[R] Constrained non linear regression using ML

[Corrado]

Dear Arne, Gabor,

I solved the problem with betareg (downloaded the package). I run it on 
my data, and unfortunately the  constraint is definitively active, if I 
remove the active variables, I then remove the most significant variables!

Of course the error is important, not the distribution of the variable.

In this case, one of the assumptions is that the error may be 
distributed ~ beta. I think that betareg makes this assumption, am I right?

I am finding it difficult to solve two problems:

1) write the maximum likelihood function (what do you suggest?)
2) deal with the fact that a few factors actually have values of y (the 
response) at the extremes: that is 0 and 1. But that mean that the link 
function returns Infinite values in that case ....
3) the error is dependent on E(y).

PS: Additional silly question: what is the discrete equivalent of beta? 
binomial?

Arne Henningsen wrote:
> On 17 March 2010 14:22, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
>   
>> Contact the maintainer regarding problems with the package.  Not sure
>> if this is acceptable but if you get it to run you could consider just
>> dropping the variables from your model that correspond to active
>> constraints.
>>
>> Also try the maxLik package.  You will have to define the likelihood
>> yourself but it does support constraints.
>>     
>
> Yes. And specifying the likelihood function is probably (depending on
> your distributional assumptions) not too complicated.
>
> BTW: Even if your y follows a beta distribution, it does not mean that
> your error term also follows a beta distribution. And it the
> distribution of the error term which is crucial for specifying the
> likelihood function.
>
> /Arne
>   
-- 

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: ct529 at york.ac.uk