rlm(x, ...)## S3 method for class 'formula':
rlm(formula, data, weights, \dots, subset, na.action,
method = c("M", "MM", "model.frame"),
wt.method = c("inv.var", "case"),
model = TRUE, x.ret = TRUE, y.ret = FALSE, contrasts = NULL)
## S3 method for class 'default':
rlm(x, y, weights, \dots, w = rep(1, nrow(x)),
init = "ls", psi = psi.huber,
scale.est = c("MAD", "Huber", "proposal 2"), k2 = 1.345,
method = c("M", "MM"), wt.method = c("inv.var", "case"),
maxit = 20, acc = 1e-4, test.vec = "resid", lqs.control = NULL)
psi.huber(u, k = 1.345, deriv = 0)
psi.hampel(u, a = 2, b = 4, c = 8, deriv = 0)
psi.bisquare(u, c = 4.685, deriv = 0)
y ~ x1 + x2 + ...
.formula
are
preferentially to be taken.NA
s are found.
The na.omit
, and can be changed by
x
.formula
method only) find the model frame. MM-estimation
is M-estimation with Tukey's biweight initialized by a specific
S-estimator. See the lm
.coef
component. Known
methods are "ls"
(the default) for an initial least-squares fit
using weights g(x, ..., deriv)
that for
deriv=0
returns psi(x)/x and for deriv=1
returns
psi'(x). Tuning constants will be pa"Huber"
or "proposal 2"
).rlm.default
or to the psi
function.lqs
.0
or 1
: compute values of the psi function or of its
first derivative."rlm"
inheriting from "lm"
.
The additional components not in an lm
object are"inv.var"
weights only. Psi functions are supplied for the Huber, Hampel and Tukey bisquare
proposals as psi.huber
, psi.hampel
and
psi.bisquare
. Huber's corresponds to a convex optimization
problem and gives a unique solution (up to collinearity). The other
two will have multiple local minima, and a good starting point is
desirable.
Selecting method = "MM"
selects a specific set of options which
ensures that the estimator has a high breakdown point. The initial set
of coefficients and the final scale are selected by an S-estimator
with k0 = 1.548
; this gives (for $n \gg p$)
breakdown point 0.5.
The final estimator is an M-estimator with Tukey's biweight and fixed
scale that will inherit this breakdown point provided c > k0
;
this is true for the default value of c
that corresponds to
95% relative efficiency at the normal. Case weights are not
supported for method = "MM"
.
F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw and W. A. Stahel (1986) Robust Statistics: The Approach based on Influence Functions. Wiley.
A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth & Brooks/Cole.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
lm
, lqs
.summary(rlm(stack.loss ~ ., stackloss))
rlm(stack.loss ~ ., stackloss, psi = psi.hampel, init = "lts")
rlm(stack.loss ~ ., stackloss, psi = psi.bisquare)
Run the code above in your browser using DataCamp Workspace