[R] Constrained non linear regression using ML

[Corrado]

Dear Gabor, Arne, Ravi, R users,

I am firstly trying the maximum likelihood approach, then will try the 
Bayesian approach.

The likelihood function, and the log likelihood function, will depend on 
the pdf of the error e in the formula:

y=f(theta*x)+e

Now let's say that e is  Gaussian distributed, then I can use LS which 
is the same as ML in this case, and the residuals would be distributed 
Gaussian. Is that right?

If e is distributed differently (for example: beta, in the continuous 
case,  or binomial, in the discrete case), then I am better off by using 
Maximum Likelihood. How would the residual be distributed? Should they 
not be distributed the same as e?

Best,

Gabor Grothendieck wrote:
> For specific questions on the betareg package contact the maintainer.
> If the likelihood based approaches are giving too much difficulty try
> moving to a Bayesian framework (WinBUGS/R2WinBUGS, JAGS/r2jags, etc.)
>
> On Wed, Mar 17, 2010 at 10:03 AM, Corrado <ct529 at york.ac.uk> wrote:
>   
>> 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
>>
>>
>>     


-- 
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