rlm(x, ...)
rlm.formula(formula, data, weights, ..., subset, na.action = na.fail,
method = c("M", "MM", "model.frame"),
wt.method = c("case", "inv.var"),
model = TRUE, x.ret = TRUE, y.ret = FALSE, contrasts = NULL)
rlm.default(x, y, weights, ..., w = rep(1, nrow(x)),
init, psi = psi.huber, scale.est, k2 = 1.345,
method = c("M", "MM"), wt.method = c("case", "inv.var"),
maxit = 20, acc = 1e-4, test.vec = "resid")
y ~ x1 + x2 + ....
formula are
preferentially to be taken.
NAs are found. The
default action is for the procedure to fail. An alternative is
na.omit, which leads to omission of cases with missing values on any
required variable.
x.
lm.
coef component. Known
methods are
"ls" (the default) for an initial least-squares fit
using weights
w*weights, and
"lqs" for an unweighted least-trimmed
squares fit with 200 samples.
g(x, ..., deriv) that for
deriv=0
returns psi(x)/x and for
deriv=1 returns psi(x). Tuning constants
will be passed in via
....
rlm.default or to the
psi
function.
"rlm" inheriting from
"lm".
The additional components not in an
lm object are
Fitting is done by iterated re-weighted least squares (IWLS).
Psi functions are supplied for the Huber, Hampel and Tukey bisquare
proposals as
psi.huber,
psi.hampel and
psi.bisquare. Hubers 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 >> 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.
P. J. Huber (1981)
Robust Statistics.
Wiley.
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.
stackloss <- data.frame(stack.x, stack.loss) summary(rlm(stack.loss ~ ., stackloss)) rlm(stack.loss ~ ., stackloss, psi = psi.hampel, init = "lts") rlm(stack.loss ~ ., stackloss, psi = psi.bisquare)