MASS (version 7.3-66)

lqs: Resistant Regression

Description

Fit a regression to the good points in the dataset, thereby achieving a regression estimator with a high breakdown point. lmsreg and ltsreg are compatibility wrappers.

Usage

lqs(x, ...)
# 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, ...)
lmsreg(...)
ltsreg(...)

Value

An object of class "lqs". This is a list with components

crit

the value of the criterion for the best solution found, in the case of method == "S" before IWLS refinement.

sing

character. A message about the number of samples which resulted in singular fits.

coefficients

of the fitted linear model

bestone

the indices of those points fitted by the best sample found (prior to adjustment of the intercept, if requested).

fitted.values

the fitted values.

residuals

the residuals.

scale

estimate(s) of the scale of the error. The first is based on the fit criterion. The second (not present for method == "S") is based on the variance of those residuals whose absolute value is less than 2.5 times the initial estimate.

Details

Suppose there are n data points and p regressors, including any intercept.

The first three methods minimize some function of the sorted squared residuals. For methods "lqs" and "lms" is the quantile squared residual, and for "lts" it is the sum of the quantile smallest squared residuals. "lqs" and "lms" differ in the defaults for quantile, which are floor((n+p+1)/2) and floor((n+1)/2) respectively. For "lts" the default is floor(n/2) + floor((p+1)/2).

The "S" estimation method solves for the scale s such that the average of a function chi of the residuals divided by s is equal to a given constant.

The control argument is a list with components

psamp:

the size of each sample. Defaults to p.

nsamp:

the number of samples or "best" (the default) or "exact" or "sample". If "sample" the number chosen is min(5*p, 3000), taken from Rousseeuw and Hubert (1997). If "best" exhaustive enumeration is done up to 5000 samples; if "exact" exhaustive enumeration will be attempted however many samples are needed.

adjust:

should the intercept be optimized for each sample? Defaults to TRUE.

References

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.

See Also

predict.lqs

Examples

## IGNORE_RDIFF_BEGIN
set.seed(123) # make reproducible
lqs(stack.loss ~ ., data = stackloss)
lqs(stack.loss ~ ., data = stackloss, method = "S", nsamp = "exact")
## IGNORE_RDIFF_END