| line {stats} | R Documentation |
Robust Line Fitting
Description
Fit a line robustly as recommended in Exploratory Data Analysis.
Currently by default (iter = 1) 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
|
iter |
positive integer specifying the number of
“polishing” iterations. Note that this was hard coded to
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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.
Value
An object of class "tukeyline".
Methods are available for the generic functions coef,
residuals, fitted, and print.
References
Tukey JW (1977). Exploratory Data Analysis, number 2 series Addison-Wesley series in behavioral science. Addison-Wesley Publishing Company. ISBN 9780201076165.
Velleman PF, Hoaglin DC (1981). Applications, Basics, and Computing of Exploratory Data Analysis, series Duxbury series in statistics and decision sciences. Duxbury Press. ISBN 9780878722730. 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.
Johnstone IM, Velleman PF (1985). “The Resistant Line and Related Regression Methods.” Journal of the American Statistical Association, 80(392), 1041–1054. doi:10.1080/01621459.1985.10478222.
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
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