qresiduals {topmodels}R Documentation

(Randomized) Quantile Residuals

Description

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

Usage

qresiduals(object, ...)

## Default S3 method:
qresiduals(object, newdata = NULL, trafo = qnorm,
  type = c("random", "quantile"), nsim = 1L, prob = 0.5, ...)

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.

newdata

optionally, a data frame in which to look for variables with which to predict. If omitted, the original observations are used.

trafo

function for tranforming residuals from probability scale to a different distribution scale (default: Gaussian).

type

character specifying whether - in the case of discrete response distributions - randomized quantile residuals or their corresponding quantiles should be computed.

nsim

numeric. The number of simulated randomized quantile residuals per observation (for type = "numeric").

prob

numeric. The probabilities at which quantile residuals should be computed (for type = "quantile"), defaulting to the median.

...

further parameters passed to methods.

Details

(Randomized) quantile residuals have been suggested by Dunn and Smyth (1996). For regression models with a continuous response distribution this simply computes theoretical standard normal quantiles corresponding to the probability integral transform of the fitted distribution. For discrete distributions, a random theoretical normal quantile is drawn from the range of probabilities corresponding to each observation. Hence, in qqrplot the default is to use trafo = qnorm but other transformations can also be used, specifically using the uniform probability scale (via trafo = NULL or equivalently qunif or identity).

The default qresiduals method can compute randomized quantile residuals from a vector (which essentially just calls qnorm) or a 2-column matrix of probabilities. The latter offers to either draw "random" samples from the distribution or compute corresponding "quantile"s such as the median etc.

Value

A vector or matrix of quantile residuals.

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, 1–10.

See Also

qnorm, qqrplot

Examples

## linear regression models (homoscedastic Gaussian response)
m <- lm(dist ~ speed, data = cars)
qresiduals(m)

[Package topmodels version 0.0-1 Index]