pava {Iso}

Linear order isotonic regression.

Description

The “pool adjacent violators algorithm” (PAVA) is applied to calculate the isotonic regression of a set of data, with respect to the usual increasing (or decreasing) linear ordering on the indices.

Usage

pava(y, w, decreasing=FALSE, long.out=FALSE, stepfun=FALSE)
pava.sa(y, w, decreasing=FALSE, long.out=FALSE, stepfun=FALSE)

Arguments

y

Vector of data whose isotonic regression is to be calculated.

w

Optional vector of weights to be used for calculating a weighted isotonic regression; if w is not given, all weights are taken to equal 1.

decreasing

Logical scalar; should the isotonic regression be calculated with respect to decreasing (rather than increasing) order?

long.out

Logical argument controlling the nature of the value returned.

stepfun

Logical scalar; if TRUE a step function representation of the isotonic regression is returned.

Details

The function pava() uses dynamically loading of a fortran subroutine "pava" to effect the computations. The function pava.sa() ("sa" for "stand-alone") does all of the computations in raw R. Thus pava.sa() could be considerably slower for large data sets.

The x values for the step function returned by these functions (if stepfun is TRUE) are thought of as being 1, 2, ..., n=length(y). The knots of the step function are the x values (indices) following changes in the y values (i.e. the starting indices of the level sets, except for the first level set). The y value corresponding to the first level set is the “left hand” value of y or yleft. The step function is formed using the default arguments of stepfun(). In particular it is right continuous.

Value

If long.out is TRUE then the result returned consists of a list whose components are:

y

the fitted values

w

the final weights

tr

a set of indices made up of the smallest index in each level set, which thus "keeps track" of the level sets.

h

a step function which represents the results of the isotonic regression. This component is present only if stepfun is TRUE.

If long.out is FALSE and stepfun is TRUE then only the step function is returned.

If long.out and stepfun are both FALSE then only the vector of fitted values is returned.

Author(s)

Rolf Turner [e-mail]

References

Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference. Wiley, New York.

See Also

ufit() stepfun() biviso()

Examples

# Increasing order:
y <- (1:20) + rnorm(20)
ystar <- pava(y)
plot(y)
lines(ystar,type='s')
# Decreasing order:
z <- NULL
for(i in 4:8) {
	z <- c(z,rep(8-i+1,i)+0.05*(0:(i-1)))
}
zstar <- pava(z,decreasing=TRUE)
plot(z)
lines(zstar,type='s')
# Using the stepfunction:
zstar <- pava(z,decreasing=TRUE,stepfun=TRUE)
plot(z)
plot(zstar,add=TRUE,verticals=FALSE,pch=20,col.points="red")