R help - Oct 2005 - 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

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
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                                                                   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

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PLEASE do read the posting guide!
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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 <neo27 at t-online.de>
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 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
>