[R] nls() fit to Kahnemann/ Tversky function

[apjaworski@mmm.com]

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: apjaworski at mmm.com
Tel:  (651) 733-6092
Fax:  (651) 736-3122


                                                                           
             Mark Hempelmann                                               
             <neo27 at t-online.d                                             
             e>                                                         To 
             Sent by:                  r-help at stat.math.ethz.ch            
             r-help-bounces at st                                          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 at 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