Re: Constrained non linear regression using ML

[Jaroslav Hajek]

On Tue, Mar 16, 2010 at 8:01 PM, Corrado <address@hidden> wrote:
> Dear Octave users,
>
> I have to fit the non linear regression:
>
> y~1-exp(-(k0+k1*p1+k2*p2+ .... +kn*pn))
>
> where ki>=0 for each i in [1 .... n] and pi are on R+.
>
> I am using, at the moment, nls, but I would rather use a Maximum
> Likelhood based algorithm. The error is not necessarily normally
> distributed.
>

You should have an idea of an alternative error distribution, then. Do you?

In any case I'd start from transforming

x = -log1p (-y);

and fitting the linear nonnegative model

x ~ k0 + k1*p1 + ...

as an initial guess. But maybe you already do that? It is even
possible that the error distribution in x will be closer to normal
than in z. If this makes a good initial guess,
expectation-maximization can bring you to the ML estimate with little
effort, but you still need to make a parametrized assumption about the
error distribution.


> --
> Corrado Topi
> PhD Researcher
> Global Climate Change and Biodiversity
> Area 18,Department of Biology
> University of York, York, YO10 5YW, UK
> Phone: + 44 (0) 1904 328645, E-mail: address@hidden
>
>
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-- 
RNDr. Jaroslav Hajek, PhD
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz