Hello,

Fitting a piecewise smooth curve to a set of points (and a piecewise

linear function in particular) seems to be a recurring question on

this list. Nevertheless, I was not able to find an answer to a

question that bothers me.

Suppose I have the following data set, and would want to fit it with a

piecewise smooth curve, In this model data, one curve is valid for up

to 3 and another one for onwards. However, suppose I don't have this

data.

x <- 0:8

y <- c(0.5, 0.5, 0.5, 0.5, 1.914214, 2.5, 2.949490, 3.328427, 3.662278)

plot(x, y)

# Neither of these seem to work

f <- function(x, x0, y0, k) { ifelse(x < x0, y0, y0 + sqrt(k*(x-x0))) }

# f <- function(x, x0, y0, k) { (x < x0)*y0 + (x >= x0)*(y0 + sqrt(k*(x-x0))) }

fmodel <- nls(y ~ f(x, x0, y0, k), start = list(x0 = 1, y0 = 1, k = 1))

What's the proper way to deal with such a case? Am I supposed to

somehow obtain the break point separately, and then fit only y0 and k?

What is the preferred method for obtaining break point (I am not even

sure if I am using this term correctly).

Thanks in advance,

Primož

--

Primož Peterlin, Inštitut za biofiziko, Med. fakulteta, Univerza v Ljubljani

Lipičeva 2, SI-1000 Ljubljana, Slovenija.

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