Fit a regression to the good points in the dataset, thereby
achieving a regression estimator with a high breakdown point.
ltsreg are compatibility wrappers.
# S3 method for formula lqs(formula, data, ..., method = c("lts", "lqs", "lms", "S", "model.frame"), subset, na.action, model = TRUE, x.ret = FALSE, y.ret = FALSE, contrasts = NULL)
# S3 method for default lqs(x, y, intercept = TRUE, method = c("lts", "lqs", "lms", "S"), quantile, control = lqs.control(...), k0 = 1.548, seed, ...)
An object of class
"lqs". This is a list with components
the value of the criterion for the best solution found, in
the case of
method == "S" before IWLS refinement.
character. A message about the number of samples which resulted in singular fits.
of the fitted linear model
the indices of those points fitted by the best sample found (prior to adjustment of the intercept, if requested).
the fitted values.
estimate(s) of the scale of the error. The first is based
on the fit criterion. The second (not present for
"S") is based on the variance of those residuals whose absolute
value is less than 2.5 times the initial estimate.
a formula of the form
y ~ x1 + x2 + ....
an optional data frame, list or environemnt from which
variables specified in
formula are preferentially to be taken.
an index vector specifying the cases to be used in fitting. (NOTE: If given, this argument must be named exactly.)
function to specify the action to be taken if
NAs are found. The default action is for the procedure to
fail. Alternatives include
na.exclude, which lead to omission of
cases with missing values on any required variable. (NOTE: If
given, this argument must be named exactly.)
TRUE the model frame,
the model matrix and the response are returned, respectively.
an optional list. See the
a matrix or data frame containing the explanatory variables.
the response: a vector of length the number of rows of
should the model include an intercept?
the method to be used.
model.frame returns the model frame: for the
others see the
Details section. Using
the quantile to be used: see
Details. This is over-ridden if
method = "lms".
additional control items: see
the cutoff / tuning constant used for \(\chi()\)
and \(\psi()\) functions when
method = "S", currently
corresponding to Tukey's ‘biweight’.
the seed to be used for random sampling: see
current value of
.Random.seed will be preserved if it is set..
arguments to be passed to
control above and
Suppose there are
n data points and
including any intercept.
The first three methods minimize some function of the sorted squared
residuals. For methods
"lms" is the
quantile squared residual, and for
"lts" it is the sum
quantile smallest squared residuals.
"lms" differ in the defaults for
quantile, which are
"lts" the default is
floor(n/2) + floor((p+1)/2).
"S" estimation method solves for the scale
such that the average of a function chi of the residuals divided
s is equal to a given constant.
control argument is a list with components
the size of each sample. Defaults to
the number of samples or
"sample" the number chosen is
taken from Rousseeuw and Hubert (1997).
"best" exhaustive enumeration is done up to 5000 samples;
"exact" exhaustive enumeration will be attempted however
many samples are needed.
should the intercept be optimized for each
sample? Defaults to
P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.
A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth and Brooks/Cole.
P. Rousseeuw and M. Hubert (1997) Recent developments in PROGRESS. In L1-Statistical Procedures and Related Topics, ed Y. Dodge, IMS Lecture Notes volume 31, pp. 201--214.