ltsReg {rrcov}R Documentation

Robust regression with high breakdown point


Carries out least trimmed squares (LTS) regression.


ltsReg(x, y, intercept=TRUE, alpha=NULL, nsamp=500, adjust=FALSE, mcd=TRUE, qr.out=FALSE, yname=NULL, seed=0)


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 itted; otherwise no constant term will be included. Default is intercept = TRUE
alpha the percentage of squared residuals whose sum will be minimized. Its default value is 0.5. In general, alpha must be a value between 0.5 and 1.
nsamp number of subsets used for initial estimates. Default is nsamp = 500
adjust whether to perform intercept adjustment at each step. This could be quite time consuming, therefore the default is adjust = FALSE
mcd whether to compute robust distances using Fast-MCD.
qr.out whether to return the QR decomposition. Default is qr.out = FALSE
yname the name of the dependent variable. Default is yname = NULL
seed starting value for random generator. Default is seed = 0


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 computations are performed using the Fast LTS algorithm proposed by Rousseeuw and Van Driessen (1999).


An object of class '"lts"'. This is a list with 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,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.
rsquared robust version of R squared.
alpha same as the input parameter alpha.
quan the number h of observations that have determined the least trimmed squares estimator
intercept same as the input parameter intercept.
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.
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.


p. j. Rousseeuw (1984), Least Median of Squares Regression. Journal of the American Statistical Association, 79, pp. 871-881.

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

P. J. Rousseeuw and K. van Driessen (1999) Computing LTS Regression for Large Data Sets, Technical Report, University of Antwerp, submitted

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



ltsReg(heart.x, heart.y)

[Package rrcov version 0.2-5 Index]