R help - May 2004 - Fitting data from a spectrophotometer.

Dear R-list,

	It is not uncommon for laboratory equipment (e.g. spectrophotometers) to have a
linear response in a certain interval and then go into saturation. I wonder if
there is an R-function that models this; for instance by estimating the
breakpoint and fitting a line below the breakpoint and a constant above.

Best regards
Thomas Poulsen

--
Thomas Poulsen		      Research Scientist. PhD, MSc
Novozymes A/S			Protein Design / Bioinformatics
Brudelysvej 26, 1US.24		Phone:	+45 44 42 27 23
DK-2880 Bagsv??rd.

TAPO (Thomas Agersten Poulsen) wrote:
 > Dear R-list,
 >
 > 	It is not uncommon for laboratory equipment (e.g. 
spectrophotometers) to have a linear response in a certain interval and 
then go into saturation. I wonder if there is an R-function that models 
this; for instance by estimating the breakpoint and fitting a line below 
the breakpoint and a constant above.
 >
 > Best regards
 > Thomas Poulsen
 >
 > --
 > Thomas Poulsen		      Research Scientist. PhD, MSc
 > Novozymes A/S			Protein Design / Bioinformatics
 > Brudelysvej 26, 1US.24		Phone:	+45 44 42 27 23
 > DK-2880 Bagsv??rd.
 >
 > ______________________________________________
 > R-help at stat.math.ethz.ch mailing list
 > https://www.stat.math.ethz.ch/mailman/listinfo/r-help
 > PLEASE do read the posting guide! 
http://www.R-project.org/posting-guide.html

I don't know if there is something this specific out there already, but 
you could use ?optim to do this. Here's a quick example:

set.seed(1)
x <- rnorm(100)
y <- ifelse(x < 0, 1 + 4 * x, 1) + rnorm(100, sd = 0.2)

brk <- function(par, x, y) {
   a <- par[1] # intercept
   b <- par[2] # slope
   p <- par[3] # break point
   h <- par[4] # height of saturation
   yhat <- ifelse(x < p, a + b * x, h)
   sum((y - yhat)^2)
}

st <- coef(lm(y ~ x)) # starting values
fit <- optim(c(st, 0, 0), brk, x = x, y = y)
a <- fit$par[1]
b <- fit$par[2]
p <- fit$par[3]
h <- fit$par[4]

yhat <- ifelse(x < p, a + b * x, h)
plot(y ~ x)
lines(x[order(x)], yhat[order(x)])

Perhaps you really prefer something with a continuous first derivative?
In that case, all the continuous cumulative distribution functions have 
a sigmoidal shape and might be suitable.  You could fit pnorm, plogis or tanh
with suitable scaling and location parameters using nls.  An example
of fitting a logistic is at

https://stat.ethz.ch/pipermail/r-help/2004-April/048385.html 


TAPO (Thomas Agersten Poulsen <tapo <at> novozymes.com> writes:

: 
: Dear R-list,
: 
: 	It is not uncommon for laboratory equipment (e.g. spectrophotometers) 
to have a linear response in a
: certain interval and then go into saturation. I wonder if there is an R-
function that models this; for
: instance by estimating the breakpoint and fitting a line below the 
breakpoint and a constant above.
: 
: Best regards
: Thomas Poulsen