(100, 0, 10)
y <- x + rnorm(100)
## quantile model
mod <- rq(y ~ x, tau = 0.5)
res <- resid(mod)
## non-conditional quantile model
mod_nl <- rq(y ~ 1, tau = 0.5)
#> Warning: Solution may be nonunique
rsd_nl <- resid(mod_nl)
goodfit(res, rsd_nl, 0.5)
#> [1] 0.728844
## r2 of mean model for comparison
mod_lm <- lm(y ~ x)
summary(mod_lm)$r.squared
#> [1] 0.9089283