Can I multiply and round proportion data for analysis in a GL(M)M with Poisson errors?

Question

Maybe the dumbiest question ever posted on CV:

I want to analyze the relationship between proportion data and some covariates in a generalized linear (mixed, but I don't think it matters) model.

The natural distribution to use would be binomial but most of the proportions are close to 0 and their distribution looks like a (slightly overdispersed) Poisson.

My proportions are by definition not integer values, and so cannot be directly modeled using some implementations of gl(m)m with Poisson errors. For instance I'm using MCMCglmm in R which (rightfully) only allows integer values (and Beta-binomial is not implemented).

Could I simply multiply my proportion by let's say 1000 (to keep some accuracy), round them (to make them integer) and do the glmm with Poisson errors on them. Then I could rescale the parameter estimates (and in glmm the relative importance of variance components will stay the same)?

I assume (maybe wrongly) that there would be not problem with this, but as I've been unable to find it discussed somewhere, I'm starting to doubt, and would be pleased if others thinking about this later can find an answer (whatever it is) here.

Many thanks for the support.

Answer 1

A possible way around this is to use an offset:

Achim Zeileis says (here: http://www.mail-archive.com/r-help@r-project.org/msg69617.html):

If it is a ratio of (integer-valued) counts in the numerator and some known denominator, say ratio = count/denom then one standard approach would be to fit

glm(count ~ ..., offset = log(denom), data = ..., family = poisson)

because this corresponds to log(count) = x'beta + log(denom) <=> log(count/denom) = x'beta

And here is how to do it with MCMCglmm: http://markmail.org/thread/66hxxbikx5a4yzam#query:+page:1+mid:dgrpip73futd3vok+state:results

Answer 2

I don't see why you want to take proportions and model them with Poisson. The proportions are possibly any number in [0,1] while the Poisson is discrete over the non-negative integers. A beta distrbution would make more sense as a model. Also since you say that you expect p to be dependent on covariates perhaps the data you see is a mixture of binomial proportions where p depends on the covariate values.