robustbase (version 0.2-7)

ltsReg: Least Trimmed Squares Robust (High Breakdown) Regression

Description

Carries out least trimmed squares (LTS) robust (high breakdown point) regression.

Usage

ltsReg(x, ...)

## S3 method for class 'formula':
ltsReg(formula, data, subset, weights, na.action,
       model = TRUE, x.ret = FALSE, y.ret = FALSE,
       contrasts = NULL, offset, \dots)

## S3 method for class 'default':
ltsReg(x, y, intercept = TRUE, alpha = 1/2, nsamp = 500,
       adjust = FALSE, mcd = TRUE, qr.out = FALSE, yname = NULL,
       seed = NULL, use.correction=TRUE, control, \dots)

Arguments

formula

a formula of the form y ~ x1 + x2 + ....

data

data frame from which variables specified in formula are to be taken.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. NO USED YET.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is

model, x.ret, y.ret

logicals indicating if the model frame, the model matrix and the response are to be returned, respectively.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. An offset term can be included in the formula instead or as well, and i

x

a matrix or data frame containing the explanatory variables.

y

the response: a vector of length the number of rows of x.

intercept

if true, a model with constant term will be estimated; otherwise no constant term will be included. Default is intercept = TRUE

alpha

the percentage of squared residuals whose sum will be minimized, by default 0.5. In general, alpha must between 0.5 and 1.

nsamp

number of subsets used for initial estimates or "best" or "exact". Default is nsamp = 500. For nsamp="best" exhaustive enumeration is done, as long as the number of trials does not excee

adjust

whether to perform intercept adjustment at each step. Since this can be time consuming, the default is adjust = FALSE.

mcd

whether to compute robust distances using Fast-MCD.

qr.out

whether to return the QR decomposition (see qr); defaults to false.

yname

the name of the dependent variable. Default is yname = NULL

seed

initial seed for random generator, see rrcov.control.

use.correction

whether to use finite sample correction factors. Default is use.correction=TRUE

control

a list with estimation options - same as these provided in the function specification. If the control object is supplied, the parameters from it will be used. If parameters are passed also in the invocation statement, they will override the cor

...

arguments passed to or from other methods.

Value

• The function ltsReg returns an object of class "lts". The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted.values and residuals extract various useful features of the value returned by ltsReg. An object of class lts is a list containing at least the following components:
• crit
  the value of the objective function of the LTS regression method, i.e., the sum of the $h$ smallest squared raw residuals.
• coefficients
  vector of coefficient estimates (including the intercept by default when intercept=TRUE), obtained after reweighting.
• best
  the best subset found and used for computing the raw estimates. The size of best is equal to quan.
• fitted.values
  vector like y containing the fitted values of the response after reweighting.
• residuals
  vector like y containing the residuals from the weighted least squares regression.
• scale
  scale estimate of the reweighted residuals.
• alpha
  same as the input parameter alpha.
• quan
  the number $h$ of observations which have determined the least trimmed squares estimator.
• intercept
  same as the input parameter intercept.
• cnp2
  a vector of length two containing the consistency correction factor and the finite sample correction factor of the final estimate of the error scale.
• raw.coefficients
  vector of raw coefficient estimates (including the intercept, when intercept=TRUE).
• raw.scale
  scale estimate of the raw residuals.
• raw.resid
  vector like y containing the raw residuals from the regression.
• raw.cnp2
  a vector of length two containing the consistency correction factor and the finite sample correction factor of the raw estimate of the error scale.
• lts.wt
  vector like y containing weights that can be used in a weighted least squares. These weights are 1 for points with reasonably small raw residuals, and 0 for points with large raw residuals.
• method
  character string naming the method (Least Trimmed Squares).
• X
  the input data as a matrix.
• Y
  the response variable as a vector.

concept

High breakdown point

Details

The LTS regression method minimizes the sum of the h smallest squared residuals, where h must be at least half the number of observations. The default value of h is roughly 0.5n where n is the total number of observations, but the user may choose any value between n/2 and n. The LTS estimate of the error scale is given by the minimum of the objective function multiplied by a consistency factor and a finite sample correction factor - see Pison et al. (2002) for details. The rescaling factors for the raw and final estimates are returned also in the vectors raw.cnp2 and cnp2 of length 2 respectively. The finite sample corrections can be suppressed by setting use.correction=FALSE. The computations are performed using the Fast LTS algorithm proposed by Rousseeuw and Van Driessen (1999). As always, the formula interface has an implied intercept term which can be removed either by y ~ x - 1 or y ~ 0 + x. See formula for more details.

References

Peter J. Rousseeuw (1984), Least Median of Squares Regression. Journal of the American Statistical Association 79, 871--881. P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley. P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223. Pison, G., Van Aelst, S., and Willems, G. (2002) Small Sample Corrections for LTS and MCD. Metrika 55, 111-123.

See Also

lmrob.S() provides a fast S estimator with similar breakdown point as ltsReg() but better efficiency. For data analysis, rather use lmrob which is based on lmrob.S. covMcd; summary.lts for summaries. The generic functions coef, residuals, fitted.

Examples

data(heart)
## Default method works with 'x'-matrix and y-var:
heart.x <- data.matrix(heart[, 1:2]) # the X-variables
heart.y <- heart[,"clength"]
ltsReg(heart.x, heart.y)

data(stackloss)
ltsReg(stack.loss ~ ., data = stackloss)