stats (version 3.5.3)

line: Robust Line Fitting

Description

Fit a line robustly as recommended in Exploratory Data Analysis.

Currently the initial median-median line is not iterated (as opposed to Tukey's “resistant line” in the references).

Usage

line(x, y, iter = 1)

Arguments

x, y

the arguments can be any way of specifying x-y pairs. See xy.coords.

iter

positive integer specifying the number of “polishing” iterations. Note that this was hard coded to 1 in R versions before 3.5.0, and more importantly that such simple iterations may not converge, see Siegel's 9-point example.

Value

An object of class "tukeyline".

Methods are available for the generic functions coef, residuals, fitted, and print.

Details

Cases with missing values are omitted.

Contrary to the references where the data is split in three (almost) equally sized groups with symmetric sizes depending on \(n\) and n %% 3 and computes medians inside each group, the line() code splits into three groups using all observations with x[.] <= q1 and x[.] >= q2, where q1, q2 are (a kind of) quantiles for probabilities \(p = 1/3\) and \(p = 2/3\) of the form (x[j1]+x[j2])/2 where j1 = floor(p*(n-1)) and j2 = ceiling(p(n-1)), n = length(x).

Long vectors are not supported yet.

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading Massachusetts: Addison-Wesley.

Velleman, P. F. and Hoaglin, D. C. (1981). Applications, Basics and Computing of Exploratory Data Analysis, Duxbury Press. Chapter 5.

Emerson, J. D. and Hoaglin, D. C. (1983). Resistant Lines for \(y\) versus \(x\). Chapter 5 of Understanding Robust and Exploratory Data Analysis, eds. David C. Hoaglin, Frederick Mosteller and John W. Tukey. Wiley.

Iain M. Johnstone and Paul F. Velleman (1985). The Resistant Line and Related Regression Methods. Journal of the American Statistical Association, 80, 1041--1054. 10.2307/2288572.

See Also

lm.

There are alternatives for robust linear regression more robust and more (statistically) efficient, see rlm() from MASS, or lmrob() from robustbase.

Examples

# NOT RUN {
require(graphics)

plot(cars)
(z <- line(cars))
abline(coef(z))
## Tukey-Anscombe Plot :
plot(residuals(z) ~ fitted(z), main = deparse(z$call))

## Andrew Siegel's pathological 9-point data, y-values multiplied by 3:
d.AS <- data.frame(x = c(-4:3, 12), y = 3*c(rep(0,6), -5, 5, 1))
cAS <- with(d.AS, t(sapply(1:10,
                   function(it) line(x,y, iter=it)$coefficients)))
dimnames(cAS) <- list(paste("it =", format(1:10)), c("intercept", "slope"))
cAS
## iterations started to oscillate, repeating iteration 7,8 indefinitely
# }