[R-sig-eco] Error distribution for fractional response

[Scott Foster]

Hi again,

Mollie, you are right (I should have checked) -- suggestions based on the binomial should not be considered as there may be more than 1 sapling per adult.

Scott

On 31/01/14 01:48, Mollie Brooks wrote:
> Dear Adhara,
>
> I agree with Bob and Scott that transforming the data is probably not the best option.
>
> I basically agree with Bob�s suggestion, except that his answer assumes you have a covariate and I don�t see one in your data.
> Without a covariate, I would do the following
> Let lambda be the expected number of seedlings E(S) for a given number of adults, A.
> Let g be the number of saplings per adult.
> E(S)=lambda= g*A
> If you use a log link in either a poisson or negative binomial model, this gives you
> log(lambda)=log(g*A)=log(g)+log(A)
> You can fit this using an offset and an intercept. Then the intercept gives you an estimate of log(g). So to get the biologically meaningful 
> parameter(g) back, take the exponential.
>
> ndat=50
> maxad=10
> g=.1
> A=sample(1:maxad, ndat, replace=TRUE)
> S=rpois(ndat, lambda=g*A)
> dat=data.frame(S=S, A=A)
>
> m1=glm(S~1, offset=log(A), family=poisson, data=dat)
> g_est=exp(coef(m1))
>
> If you want to do some model comparison, it�s best if they are all fit in the same package.
> install.packages("glmmADMB",
>    repos=c("http://glmmadmb.r-forge.r-project.org/repos",
>            getOption("repos")),type="source")
> library(glmmADMB)
> pois1=glmmadmb(S~1+ offset(log(A)), family="poisson", data=dat)
> nbin1=glmmadmb(S~1+ offset(log(A)), family="nbinom", data=dat)
> zip1=glmmadmb(S~1+ offset(log(A)), family="poisson", data=dat, zeroInflation=TRUE)
> library(bbmle) #forAICtab
> AICtab(pois1, nbin1, zip1)
>
> I would not use a binomial distribution as suggested below because it assumes you can only have one sapling per adult and I think I see at least one 
> instance in your data where S>A.
>
> cheers,
> Mollie
>
> ------------------------
> Mollie Brooks, PhD
> Postdoctoral Researcher, Population Ecology Research Group http://www.popecol.org <http://www.popecol.org>
> Institute of Evolutionary Biology & Environmental Studies, University of Z�rich
>
>
> On 30 Jan 2014, at 11:08 AM, Bob O'Hara <bohara at senckenberg.de> wrote:
>
> > On 30/01/14 10:58, Adhara Pardo wrote:
> >> Dear R users,
> >>
> >> I would like to fit a GLM to some plant regeneration data (see bottom
> >> of this e-mail). The dependent variable, an index of regeneration, was
> >> obtained by diviving the number of saplings by the number of adults
> >> plants present in each plot. The result is a highly skewed variable and
> >> thus, specifying, for instance, a
> >> Gaussian distribution does not seem to be appropriate. Data
> >> transformation does not help either. Do you have any suggestion on the
> >> best distribution to choose?
> > Rather than use an index, it might be better to use the number of saplings directly, and assume they are Poisson distributed (or some form of 
> over-dispersed Poisson). You can use the log of the number of adults as an offset:
> >
> > glm(saplings ~ something + offset(log(adults))
> >
> > The model is
> >
> > saplings ~ Poisson(lambda)
> > log(lambda) = alpha + beta*something + log(adults)
> >
> > where alpha and beta are the parameters being estimated (lambda is the expected number of saplings). This model is the same as
> >
> > lambda = adult*exp(alpha + beta*something)
> >
> > so it's equivalent to modelling saplings/adults: the adults have just been moved to the other side of the equation.
> >
> > Bob
> >
> > --
> >
> > Bob O'Hara
> >
> > Biodiversity and Climate Research Centre
> > Senckenberganlage 25
> > D-60325 Frankfurt am Main,
> > Germany
> >
> > Tel: +49 69 7542 1863
> > Mobile: +49 1515 888 5440
> > WWW: http://www.bik-f.de/root/index.php?page_id=219
> > Blog: http://blogs.nature.com/boboh
> > Journal of Negative Results - EEB: www.jnr-eeb.org <http://www.jnr-eeb.org>
> >
> > _______________________________________________
> > R-sig-ecology mailing list
> > R-sig-ecology at r-project.org
> > https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> >
>
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology

-- 
Scott Foster
Computational Informatics
CSIRO
E scott.foster at csiro.au T +61 3 6232 5178
Postal address: CSIRO Computational Informatics, GPO Box 1538, Hobart TAS 7001
Street Address: CSIRO Computational Informatics, Castray Esplanade, Hobart Tas 7001, Australia
www.csiro.au