Re: [R] nls() fit to Kahnemann/ Tversky function
Note that a simple logistic with a saturation level of 1 seems to do quite well. Below we have removed the last point in order to avoid the singularity: x <- p.kum[-10] y <- felt.prob.kum[-10] plot(log(y/(1-y)) ~ x) abline(lm(log(y/(1-y)) ~ x), col = "red") On 10/31/05, Mark Hempelmann <[EMAIL PROTECTED]> wrote: > Dear WizaRds, > > I would like to fit a curve to ten points with nls() for one > unknown parameter gamma in the Kahnemann/ Tversky function, but somehow > it won't work and I am unable to locate my mistake. > > p.kum <- seq(0.1,1, by=0.1) > felt.prob.kum <- c(0.16, 0.23, 0.36, 0.49, 0.61, 0.71, 0.85, 0.89, 0.95, > 1) ## how to find a function that fits these points nicely? > plot(p.kum, felt.prob.kum) ## looks a little like an "S" > > gamma <- rep(0.5, 10) > nls.dataframe <- data.frame(p.kum,felt.prob.kum, gamma) > > nls.kurve <- nls( formula = felt.prob.kum ~ > p.kum^gamma/(p.kum^gamma+(1-p.kum)^gamma)^(1/gamma), data=nls.dataframe, > start=c(gamma=gamma), algorithm="plinear" ) > > summary(nls.kurve) > > gives: Error in La.chol2inv(x, size) : 'size' cannot exceed nrow(x) = 10 > > If I go with the Gauss-Newton algorithm I get an singular gradient > matrix error, so I tried the Golub-Pereyra algorithm for partially > linear least-squares. > > It also seems the nls model tries to find ten different gammas, but > I want only one single gamma parameter for the function. I appreciate > your help and support. Thank you. > > sol lucet omnibus > Mark Hempelmann > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] nls() fit to Kahnemann/ Tversky function
Mark, The parameter of your model (gamma) should not be a part of the dataframe. In addition, the start argument should be a named list. Something like this works nls.dataframe <- data.frame(p.kum,felt.prob.kum) nls.kurve <- nls( formula = felt.prob.kum ~ p.kum^gamma/(p.kum^gamma+(1-p.kum)^gamma)^(1/gamma), data=nls.dataframe, start=list(gamma=.5), trace=TRUE) # trace shows convergence of the algorithm. but the fit is not very good as the fitted gamma is essentially 1. Hope this helps, Andy __ Andy Jaworski 518-1-01 Process Laboratory 3M Corporate Research Laboratory - E-mail: [EMAIL PROTECTED] Tel: (651) 733-6092 Fax: (651) 736-3122 Mark Hempelmann <[EMAIL PROTECTED] e> To Sent by: r-help@stat.math.ethz.ch [EMAIL PROTECTED] cc at.math.ethz.ch Subject [R] nls() fit to Kahnemann/ Tversky 10/31/2005 04:14 function PM Dear WizaRds, I would like to fit a curve to ten points with nls() for one unknown parameter gamma in the Kahnemann/ Tversky function, but somehow it won't work and I am unable to locate my mistake. p.kum <- seq(0.1,1, by=0.1) felt.prob.kum <- c(0.16, 0.23, 0.36, 0.49, 0.61, 0.71, 0.85, 0.89, 0.95, 1) ## how to find a function that fits these points nicely? plot(p.kum, felt.prob.kum) ## looks a little like an "S" gamma <- rep(0.5, 10) nls.dataframe <- data.frame(p.kum,felt.prob.kum, gamma) nls.kurve <- nls( formula = felt.prob.kum ~ p.kum^gamma/(p.kum^gamma+(1-p.kum)^gamma)^(1/gamma), data=nls.dataframe, start=c(gamma=gamma), algorithm="plinear" ) summary(nls.kurve) gives: Error in La.chol2inv(x, size) : 'size' cannot exceed nrow(x) = 10 If I go with the Gauss-Newton algorithm I get an singular gradient matrix error, so I tried the Golub-Pereyra algorithm for partially linear least-squares. It also seems the nls model tries to find ten different gammas, but I want only one single gamma parameter for the function. I appreciate your help and support. Thank you. sol lucet omnibus Mark Hempelmann __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
[R] nls() fit to Kahnemann/ Tversky function
Dear WizaRds, I would like to fit a curve to ten points with nls() for one unknown parameter gamma in the Kahnemann/ Tversky function, but somehow it won't work and I am unable to locate my mistake. p.kum <- seq(0.1,1, by=0.1) felt.prob.kum <- c(0.16, 0.23, 0.36, 0.49, 0.61, 0.71, 0.85, 0.89, 0.95, 1) ## how to find a function that fits these points nicely? plot(p.kum, felt.prob.kum) ## looks a little like an "S" gamma <- rep(0.5, 10) nls.dataframe <- data.frame(p.kum,felt.prob.kum, gamma) nls.kurve <- nls( formula = felt.prob.kum ~ p.kum^gamma/(p.kum^gamma+(1-p.kum)^gamma)^(1/gamma), data=nls.dataframe, start=c(gamma=gamma), algorithm="plinear" ) summary(nls.kurve) gives: Error in La.chol2inv(x, size) : 'size' cannot exceed nrow(x) = 10 If I go with the Gauss-Newton algorithm I get an singular gradient matrix error, so I tried the Golub-Pereyra algorithm for partially linear least-squares. It also seems the nls model tries to find ten different gammas, but I want only one single gamma parameter for the function. I appreciate your help and support. Thank you. sol lucet omnibus Mark Hempelmann __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
