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\name{lmrob.control}
\title{Tuning Parameters for lmrob() and Auxiliaries}
\encoding{utf8}
\alias{lmrob.control}
\alias{lmrob.control}
\alias{.Mchi.tuning.default}
\alias{.Mpsi.tuning.default}
\alias{.Mchi.tuning.defaults}
\alias{.Mpsi.tuning.defaults}
\description{
Tuning parameters for \code{\link{lmrob}}, the MM-type regression
estimator and the associated S-, M- and D-estimators. Using
\code{setting="KS2011"} sets the defaults as suggested by
Koller and Stahel (2011).
}
\usage{
lmrob.control(setting, seed = NULL, nResample = 500,
tuning.chi = NULL, bb = 0.5, tuning.psi = NULL,
max.it = 50, groups = 5, n.group = 400,
k.fast.s = 1, best.r.s = 2,
k.max = 200, maxit.scale = 200, k.m_s = 20,
refine.tol = 1e-7, rel.tol = 1e-7, solve.tol = 1e-7,
trace.lev = 0,
mts = 1000, subsampling = c("nonsingular", "simple"),
compute.rd = FALSE, method = "MM", psi = "bisquare",
numpoints = 10, cov = NULL,
split.type = c("f", "fi", "fii"), fast.s.large.n = 2000, ...)
.Mchi.tuning.defaults
.Mchi.tuning.default(psi)
.Mpsi.tuning.defaults
.Mpsi.tuning.default(psi)
}
\arguments{
\item{setting}{a string specifying alternative default values. Leave
empty for the defaults or use \code{"KS2011"} for the defaults
suggested by Koller and Stahel (2011). See \emph{Details}.}
\item{seed}{\code{NULL} or an integer vector compatible with
\code{\link{.Random.seed}}: the seed to be used for random
re-sampling used in obtaining candidates for the initial
S-estimator. The current value of \code{.Random.seed} will be
preserved if \code{seed} is set, i.e. non-\code{NULL};
otherwise, as by default, \code{.Random.seed} will be used and
modified as usual from calls to \code{\link{runif}()} etc.
}
\item{nResample}{number of re-sampling candidates to be
used to find the initial S-estimator. Currently defaults to 500
which works well in most situations (see references).}
\item{tuning.chi}{tuning constant vector for the S-estimator. If
\code{NULL}, as by default, sensible defaults are set (depending on
\code{psi}) to yield a 50\% breakdown estimator. See \emph{Details}.}
\item{bb}{expected value under the normal model of the
\dQuote{chi} (rather \eqn{\rho (rho)}{rho}) function with tuning
constant equal to \code{tuning.chi}. This is used to compute the
S-estimator.}
\item{tuning.psi}{tuning constant vector for the redescending
M-estimator. If \code{NULL}, as by default, this is set (depending
on \code{psi}) to yield an estimator with asymptotic efficiency of
95\% for normal errors. See \emph{Details}.}
\item{max.it}{integer specifying the maximum number of IRWLS iterations.}
\item{groups}{(for the fast-S algorithm): Number of
random subsets to use when the data set is large.}
\item{n.group}{(for the fast-S algorithm): Size of each of the
\code{groups} above. Note that this must be at least \eqn{p}.}
\item{k.fast.s}{(for the fast-S algorithm): Number of
local improvement steps (\dQuote{\emph{I-steps}}) for each
re-sampling candidate.}
\item{k.m_s}{(for the M-S algorithm): specifies after how many
unsucessful refinement steps the algorithm stops.}
\item{best.r.s}{(for the fast-S algorithm): Number of
of best candidates to be iterated further (i.e.,
\dQuote{\emph{\bold{r}efined}}); is denoted \eqn{t} in
Salibian-Barrera & Yohai(2006).}
\item{k.max}{(for the fast-S algorithm): maximal number of
refinement steps for the \dQuote{fully} iterated best candidates.}
\item{maxit.scale}{integer specifying the maximum number of C level
\code{find_scale()} iterations.}
\item{refine.tol}{(for the fast-S algorithm): relative convergence
tolerance for the fully iterated best candidates.}
\item{rel.tol}{(for the RWLS iterations of the MM algorithm): relative
convergence tolerance for the parameter vector.}
\item{solve.tol}{(for the S algorithm): relative
tolerance for inversion. Hence, this corresponds to
\code{\link{solve.default}()}'s \code{tol}.}
\item{trace.lev}{integer indicating if the progress of the MM-algorithm
should be traced (increasingly); default \code{trace.lev = 0} does
no tracing.}
\item{mts}{maximum number of samples to try in subsampling
algorithm.}
\item{subsampling}{type of subsampling to be used, a string:
\code{"simple"} for simple subsampling (default prior to version 0.9),
\code{"nonsingular"} for nonsingular subsampling. See also
\code{\link{lmrob.S}}.}
\item{compute.rd}{logical indicating if robust distances (based on
the MCD robust covariance estimator \code{\link{covMcd}}) are to be
computed for the robust diagnostic plots. This may take some
time to finish, particularly for large data sets, and can lead to
singularity problems when there are \code{\link{factor}} explanatory
variables (with many levels, or levels with \dQuote{few}
observations). Hence, is \code{FALSE} by default.}
\item{method}{string specifying the estimator-chain. \code{MM}
is interpreted as \code{SM}. See \emph{Details} of
\code{\link{lmrob}} for a description of the possible values.}
\item{psi}{string specifying the type \eqn{\psi}-function
used. See \emph{Details} of \code{\link{lmrob}}. Defaults to
\code{"bisquare"} for S and MM-estimates, otherwise \code{"lqq"}.}
\item{numpoints}{number of points used in Gauss quadrature.}
\item{cov}{function or string with function name to be used to
calculate covariance matrix estimate. The default is
\code{if(method \%in\% c('SM', 'MM')) ".vcov.avar1" else ".vcov.w"}.
See \emph{Details} of \code{\link{lmrob}}.}
\item{split.type}{determines how categorical and continuous variables
are split. See \code{\link{splitFrame}}.}
\item{fast.s.large.n}{minimum number of observations required to
switch from ordinary \dQuote{fast S} algorithm to an efficient
\dQuote{large n} strategy.}
\item{...}{further arguments to be added as \code{\link{list}}
components to the result, e.g., those to be used in \code{.vcov.w()}.}
}
\value{
\code{.Mchi.tuning.default(psi)} and \code{.Mpsi.tuning.default(psi)}
return a short \code{\link{numeric}} vector of tuning constants which
are defaults for the corresponding psi-function, see the \emph{Details}.
They are based on the named \code{\link{list}}s
\code{.Mchi.tuning.defaults} and \code{.Mpsi.tuning.defaults},
respectively.
\code{lmrob.control()} returns a named \code{\link{list}} with over
twenty components, corresponding to the arguments, where
\code{tuning.psi} and \code{tuning.chi} are typically computed, as
\code{.Mpsi.tuning.default(psi)} or \code{.Mchi.tuning.default(psi)},
respectively.
}
\details{The option \code{setting="KS2011"} alters the default
arguments. They are changed to \code{method = 'SMDM', psi = 'lqq',
max.it = 500, k.max = 2000, cov = '.vcov.w'}. The defaults of all
the remaining arguments are not changed.
By default, and in \code{.Mpsi.tuning.default()} and \code{.Mchi.tuning.default()},
\code{tuning.chi} and \code{tuning.psi} are set to
yield an MM-estimate with break-down point \eqn{0.5} and efficiency of
95\% at the normal.
To get these defaults, e.g., \code{.Mpsi.tuning.default(psi)} is
equivalent to but more efficient than the formerly widely used
\code{lmrob.control(psi = psi)$tuning.psi}.
These defaults are:
\tabular{rll}{
\code{psi} \tab \code{tuning.chi} \tab \code{tuning.psi} \cr
\code{bisquare} \tab \code{1.54764} \tab \code{4.685061} \cr
\code{welsh} \tab \code{0.5773502} \tab \code{2.11} \cr
\code{ggw} \tab \code{c(-0.5, 1.5, NA, 0.5)} \tab
\code{c(-0.5, 1.5, 0.95, NA)} \cr
\code{lqq} \tab \code{c(-0.5, 1.5, NA, 0.5)} \tab
\code{c(-0.5, 1.5, 0.95, NA)} \cr
\code{optimal} \tab \code{0.4047} \tab \code{1.060158} \cr
\code{hampel} \tab \code{c(1.5, 3.5, 8)*0.2119163} \tab
\code{c(1.5, 3.5, 8)*0.9014}
}
The values for the tuning constant for the \code{ggw} psi function are
hard coded. The constants vector has four elements: minimal slope, b
(controlling the bend at the maximum of the curve), efficiency,
break-down point. Use \code{NA} for an unspecified value, see examples
in the tables.
The constants for the \code{"hampel"} psi function are chosen to have a
redescending slope of \eqn{-1/3}. Constants for a slope of \eqn{-1/2}
would be
\tabular{rll}{
\code{psi} \tab \code{tuning.chi} \tab \code{tuning.psi} \cr
\code{"hampel"} \tab \code{c(2, 4, 8) * 0.1981319} \tab
\code{c(2, 4, 8) * 0.690794}
}
Alternative coefficients for an efficiency of 85\%
at the normal are given in the table below.
\tabular{rl}{
\code{psi} \tab \code{tuning.psi} \cr
\code{bisquare} \tab \code{3.443689} \cr
\code{welsh} \tab \code{1.456} \cr
\code{ggw}, \code{lqq} \tab \code{c(-0.5, 1.5, 0.85, NA)} \cr
\code{optimal} \tab \code{0.8684} \cr
\code{hampel} (-1/3) \tab \code{c(1.5, 3.5, 8)* 0.5704545} \cr
\code{hampel} (-1/2) \tab \code{c( 2, 4, 8) * 0.4769578}
}
}
\references{
Koller, M. and Stahel, W.A. (2011)
Sharpening Wald-type inference in robust regression for small samples.
\emph{Computational Statistics & Data Analysis} \bold{55}(8), 2504--2515.
}
\author{ Matias Salibian-Barrera, Martin Maechler and Manuel Koller}
\seealso{ \code{\link{lmrob}}, also for references and examples.
}
\examples{
## Show the default settings:
str(lmrob.control())
## Artificial data for a simple "robust t test":
set.seed(17)
y <- y0 <- rnorm(200)
y[sample(200,20)] <- 100*rnorm(20)
gr <- as.factor(rbinom(200, 1, prob = 1/8))
lmrob(y0 ~ 0+gr)
## Use Koller & Stahel(2011)'s recommendation but a larger 'max.it':
str(ctrl <- lmrob.control("KS2011", max.it = 1000))
str(.Mpsi.tuning.defaults)
stopifnot(identical(.Mpsi.tuning.defaults,
sapply(names(.Mpsi.tuning.defaults),
.Mpsi.tuning.default)))
}
\keyword{robust}
\keyword{regression}
|
