[R] Supply linear constrain to optimizer

[Ben Bolker]

  I agree with the suggestion to reparameterize the data, but the problem
here is not readjusting the range (the box constraints in optim/L-BFGS-B
work just fine).
  A transformation I have used for compositional data:

  c(1) <-> p(1)
  c(2) <-> p(2)/(1-p(1))
  ...
  c(n) <-> p(n)/(1-sum p(1)..p(n-1))


On Fri, 14 Sep 2001, Philippe Grosjean wrote:

> Try reparameterize the function. Replace c1 and c2 by functions such they
> return values in the range you want. Hints: use ln(c) instead of c for
> returning a positive number; to obtain a range like [a, b], you can use a
> 4-parameter logistic function,... OK, it's not easy in the present case, but
> it is a way to get around your problem.
> Best regards,
>
> Philippe Grosjean
>
>
> ...........]<(({?<...............<?}))><...............................
>  ) ) ) ) )	 __               	 __
> ( ( ( ( ( 	|__)              	|  _
>  ) ) ) ) )	|   hilippe       	|__)rosjean
> ( ( ( ( ( 	Marine Biol. Lab., ULB, Belgium
>  ) ) ) ) )	                  	 __
> ( ( ( ( ( 	|\  /|            	|__)
>  ) ) ) ) )	| \/ |ariculture &	|__)iostatistics
> ( ( ( ( (
>  ) ) ) ) )	e-mail: phgrosje at ulb.ac.be or phgrosjean at sciviews.org
> ( ( ( ( ( 	SciViews project coordinator (http://www.sciviews.org)
>  ) ) ) ) )      tel: 00-32-2-650.29.70 (lab), 00-32-2-673.31.33 (home)
> ( ( ( ( (
>  ) ) ) ) )      "I'm 100% confident that p is between 0 and 1"
> ( ( ( ( (                                  L. Gonick & W. Smith (1993)
>  ) ) ) ) )
> ......................................................................
>
>
> >Dear R and S users,
>
> >I've been working on fitting finite mixture of negative exponential
> >distributions using maximum likelihood based on the example given in MASS.
> >So far I had much success in fitting two components. The problem started
> >when I tried to extend the procedure to fit three components.
> >More specifically,
>
> >likelihood = sum( ln(c1*exp(-x/lambda1)/lambda1 +
> >c2*exp(-x/lambda2)/lambda2 + (1-c1-c2)*exp(-x/lambda3)/lambda3) )
>
> >I've used optimizers such as ms and nlminb (SPLUS 5.0 for UNIX), and
> >provided parameters constrains (0 <= c1, c2 <= 1) to nlminb via lower and
> >upper. But these constrains provide no protection for (1-c1-c2) being
> >between interval [0,1], which resulted in generating NAs in the likelihood
> >function during iteration.
>
> >I've been looking at various documentations, but didn't see anywhere
> >mentioning setting linear constrain, in this case, c1 + c2 <= 1.
>
> >Any suggestion and pointers will be greatly apprepciated.
>
> >Kevin Xie
> >Research Student
> >Cavendish School of Computer Science
> >University of Westminster
> >London, UK
>
>
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-- 
318 Carr Hall                                bolker at zoo.ufl.edu
Zoology Department, University of Florida    http://www.zoo.ufl.edu/bolker
Box 118525                                   (ph)  352-392-5697
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