Monotone Regression: Isotonic Regression and Antitonic Regression
monoreg performs monotone regression (either isotonic
or antitonic) with weights.
monoreg(x, y=NULL, w=rep(1, length(x)), type=c("isotonic", "antitonic"))x, y |
coordinate vectors of the regression
points. Alternatively a single “plotting” structure can be
specified: see |
w |
data weights (default values: 1). |
type |
fit a monotonely increasing ("isotonic") or monotonely decreasing ("antitonic") function. |
monoreg is similar to isoreg, with the addition
that monoreg accepts weights.
If several identical x values are given as input, the
corresponding y values and the
weights w are automatically merged, and a warning is issued.
The plot.monoreg function optionally plots the cumulative
sum diagram with the greatest convex minorant (isotonic regression)
or the least concave majorant (antitonic regression), see the
examples below.
A list with the following entries:
x |
the sorted and unique x values |
y |
the corresponding y values |
w |
the corresponding weights |
yf |
the fitted y values |
type |
the type of monotone regression ("isotonic" or "antitonic" |
call |
the function call |
Korbinian Strimmer (http://www.strimmerlab.org).
Part of this function is C code that has been ported from R code originally written by Kaspar Rufibach.
Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order restricted statistical inference. John Wiley and Sons.
# load "fdrtool" library
library("fdrtool")
# an example with weights
# Example 1.1.1. (dental study) from Robertson, Wright and Dykstra (1988)
age = c(14, 14, 8, 8, 8, 10, 10, 10, 12, 12, 12)
size = c(23.5, 25, 21, 23.5, 23, 24, 21, 25, 21.5, 22, 19)
mr = monoreg(age, size)
# sorted x values
mr$x # 8 10 12 14
# weights and merged y values
mr$w # 3 3 3 2
mr$y # 22.50000 23.33333 20.83333 24.25000
# fitted y values
mr$yf # 22.22222 22.22222 22.22222 24.25000
fitted(mr)
residuals(mr)
plot(mr, ylim=c(18, 26)) # this shows the averaged data points
points(age, size, pch=2) # add original data points
###
y = c(1,0,1,0,0,1,0,1,1,0,1,0)
x = 1:length(y)
mr = monoreg(y)
# plot with greatest convex minorant
plot(mr, plot.type="row.wise")
# this is the same
mr = monoreg(x,y)
plot(mr)
# antitonic regression and least concave majorant
mr = monoreg(-y, type="a")
plot(mr, plot.type="row.wise")
# the fit yf is independent of the location of x and y
plot(monoreg(x + runif(1, -1000, 1000),
y +runif(1, -1000, 1000)) )
###
y = c(0,0,2/4,1/5,2/4,1/2,4/5,5/8,7/11,10/11)
x = c(5,9,13,18,22,24,29,109,120,131)
mr = monoreg(x,y)
plot(mr, plot.type="row.wise")
# the fit (yf) only depends on the ordering of x
monoreg(1:length(y), y)$yf
monoreg(x, y)$yfPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.