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Last data update: 2014.03.03

R: Minimum absolute residual (L1) regression

l1fit

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)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(L1pack)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/L1pack/l1fit.Rd_%03d_medium.png", width=480, height=480)
> ### Name: l1fit
> ### Title: Minimum absolute residual (L1) regression
> ### Aliases: l1fit
> ### Keywords: regression
> 
> ### ** Examples
> 
> l1fit(stack.x, stack.loss)
$coefficients
   Intercept     Air.Flow   Water.Temp   Acid.Conc. 
-39.68985367   0.83188403   0.57391310  -0.06086957 

$minimum
[1] 42.08116

$fitted.values
 [1] 36.939131 37.000000 31.571015 20.365218 19.217392 19.791305 20.000001
 [8] 20.000001 16.463769 14.020290 13.472464 12.959421 13.898551 13.802899
[15]  6.817392  7.000001  8.426088  8.000001  8.513044 13.382609 24.481160

$residuals
 [1]  5.0608706  0.0000000  5.4289861  7.6347828 -1.2173911 -1.7913042
 [7] -1.0000000  0.0000000 -1.4637681 -0.0202896  0.5275363  0.0405799
[13] -2.8985507 -1.8028984  1.1826082  0.0000000 -0.4260873  0.0000000
[19]  0.4869561  1.6173913 -9.4811592

$rank
[1] 4

$numIter
[1] 7

$info
[1] 1

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>