| isoreg {stats} | R Documentation |
Compute the isotonic (monotonely increasing nonparametric) least squares regression which is piecewise constant.
isoreg(x, y = NULL)
x, y |
coordinate vectors of the regression points. Alternatively a single
plotting structure can be specified: see |
The algorithm determines the convex minorant m(x) of the
cumulative data (i.e., cumsum(y)) which is piecewise
linear and the result is m'(x), a step function with level
changes at locations where the convex m(x) touches the
cumulative data polygon and changes slope.
as.stepfun() returns a stepfun
object which can be more parsimonious.
isoreg() returns an object of class isoreg which is
basically a list with components
x |
original (constructed) abscissa values |
y |
corresponding y values. |
yf |
fitted values corresponding to ordered x values. |
yc |
cumulative y values corresponding to ordered x values. |
iKnots |
integer vector giving indices where the fitted curve jumps, i.e., where the convex minorant has kinks. |
isOrd |
logical indicating if original x values were ordered increasingly already. |
ord |
|
call |
the |
The code should be improved to accept weights additionally and
solve the corresponding weighted least squares problem.
‘Patches are welcome!’
Barlow, R. E., Bartholomew, D. J., Bremner, J. M., and Brunk, H. D. (1972) Statistical inference under order restrictions; Wiley, London.
Robertson, T., Wright, F. T. and Dykstra, R. L. (1988) Order Restricted Statistical Inference; Wiley, New York.
the plotting method plot.isoreg with more examples;
isoMDS() from the MASS package internally
uses isotonic regression.
require(graphics)
(ir <- isoreg(c(1,0,4,3,3,5,4,2,0)))
plot(ir, plot.type = "row")
(ir3 <- isoreg(y3 <- c(1,0,4,3,3,5,4,2, 3))) # last "3", not "0"
(fi3 <- as.stepfun(ir3))
(ir4 <- isoreg(1:10, y4 <- c(5, 9, 1:2, 5:8, 3, 8)))
cat(sprintf("R^2 = %.2f\n",
1 - sum(residuals(ir4)^2) / ((10-1)*var(y4))))
## If you are interested in the knots alone :
with(ir4, cbind(iKnots, yf[iKnots]))
## Example of unordered x[] with ties:
x <- sample((0:30)/8)
y <- exp(x)
x. <- round(x) # ties!
plot(m <- isoreg(x., y))
stopifnot(all.equal(with(m, yf[iKnots]),
as.vector(tapply(y, x., mean))))