# [R] info

Spencer Graves spencer.graves at pdf.com
Fri Jul 11 11:43:29 CEST 2003

```I assume you mean the following:

chemYield <-
function(a, x)(a+(a-a)/(1+exp(-a*(x-a))

If you want to estimate parameters a[1:4] from data on pairs of (x,
y=chemYield), create a data.frame(x, y), and estimate the parameter
vector "a" using "nls".

If you have trouble getting "nls" to converge, I would plot the data
and make a serious effort to get good starting values for "a" from the
plot.  If I still have trouble, I'd try "optim", then feed the output
from "optim" into "nls".

I seem to recall having seen problems like this discussed in Bates
and Watts (1988) Nonlinear Regression Analysis and Its Applications
(Wiley).  I don't have the book in hand at the moment, so I can't give
you a page reference, but they discuss problems of this nature.  Bates
was a pioneer in developing measures of intrinsic vs. parameter effects
curvature.  Bates and Watts studied many published data sets and found
that in nearly all cases, the parameter effects curvature was at least
an order of magnitude larger than the intrinsic curvature.  That means
that numerical difficulties can often (usually?) be improved by trying
different parameterizations for the same problem.

The function "nls" and similar functions are described among other
places in Venables and Ripley (2002) Modern Applied Statistics with S,
4th ed. (Springer, ch. 8).

hope this helps.  spencer graves

Andrea Calandra wrote:
> HI
>
> I'm a student in chemical engineering, and i have
to implement an algoritm about FIVE PARAMETERS
INTERPOLATION for a calibration curve (dose, optical density)
>
> y = a + (c - a) /(1+ e[-b(x-m])
>
> where
> x = ln(analyte dose + 1)
> y = the optical absorbance data
> a = the curves top asymptote
> b = the slope of the curve
> c = the curves bottom asymptote
> m = the curve X intercept
>
> Have you never seen this formula, because i don't fine information or
> lecterature about solution of this!!!
>
> Can i help me
>
> Hi
> Mr. Calandra
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

```