(Randomized) Quantile Residuals

Generic function and methods for computing (randomized) quantile residuals.

qresiduals(object, ...)

# S3 method for default
qresiduals(object, scale = "normal", ...)

Arguments

object

an object. For the default method this needs to be either a specification of probabilities (vector or 2-dimensional matrix of probabilities) or an object from which the these can be obtained with procast.

...

further parameters passed to pitresiduals.

scale

On which scale should the PIT residuals be shown; on the probability scale ("uniform") or on the normal scale ("normal"). Here, for (randomized) quantile residuals, the quantiles of the standard normal distribution are computed per default.

Value

A vector or matrix of quantile residuals.

Details

(Randomized) quantile residuals are simply the theoretical standard normal quantiles evaluated at the PIT residuals as suggested by Dunn and Smyth (1996). For regression models with a continuous response distribution these are exact; for discrete distributions, PIT residuals are drawn from the range of probabilities corresponding to each observation, hence quantile residuals must be random as well.

The default qresiduals method calls pitresiduals with scale equal "normal", as employed in normal Q-Q plots (qqrplot).

Note

Note that there is also a qresiduals function in the statmod package that is not generic and always returns a single random quantile residual.

References

Dunn KP, Smyth GK (1996). “Randomized Quantile Residuals.” Journal of Computational and Graphical Statistics, 5(3), 236--244. doi:10.2307/1390802

See also

pitresiduals, qnorm, qqrplot

Examples

## linear regression models (homoscedastic Gaussian response)
m <- lm(dist ~ speed, data = cars)
qresiduals(m)
#>           1           2           3           4           5           6 
#>  0.25545799  0.78635431 -0.39470591  0.79981078  0.14067589 -0.51845901 
#>           7           8           9          10          11          12 
#> -0.24852535  0.28237096  0.81326725 -0.57585005  0.15413237 -1.03589883 
#>          13          14          15          16          17          18 
#> -0.63772660 -0.37227844 -0.10683030 -0.50051704  0.03037928  0.03037928 
#>          19          20          21          22          23          24 
#>  0.82672373 -0.76147969 -0.09785931  1.49482961  2.82207038 -1.42061458 
#>          25          26          27          28          29          30 
#> -1.02244235  0.83569472 -0.88523278 -0.35433648 -1.14619544 -0.61529914 
#>          31          32          33          34          35          36 
#>  0.04832124 -0.74353772  0.18553081  1.51277158  2.04366789 -1.40267261 
#>          37          38          39          40          41          42 
#> -0.73905224  0.72091261 -1.92908343 -0.86729081 -0.60184266 -0.33639451 
#>          43          44          45          46          47          48 
#>  0.19450179 -0.19469944 -1.25200657 -0.45117662  1.00878823  1.07515027 
#>          49          50 
#>  2.86692531  0.28329130