R help - Sep 2006 - non linear modelling with nls: starting values

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

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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