Function to compute quantile and response residuals.

# S3 method for bamlss
residuals(object, type = c("quantile", "response"),
nsamps = NULL, ...)
# S3 method for bamlss.residuals
plot(x, which = c("hist-resid", "qq-resid"),
spar = TRUE, ...)

## Arguments

object |
An object of class `"bamlss"` . |

type |
The type of residuals wanted, possible types are
`"quantile"` residuals and `"response"` residuals. |

nsamps |
If the fitted `bamlss` object contains samples of parameters,
computing residuals may take quite some time. Therefore, to get a first feeling it can
be useful to compute residuals only based on `nsamps` samples, i.e., `nsamps`
specifies the number of samples which are extracted on equidistant intervals. |

x |
Object returned from function `residuals.bamlss()` . |

which |
Should a histogram with kernel density estimates be plotted or a qq-plot? |

spar |
Should graphical parameters be set by the plotting function? |

… |
For function `residuals.bamlss()` arguments passed to possible
`$residuals()` functions that may be part of a `bamlss.family` . For function
`plot.bamlss.residuals()` arguments passed to function
`hist.default` and `qqnorm.default` . |

## Details

Response residuals are the raw residuals, i.e., the response data minus the fitted distributional
mean. If the `bamlss.family`

object contains a function `$mu(par, …)`

, then
raw residuals are computed with `y - mu(par)`

where `par`

is the named list of fitted
values of distributional parameters. If `$mu(par, ...)`

is missing, then the fitted values
of the first distributional parameter are used.

Randomized quantile residuals are based on the cumulative distribution function of the
`bamlss.family`

object, i.e., the `$p(y, par, ...)`

function.

## Value

A vector of residuals.

## References

Dunn P. K., and Smyth G. K. (1996). Randomized Quantile Residuals.
*Journal of Computational and Graphical Statistics* **5**, 236-244.

## See also

## Examples

# NOT RUN {
## Generate data.
d <- GAMart()
## Estimate models.
b1 <- bamlss(num ~ s(x1), data = d)
b2 <- bamlss(num ~ s(x1) + s(x2) + s(x3), data = d)
## Extract quantile residuals.
e1 <- residuals(b1, type = "quantile")
e2 <- residuals(b2, type = "quantile")
## Plots.
plot(e1)
plot(e2)
# }