# lmrob.lar: Least Absolute Residuals / L1 Regression In robustbase: Basic Robust Statistics

## Description

To compute least absolute residuals (LAR) or “L1” regression, `lmrob.lar` implements the routine L1 in Barrodale and Roberts (1974), which is based on the simplex method of linear programming. It is a copy of `lmRob.lar` (in early 2012) from the robust package.

## Usage

 `1` ```lmrob.lar(x, y, control, ...) ```

## Arguments

 `x` numeric matrix for the predictors. `y` numeric vector for the response. `control` `list` as returned by `lmrob.control()` . `...` (unused but needed when called as `init(x,y,ctrl, mf)` from `lmrob()`)

## Details

This method is used for computing the M-S estimate and typically not to be used on its own.

A description of the Fortran subroutines used can be found in Marazzi (1993). In the book, the main method is named `RILARS`.

## Value

A list that includes the following components:

 `coef ` The L1-estimate of the coefficient vector `scale ` The residual scale estimate (mad) `resid ` The residuals `iter ` The number of iterations required by the simplex algorithm `status ` Return status (0: optimal, but non unique solution, 1: optimal unique solution) `converged ` Convergence status (always `TRUE`), needed for `lmrob.fit`.

Manuel Koller

## References

Marazzi, A. (1993). Algorithms, routines, and S functions for robust statistics. Wadsworth & Brooks/Cole, Pacific Grove, CA.

`rq` from package quantreg.
 ```1 2 3 4 5 6 7 8 9``` ```data(stackloss) X <- model.matrix(stack.loss ~ . , data = stackloss) y <- stack.loss (fm.L1 <- lmrob.lar(X, y)) with(fm.L1, stopifnot(converged , status == 1L , all.equal(scale, 1.5291576438) , sum(abs(residuals) < 1e-15) == 4 # p=4 exactly fitted obs. )) ```