proportion data with many zeros

Hi Valerie,
The best advice I was ever given with regards to distribution was to choose the one with the best fit i.e. no pattern in the residuals.
The 2 things to think about when fitting a GLM are the type of data you've collected (binomial, counts etc) so that you can get an idea of which link will linearise 
your model correctly and return realistic results (non negative etc).
The second is to think about the mean-variance relationship. This is what will generally show up in the residuals. Gaussian assumes no relationship (constant) 
but most proportion/abundance measures will have a variance which varies in some way with the mean. Try plotting your means against your variances and > 
have a look at the share of the distribution of your raw data. Then experiment with some suitable exponential family distributions and see which residuals > > 
have no pattern.

I think you're correct in not modeling the zeroes as a hurdle - as they are not 'unknowns'. 
Proportion data is very tricky - I've been grappling with percent cover data for a while. Tweedie worked well for me for measures where cover values were 
mid to low, but not well when they were close to 100%.
If i were you, i'd consider changing the way you use the data to make it simpler. Perhaps just analyse each type of pollen individually over the time periods. I 
assume each time period is the same for the samples and I think n=300 for each of the samples taken?

So why not just try a quasi poisson (or negative binomial) and a tweedie GLM for each type of pollen separately vs time and see which has better residuals. 

Then you can get a significance value for the abundance of each pollen type with each bee at each time period. It is really the same as finding out the relative 
proportions. 

Package tweedie on R works pretty much the same as any GLM. You just need a little but of code (in help files) to estimate an alpha (shape) parameter for 
each set of values. It should lie between 1-2. If not, your data is prob not suited.

Let me know if you need any more help.
Liz

On 04/02/2013, at 2:10 AM, v_coudrain at voila.fr wrote:

Thank you Liz, 
I don't know tweedie, I'll have a look at it, but I have indeed some high values. I know about the problems linked to the arcsine transformation. I won't consider 

anyway. I'd like to use either the raw values of pollen grain counts or a logistic quasibinomial model. 
Best,
Val?rie

Message du 02/02/13 ? 20h47
De : "Liz Pryde" 
A : "v_coudrain at voila.fr" 
Copie ? : "Cade Brian" , "r-sig-ecology at r-project.org" 
Objet : Re: [R-sig-eco] proportion data with many zeros

Have you plotted the raw data to have a look at the distribution?
You could try another exponential family distribution like tweedie that has a mass at zero but is otherwise similar to poisson/gamma - so you're directly

modeling the zeroes. It won't work if you have a lot of high values though. 

Proportions are tricky. Have a read of the Warton paper (2012/11?) "the arcsine is asinine".

Liz



On 02/02/2013, at 6:34 PM, v_coudrain at voila.fr wrote:

Thank you very much for this suggestion. In fact I reconsidered my question and I am not sure that zero-inflated model is what I need. If I understood it

properly, 

a zero-inflated model is best suited when we don't know if zero values are true or false absences (right?). In my case all zero values are assumed to be 

absence and are therefore informative. However, fitting quasipoisson on raw counts or quasibinomial on proportion gives me awful distributions of 

and 

meaningless results. 

Val?rie

Message du 01/02/13 ? 17h22
De : "Cade, Brian" 
A : v_coudrain at voila.fr
Copie ? : r-sig-ecology at r-project.org
Objet : Re: [R-sig-eco] proportion data with many zeros

For a fully parametric approach, you might want to use of zero-inflated
beta distribution (e.g., as available in gamlss package), which is designed
for zero-inflated proportions. Or for a semi-parametric approach, you
could estimated a sequence of quantile regression estimates (e.g., in
package quantreg), where some interval (hopefully not to large) of the
quantiles will be uninformative because they are massed at the zero values.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818

email: brian_cade at usgs.gov
tel: 970 226-9326



On Fri, Feb 1, 2013 at 1:30 AM, wrote:

Dear all, I am trying to test how the proportion of pollen of different
plants found in the brood cells of a wild bee changes over time. I
conducted 4 sampling sessions
(thus time is a factor with 4 levels) and collected several pollen samples
for each time point (300 pollen grains counted for each sample). I thought
about applying a
quasi-binomial glm:

y = cbind(total pollen - pollen of plant X, pollen of plant X)

glm(y~time, family=quasibinomial)

The problem is that I have a lot of zero value, because the pollen of some
plants only occurred rarely or very clumped in time. I thought about
applying a zero-inflated
model, but I have never used it and I am not sure if it is suitable for
proportion data. Additionally I wondered if I have to consider the fact
that I don't have the same
number of pollen sample for each date, which makes my design unbalanced.
Thank you in advance for advice.

Best wishes
Val?rie