fdrtool (version 1.1.0)

monoreg: Monotonic Regression

Description

monoreg performs monotonic regression (either isotonic or antitonic) with weights.

Usage

monoreg(x, y=NULL, w=rep(1, length(x)), type=c("isotonic", "antitonic"))

Arguments

x, y

coordinate vectors of the regression points. Alternatively a single plotting structure can be specified: see xy.coords.

w

data weights (default values: 1).

type

fit a monontonely increasing ("isotonic") or monotonely decreasing ("antitonic") function.

Value

• 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 monotonic regression ("isotonic" or "antitonic"
• call
  the function call

Details

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.

References

Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order restricted statistical inference. John Wiley and Sons.

See Also

isoreg.

Examples

# 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)$yf 
monoreg(x, y)$yf