[R] Goodness of fit to Poisson / NegBinomial

[ben@zoo.ufl.edu]

  A couple of offhand comments (which may already have occurred to you):

 1. lumping categories is relatively straightforward but a little bit hard
to automate well (and maybe not worth automating) -- it sometimes requires
a judgement call.  For example, in this case I'd probably lump categories
5, 6, and 7, but if I had another category with 4 instances of 8 mites I'd
lump (5,6) and (7,8).  It's probably just worth looking at the category
and doing things manually ...

 [snip]

> >   tab <- table(mites)
> >   NSU <- length(mites)
> >   N <- sum(mites)
> >   NSU.Mean <- N / NSU
> >   exp <- dpois(as.numeric(dimnames(tab)[[1]]), NSU.Mean) *  NSU

 Lump and truncate both the expected and observed distributions:

  tab[6] <- sum(tab[6:8])
  tab <- tab[1:6]
  exp[6] <- sum(exp[6:8])
  exp <- exp[1:6]

> >   chi2 <- sum(((as.vector(tab) - exp)^2) / exp)
> >
> >   tab
> >   exp
> >   chi2


> > I have some small expected values and so need to collapse some
> > categories. If anyone has code to do that already ... but my
> > question is how would I do the same for a negative binomial
> > distribution?
>
> The negative binomial density function is available in my rmutil
> library. (www.luc.ac.be/~jlindsey/rcode.html)

  Two more comments:

 2. the negative binomial density is also available in the base R package
(dnbinom), although the parameterization is in terms of Bernoulli trials
(size/prob) rather than the mu/(k,theta) parameterization that most
ecologists are used to.  [Incidentally, I noticed the other day that
"rnegbin" in the MASS package appears to duplicate functionality that is
(now) available in R, namely that it can generate variates for non-integer
k/theta parameters.  In my own R libraries I've also extended the *nbinom
functions so that they can alternately take the mu/k parameters instead
of size/prob.]

 3. estimating the parameters of the neg. bin. is harder than estimating
that for the Poisson; you may want to check out theta.md, theta.ml,
theta.mm in the MASS package.

  Don't have time to do a more extended example at the moment.

  Hope this helps.


>   Jim
>
> >
> > Mark
> >
> > --
> > Mark Myatt
> >
> >
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-- 
318 Carr Hall                                bolker at zoo.ufl.edu
Zoology Department, University of Florida    http://www.zoo.ufl.edu/bolker
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