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

[Bob O'Hara]

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