R: Examples for 'stats::isoreg'

### ** Examples

require(graphics)

(ir <- isoreg(c(1,0,4,3,3,5,4,2,0)))

Isotonic regression from isoreg(x = c(1, 0, 4, 3, 3, 5, 4, 2, 0)),
  with 2 knots / breaks at obs.nr. 2 9 ;
  initially ordered 'x'
  and further components List of 4
 $ x : num [1:9] 1 2 3 4 5 6 7 8 9
 $ y : num [1:9] 1 0 4 3 3 5 4 2 0
 $ yf: num [1:9] 0.5 0.5 3 3 3 3 3 3 3
 $ yc: num [1:10] 0 1 1 5 8 11 16 20 22 22

plot(ir, plot.type = "row")

(ir3 <- isoreg(y3 <- c(1,0,4,3,3,5,4,2, 3))) # last "3", not "0"

Isotonic regression from isoreg(x = y3 <- c(1, 0, 4, 3, 3, 5, 4, 2, 3)),
  with 3 knots / breaks at obs.nr. 2 5 9 ;
  initially ordered 'x'
  and further components List of 4
 $ x : num [1:9] 1 2 3 4 5 6 7 8 9
 $ y : num [1:9] 1 0 4 3 3 5 4 2 3
 $ yf: num [1:9] 0.5 0.5 3.33 3.33 3.33 ...
 $ yc: num [1:10] 0 1 1 5 8 11 16 20 22 25

(fi3 <- as.stepfun(ir3))

Step function
Call: isoreg(x = y3 <- c(1, 0, 4, 3, 3, 5, 4, 2, 3))
 x[1:3] =      2,      5,      9
4 plateau levels =    0.5,    0.5, 3.3333,    3.5

(ir4 <- isoreg(1:10, y4 <- c(5, 9, 1:2, 5:8, 3, 8)))

Isotonic regression from isoreg(x = 1:10, y = y4 <- c(5, 9, 1:2, 5:8, 3, 8)),
  with 5 knots / breaks at obs.nr. 4 5 6 9 10 ;
  initially ordered 'x'
  and further components List of 4
 $ x : num [1:10] 1 2 3 4 5 6 7 8 9 10
 $ y : num [1:10] 5 9 1 2 5 6 7 8 3 8
 $ yf: num [1:10] 4.25 4.25 4.25 4.25 5 6 6 6 6 8
 $ yc: num [1:11] 0 5 14 15 17 22 28 35 43 46 ...

cat(sprintf("R^2 = %.2f\n",
            1 - sum(residuals(ir4)^2) / ((10-1)*var(y4))))

R^2 = 0.21

## If you are interested in the knots alone :
with(ir4, cbind(iKnots, yf[iKnots]))

     iKnots     
[1,]      4 4.25
[2,]      5 5.00
[3,]      6 6.00
[4,]      9 6.00
[5,]     10 8.00

## 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))))

Examples for 'stats::isoreg'

Isotonic / Monotone Regression