[R] Fitting Weibull Model with Levenberg-Marquardt regression method

[Gabor Grothendieck]

On Mon, Aug 23, 2010 at 11:01 AM, Veronesi, Fabio
<f.veronesi at cranfield.ac.uk> wrote:
> Hi,
> I have a problem fitting the following Weibull Model to a set of data.
> The model is this one: a-b*exp(-c*x^d)
> If I fitted the model with CurveExpert I can find a very nice set of coefficients which create a curve very close to my data, but when I use the nls.lm function in R I can't obtain the same result.
> My data are these:
> X     Y
> 15    13
> 50    13
> 75    9
> 90    4
>
> With the commercial software I obtain the following coefficients:
> Weibull Model: y=a-b*exp(-c*x^d)
> Coefficient Data:
> a =          1.31636909714E+001
> b =          7.61325570579E+002
> c =          2.82150000991E+002
> d =          -9.23838785044E-001
>
> For fitting the Levenberg-Marquardt in R I'm using the following lines:
> pS<-list(a=1,b=1,c=1,d=1)
> model<-function(pS,xx){pS$a-pS$b*exp(-pS$c*xx^-pS$d)}
> resid<-function(observed,pS,xx){observed-model(pS,xx)}
> lin<-nls.lm(pS,resid,observed=Y,xx=X)
>
> Why I can't obtain the same results?
> Many thanks in advance,
> Fabio

Note that you have 4 parameters and only 4 data points!  You are not
likely to get anything useful with that.  At any rate try this noting
that with alg = "plinear" you don't have to provide starting values
for the linear parameters:

> DF <- data.frame(X = c(15, 50, 75, 90), Y = c(13, 13, 9, 4))
>
> nls(Y ~ cbind(1, exp(-c*X^d)), DF, start = list(c = 1, d = 1), alg = "plinear")
Nonlinear regression model
  model:  Y ~ cbind(1, exp(-c * X^d))
   data:  DF
        c         d     .lin1     .lin2
1.000e+00 1.000e+00 8.667e+00 1.417e+07
 residual sum-of-squares: 40.67

Number of iterations to convergence: 0
Achieved convergence tolerance: 0