R: Minimum absolute residual (L1) regression

l1fit {L1pack} | R Documentation

## Minimum absolute residual (L1) regression

### Description

Performs an L1 regression on a matrix of explanatory variables and a vector of responses.

### Usage

    l1fit(x, y, intercept = TRUE, tolerance = 1e-07, print.it = TRUE)

### Arguments

`x` | vector or matrix of explanatory variables. Each row corresponds to an observation and each column to a variable. The number of rows of `x` should equal the number of data values in `y`, and there should be fewer columns than rows. Missing values are not allowed.
`y` | numeric vector containing the response. Missing values are not allowed.
`intercept` | logical flag. If TRUE, an intercept term is included in the regression model.
`tolerance` | numerical value used to test for singularity in the regression.
`print.it` | logical flag. If TRUE, then warnings about non-unique solutions and rank deficiency are given.

### Details

The Barrodale-Roberts algorithm, which is a specialized linear programming algorithm, is used.

### Value

list defining the regression (compare with function `lsfit`).

`coefficients` | vector of coefficients.
`residuals` | residuals from the fit.
`message` | vector of one or two character strings stating whether a non-unique solution is possible, or if the x matrix was found to be rank deficient.

### References

Barrodale, I., and Roberts, F.D.K. (1973). An improved algorithm for discrete L1 linear approximations. SIAM Journal of Numerical Analysis 10, 839-848.

Barrodale, I., and Roberts, F.D.K. (1974). Solution of an overdetermined system of equations in the L1 norm. Communications of the ACM 17, 319-320.

Bloomfield, P., and Steiger, W.L. (1983). Least Absolute Deviations: Theory, Applications, and Algorithms. Birkhauser, Boston, Mass.

### Examples

    l1fit(stack.x, stack.loss)

[Package L1pack version 0.40 Index]