R help - Oct 2003 - non linear regression with R

Dear Colleagues,

I have x, y data (pollen and seed dispersal from oaks !) that I would 
like to fit with a function which look like this:

p(a,b,x,y)=b/(2*pi*a?gamma(2/b))*exp(-(square_root(x?+y?)/a)power(b))

I am looking for a and b values that fit my data at best.
Can someone give me hints to perform such an analysis with R ?

Thanks a lot

Sophie


     Sophie Gerber                      gerber at pierroton.inra.fr
      INRA - UMR BIOGECO
      69 route d'Arcachon               tel (33) (0)5 57 12 28 30
      33612 Cestas cedex                fax (33) (0)5 57 12 28 81
       http://www.pierroton.inra.fr/genetics/Perso/Sophie/
        page_sophie_english.html

Have you considered "nls" or "optim"? 

      My way of handling this kind of problem is to assume that x and / 
or y follow some probability distribution with parameters a and b.  Then 
I write a function to compute deviance = (-2*log(likelihood)) = 
(-2*log(probability density for x and / or y given a and b)) and feed it 
to "optim" to minimize this "deviance".  Or if the response
variable is
a nonlinear model plus independent normal errors with constant variance, 
I may use "nls". 

      hope this helps.  spencer graves

Sophie Gerber wrote:
> Dear Colleagues,
>
> I have x, y data (pollen and seed dispersal from oaks !) that I would 
> like to fit with a function which look like this:
>
> p(a,b,x,y)=b/(2*pi*a?gamma(2/b))*exp(-(square_root(x?+y?)/a)power(b))
>
> I am looking for a and b values that fit my data at best.
> Can someone give me hints to perform such an analysis with R ?
>
> Thanks a lot
>
> Sophie
>
>
>     Sophie Gerber                      gerber at pierroton.inra.fr
>      INRA - UMR BIOGECO
>      69 route d'Arcachon               tel (33) (0)5 57 12 28 30
>      33612 Cestas cedex                fax (33) (0)5 57 12 28 81
>       http://www.pierroton.inra.fr/genetics/Perso/Sophie/
>        page_sophie_english.html
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

Your function is not quite complete -- you need to specify an error 
distribution such as Poisson or negative binomial (see literature from the 
past decade by J. Clark, Muller-Landau, Ribbens and others)
  Assuming Poisson errors, if x and y are locations and
d is observed density:

f <- function(p) {
  a <- p[1]
  b <- p[2]
  r <- sqrt(x^2+y^2)
  exp.dens = b/(2*pi*a^2*gamma(2/b))*exp(-(r/a)^b)
  lik = -sum(dpois(d,exp.dens,log=TRUE))
}

optim(fn=f,par=(a vector of reasonable starting values))

  I see from my e-mail that Spencer Graves has just replied to this 
message too so I'll go see what he wrote ...




On Wed, 22 Oct 2003, Sophie Gerber wrote:
> Dear Colleagues,
> 
> I have x, y data (pollen and seed dispersal from oaks !) that I would 
> like to fit with a function which look like this:
> 
> p(a,b,x,y)=b/(2*pi*a?gamma(2/b))*exp(-(square_root(x?+y?)/a)power(b))
> 
> I am looking for a and b values that fit my data at best.
> Can someone give me hints to perform such an analysis with R ?
> 
> Thanks a lot
> 
> Sophie
> 
> 
>      Sophie Gerber                      gerber at pierroton.inra.fr
>       INRA - UMR BIOGECO
>       69 route d'Arcachon               tel (33) (0)5 57 12 28 30
>       33612 Cestas cedex                fax (33) (0)5 57 12 28 81
>        http://www.pierroton.inra.fr/genetics/Perso/Sophie/
>         page_sophie_english.html
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
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