How to make monotonic (increasing) smooth spline with smooth.spline() function?

Question

I have data that are strictly increasing and would like to fit a smoothing spline that is monotonically increasing as well with the smooth.spline() function if possible, due to the ease of use of this function.

For example, my data can be effectively reproduced with the example:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")

which is not necessarily increasing everywhere. Any suggestions?

Answer 1

You could use shape-constrained splines for this, e.g. using the scam package:

require(scam)
fit = scam(testy~s(testx, k=100, bs="mpi", m=5), 
            family=gaussian(link="identity"))
plot(testx,testy)
lines(testx,predict(fit),col="red")

Or if you would like to use L1 loss as opposed to L2 loss, which is less sensitive to outliers, you could also use the cobs package for this...

Advantage of this method compared to the solution above is that it also works if the original data perhaps are not 100% monotone due to the presence of noise...

Answer 2

This doesn't use smooth.spline() but the splinefun(..., method="hyman") will fit a monotonically increasing spline and is also easy to use. So for example:

testx <- 1:100
testy <- abs(rnorm(length(testx)))^3
testy <- cumsum(testy)
plot(testx,testy)
sspl <- smooth.spline(testx,testy)
lines(sspl,col="blue")
tmp <- splinefun(x=testx, y=cumsum(testy), method="hyman")
lines(testx[-1], diff(tmp(testx)), col="red")

Yields the following figure (red are the values from the monotonically increasing spline)

From the help file of splinefun: "Method "hyman" computes a monotone cubic spline using Hyman filtering of an method = "fmm" fit for strictly monotonic inputs. (Added in R 2.15.2.)"