[R] non linear modelling with nls: starting values

[Gabor Grothendieck]

Here are some approaches:

- we only have 4 parameters so just use grid search to get
starting values as in:

https://stat.ethz.ch/pipermail/r-help/2005-September/079617.html

- there are singularities near beta_1 = beta_2 and near alpha_1 = 0
and near alpha_2 = 0 so reparameterize and use the upper and
lower bounds to avoid those regions.  You could try a separate
reduced model for those.


On 9/18/06, Sebastian P. Luque <spluque at gmail.com> wrote:
> Hi,
>
> I'm trying to fit the following model to data using 'nls':
>
>
> y = alpha_1 * beta_1 * exp(-beta_1 * x) +
>    alpha_2 * beta_2 * exp(-beta_2 * x)
>
>
> and the call I've been using is:
>
>
> nls(y ~ alpha_1 * beta_1 * exp(-beta_1 * x) +
>        alpha_2 * beta_2 * exp(-beta_2 * x),
>    start=list(alpha_1=4, alpha_2=2, beta_1=3.5, beta_2=2.5),
>    trace=TRUE, control=nls.control(maxiter = 200))
>
>
> So the model has 4 parameters (alpha_1, alpha_2, beta_1, beta_2), but
> providing appropriate starting values is proving difficult.  Although the
> data could reasonably be fit with this model, the procedure is exiting
> with "singular gradient matrix at initial parameter estimates".  How can
> one obtain appropriate starting values, assuming that is really the
> problem?  The archives show some suggestions to use 'optim', but that
> requires starting values too, so I'm not sure how to proceed.
>
> Searching for self-starting functions, I found that there's one for a
> bi-exponential model, which is very similar to the one I'm trying to fit.
> Would it be reasonable to create a modified version of this function, so
> that it returns a value that can be used for the model above?  I would
> greatly appreciate any comments and suggestions.
>
>
> --
> Seb
>
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