[R] nls - find good starting values

[Antje]

Hi Bill,

thanks for your answer.

I don't see what you mean with "fitting a gaussian distribution"...

I'm pretty sure, that I'd like to fit a gaussian probability density 
function :-) (not normalized, for example with a mean around -4 and a 
standard deviation of 0.5)
I'm not sure if I understand your solution with the quadratic regession 
model...
Maybe my approach is completely wrong but I didn't know any other solution.
Anyhow, I've solved the issue so far with the while-construct.

Antje


Bill.Venables at csiro.au wrote:
> It is not at all clear what you are trying to do.
>
> Fitting a gaussian distribution is the simplest problem in all of statistics: the sample mean and sample variance (divisor n) are the mle's of the two parameters involved.  No non-linear regresson is required.
>
> If what you are really trying to do is fit a (normalized?) gaussian probability density function as a form of non-linear regression, i.e. by least squares, that is an entirely different problem.  I'm a bit stumped as to how this form of non-linear regresion should arise, particularly with equal variance both for values near the mode as well as in the tails, but stranger things have happened, I suppose.  What I would do is, if you response values are non-negative, take logs and regress using a quadratic regression model, and then identify the approximate mean and variance parameters, which should then be reasonable starting values for the non-linear regression.  Negative responses will pose a problem, of course.
>
> Bill Venables.
> ________________________________________
> From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of Antje [niederlein-rstat at yahoo.de]
> Sent: 14 July 2009 17:21
> To: r-help at stat.math.ethz.ch
> Subject: [R] nls - find good starting values
>
> Hi there,
>
> it might be a very simple question and I'd be glad to even get a link to
> some useful documentation...
> I have several data sets, I'd like to fit to a gaussian distribution.
> I've tried to give an estimate of the mean and the sd of this
> distribution but still, I run into problems if these estimates are not
> close enough.
>
> For example, nls() breaks with this message:
> singular gradient matrix at initial parameter estimates
>
> I don't know how to avoid these bad start values because their estimate
> is automated. Better start values are often quite close.
>
> I was wondering whether there is any way to test several start-values as
> long as nls does not succeed.
> I would do it with a while construct but maybe there is another approach?
>
> Any hint is very welcome!
>
> Ciao,
> Antje
>
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