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
I assume you mean the following: chemYield <- function(a, x)(a[1]+(a[3]-a[2])/(1+exp(-a[2]*(x-a[4])) 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 haveto 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
The most commonly used dose-response functions for nonlinear calibration curves are the four- and five-parameter logistic functions. The four- parameter logistic is specified as F(z) = delta + (alpha - delta)/(1 + (z/gamma)^beta) so I'm not sure where you are getting your dose-response functional form from. In any case, you can fit this model using either nls( ) or nlme( ), depending on whether or not you want to fit a random-effects model. For references related to the four- and five-parameter logistic functions, you can read 1. Rodbard, D., and Frazier, G.R. (1975) "Statistical analysis of radioligand assay data," Methods Enzymol., vol. 37, p. 3 - 22. 2. Dudley, R.A., Edwards, P., and Ekins, R.P. (1985) "Guidelines for immunoassay data processing," Clin. Chem., vol. 31, no. 8, p. 1264 - 1271 The first of these articles introduces the four-parameter logistic, and the second refines its parametrization as well as introduces the five-parameter logistic for use in situations where the calibration curve is asymmetric. You should also acquire "Mixed Effects Models in S and Splus", by Drs. Pinheiro and Bates if you intend to do anything with mixed effects models. Best, david paul -----Original Message----- From: Andrea Calandra [mailto:a.CALANDRA at mclink.it] Sent: Thursday, July 10, 2003 11:39 AM To: R-help at stat.math.ethz.ch Subject: [R] info 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
Andrea Calandra <a.CALANDRA at mclink.it> writes:> 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!!!This is one parameterization of the four-parameter logistic growth curve. A slightly different version is available as the selfStart model SSfpl in the nls package. In R try library(nls) ?SSfpl example(SSfpl) to see how nls and SSfpl can be used. The example even produces a figure for you showing what the SSfpl parameters represent. A literature reference for the SSfpl form of the four-parameter logistic is Appendix C.6 in Pinheiro and Bates (2000), "Mixed-effects Models in S and S-PLUS", Springer.
Sorry I'm student in biomedical engineer and i have to solve this formula for immuno-assay. I need to design a calibration curve But i don't understand How can i write this formula in R language: 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 I have to calculate the parameters (a,b,c,m).After with X that i know i calculate the Y.> =========================> Date: Tue, 15 Jul 2003 19:30:31 -0700 (PDT) > From: Rick Fletcher <fletcher at uidaho.edu> > To: Andrea Calandra <a.CALANDRA at mclink.it> > Subject: Re: Info > =========================> > > Andrea, if you only have five data points, it will be very difficult > to > fit all those parameters so they give a unique solution. If > you want to > fit all of your parameters at once, you need many more data points. > > On Tue, 15 Jul 2003, Andrea Calandra wrote: > > > downloaded the R Language, it's very good! > > but i have a question > > > > i have Five point with X and Y that know (concentration and > optical density) how can interpolate the curve > > with folowing FIVE INTERPOLATION > > > > 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 > > > > > > > > > > > > > > > > > =========================> > > Date: Mon, 07 Jul 2003 11:11:28 -0700 (PDT) > > > From: Rick Fletcher <fletcher at uidaho.edu> > > > To: Andrea Calandra <a.CALANDRA at mclink.it> > > > Subject: Re: Info > > > =========================> > > > > > Did you find a solution yet? I am sorry for the delay in > response, > > > but > > > the July 4th weekend is a big holiday here. It is the day > we > > > celebrate > > > our independence from England. > > > > > > Do you still need help? > > > > > > > > > On Fri, 4 Jul 2003, Andrea Calandra wrote: > > > > > > > i take your name on the web! > > > > thank you > > > > > > > > > =========================> > > > > Date: Thu, 03 Jul 2003 11:05:24 -0700 (PDT) > > > > > From: Rick Fletcher <fletcher at uidaho.edu> > > > > > To: Andrea Calandra <a.CALANDRA at mclink.it> > > > > > Subject: Re: Info > > > > > =========================> > > > > > > > > > > > > > > Hello, > > > > > > > > > > May I ask how you got my name? Thank you. > > > > > > > > > > > > > > > On Thu, 3 Jul 2003, Andrea Calandra wrote: > > > > > > > > > > > HI > > > > > > > > > > > > I'm a student in chemical engineering at university > of > > > Rome, > > > > > 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 > > > > > > Andrea Calandra > > > > > > > > > > > > thank you > > > > > > > > > > > > > > > > > > > > > > > > > > > > Rick > > > > > T. Rick Fletcher - http://www.chem.uidaho.edu/~fletcher/ > > > > > Associate professor of chemistry | That's Idaho, not > Iowa. > > > > > | ad hominem > > > > > University of Idaho | Upper Left Hand > Corner. > > > > > | ad hominem > > > > > Moscow, ID 83844-2343 | No, I don't grow > potatoes. > > > > > | ad hominem > > > > > > > > > > > > > > > > > > Rick > > > T. Rick Fletcher - http://www.chem.uidaho.edu/~fletcher/ > > > Associate professor of chemistry | That's Idaho, not Iowa. > > > | ad hominem > > > University of Idaho | Upper Left Hand Corner. > > > | ad hominem > > > Moscow, ID 83844-2343 | No, I don't grow potatoes. > > > | ad hominem > > > > > > > > Rick > T. Rick Fletcher - http://www.chem.uidaho.edu/~fletcher/ > Associate professor of chemistry | That's Idaho, not Iowa. > | ad hominem > University of Idaho | Upper Left Hand Corner. > | ad hominem > Moscow, ID 83844-2343 | No, I don't grow potatoes. > | ad hominem
Sorry I'm student in biomedical engineer and i have to solve this formula for immuno-assay. I need to design a calibration curve But i don't understand How can i write this formula in R language: 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 I have to calculate the parameters (a,b,c,m).After with X that i know i calculate the Y. i try: yeld.fit <- nls( y ~ a + (c.-a)/(1+exp(-b*(x-m))), data = yeld, start = list( a= 0, c.=2, b= 1, m=4 ), trace = TRUE ) where yeld is a data.frame x y 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 but give me an error: << exceeded number of itwerations>> thank you Andrea