How to fit data with non linear function and plot data and fit with ggplot()

Question

A measurement shows a signal that is formed like a square root function with offset and a factor. How can I find the coefficients and plot the raw data and the fitted curve in one plot?

require(ggplot2)
require(nlmrt)  # may be this will help later..?

# generate simulated measurement data

time <- seq(-10,20,0.2)

signal <- sqrt(time + 2) # generate sqrt signal; includes some NA
signal[is.na(signal)] <- 0 # set all NA to zero
signal <- signal + rnorm(length(time)) * 0.1  # add noise

df <- data.frame(x=time, y=signal)

# find coefficiants for y ~ b * sqrt(x - a)
# no idea how...

# plot raw data and fitted curve in one ggplot diagram

ggplot()+
    geom_point(data=df, aes(x=x, y=y))

Answer 1

Provided you know where the cutpoint is and that the value before the cutpoint is zero:

sfun <- function(x,brk,a=1) {
    ifelse(x<brk,0,suppressWarnings(a*sqrt(x-brk)))
}

( suppressWarnings() is there because ifelse evaluates both the if and the else cases for all values of x , and we don't want warnings about taking the square root of negative numbers)

Test (not shown):

curve(sfun(x,1,1),from=0,to=10) ## test (not shown)

Simulate some data:

x <- seq(0,10,length=101)
set.seed(1)
y <- rnorm(length(x),sfun(x,1,1),sd=0.25)
DF <- data.frame(x,y)

Since all we need to figure out is how the square root function is scaled, we can do this with a regression through the origin (take out the -1 if you want to allow the value below the cutpoint to be non-zero):

library("ggplot2")
theme_set(theme_bw())
ggplot(DF,aes(x,y))+geom_point()+
    geom_smooth(method="lm",
                formula=y~sfun(x,brk=1)-1)
ggsave("truncsqrt.png")