Compute Residuals for RegressionScale Models
Description
Computes one of the six types of residuals available for regressionscale models.
Usage
1 2 3 4 
Arguments
object 
an object inheriting from class 
type 
character string; defines the type of residuals, with choices

weighting 
character string; defines the weight matrix that should be used in
the calculation of the residuals and diagnostics. Possible
choices are 
... 
absorbs any additional argument. 
Details
This is a method for the function residuals()
for objects
inheriting from class rsm
. As several types of residuals are
available for rsm
objects, there is an additional optional
argument type
. The "deviance"
, "pearson"
,
"r.star"
, "prob"
and "deletion"
residuals are
derived from the final IRLS fit. The "response"
residuals
are standardized residuals on the scale of the response, the
"prob"
residuals are on the Unif(0,1) scale,
whereas the remaining ones follow approximately the standard normal
distribution.
The default weighting scheme used is "observed"
. The weights
used are the values stored in the q2
component of the
rsm
object. Some of the IRLS weights
returned by rsm
may be negative if the error distribution
is Student's t or userdefined. In order to avoid missing values
in the residuals, the default weighting scheme used is then
"score"
unless otherwise specified. The "score"
weights are also used by default if Huber's least favourable error
distribution is used.
More details, in particular of the use of these residuals, are given in Brazzale (2000, Section 6.3.1).
Value
A numeric vector of residuals. See Davison and Snell (1991) for detailed definitions of each type of residual.
Note
The summary
method for rsm
objects produces
response residuals. The residuals
component of a rsm
object contains the response residuals.
References
Brazzale, A. R. (2000) Practical SmallSample Parametric Inference. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss Federal Institute of Technology Lausanne.
Davison, A. C. and Snell, E. J. (1991) Residuals and diagnostics. In Statistical Theory and Modelling: In Honour of Sir David Cox (eds. D.V. Hinkley, N. Reid, and E.J. Snell), 83–106. London: Chapman \& Hall.
Davison, A. C. and Tsai, C.L. (1992) Regression model diagnostics. Int. Stat. Rev., 60, 337–353.
Jorgensen, B. (1984). The delta algorithm and GLIM. Int. Stat. Rev., 52, 283–300.
See Also
rsm.object
, residuals
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14  ## Sea Level Data
data(venice)
attach(venice)
Year < 1:51/51
c11 < cos(2*pi*1:51/11) ; s11 < sin(2*pi*1:51/11)
c19 < cos(2*pi*1:51/18.62) ; s19 < sin(2*pi*1:51/18.62)
venice.rsm < rsm(sea ~ Year + I(Year^2) + c11 + s11 + c19 + s19,
family = extreme)
##
residuals(venice.rsm)
## deviance residuals with observed weights
residuals(venice.rsm, type = "r.star", weighting = "score")
## r* residuals with score weights
detach()
