[R] add constraints to nls or use another function

[Ben Bolker]

PtitBleu <ptit_bleu <at> yahoo.fr> writes:

> 
> Hello, 
> 
> I'm trying to fit experimental data with a model and nls.
> For some experiments, I have data with x from 0 to 1.2 and the fit is quite
> good.
> But it can happen that I have data only the [0,0.8] range (see the example
> below) and, then, the fit is not correct.
> 
> I would like to add a constraint, for example : the second derivative must
> be positive.
> But I don't know how to add this to nls and, in fact,  I'm not sure that it
> is possible.
> If not, could you give me a package and/or a function (and/or a complete
> solution, which will be great ...) ?
> 
> Thanks in advance for your help,
> Have a good day,
> Ptit Bleu.
> 

  This is much less than you asked for -- suggestions rather than
worked solutions -- but -- if you code your own least-squares function
and fit it in optim (or use bbmle::mle2 and specify that 
response~dnorm(...)) then you can add a penalty term to the objective
function that is zero when the second derivative is positive and
increases quadratically when the second derivative becomes negative.

  There may also (?) be a way to impose such a constraint on
spline fits.

  By the way, it looks like your model is actually linear
in the parameters, which might simplify things considerably ...

  Ben Bolker