Is poisson regression appropriate? Please help!

[Buggytanya]

Hello,

I have just conducted a study on patch choice in a fungus. I wanted to know whether starvation, light exposure and/or the difference between patch quality affected the fungi;s choice of habitat. Basically , the fungi gets a choice between two food patches of different quality. It then grows and covers whichever food patch it prefers. It can also grow on both patches (x% on patch a, the remainder on patch b). I measured the proportion of total fungal biomass that grew over the higher quality food source.
There were four food quality levels, and each was paired with every other pairing for a total of 6 combinations.

My independent variables are :Fungal type( a vs b) and light (exposed vs not exposed), organism weight, quality difference and an interaction between fungal type and quality difference. Quality difference is the difference in expected growth between the two habitat choices.

The trouble is that most of the individuals (95%) allocated all of their mass over one or the other patch, so my data has lots of 0's and 1's. The data looks very much like binomial data. Nevertheless 5% have in between values (ie. 0.75), and I don;t want to omit these from the dataset.

My question is:
Can Poisson regression be used with this type of data? OR should I use logistic regression?

Thank you for the help
Cheers,
T

[TheEcologist]

Hello,
I measured the proportion of total fungal biomass that grew over the higher quality food

Thank you for the help
Cheers,
T

Hi Buggytanya,

In essence the type of analysis will (and should) depend on your response variable. Therefore please give some more information on how you measured the proportion infected. Tell us what the response variable is in its essence.

E.g. Did you do this via digital photography (= number of pixels infected) , via grid count (n grids) or was it a guestimate?

In short however I can tell you that poisson is not appropriate. Not if your variable is bounded by an upper limit (100&#37.

[Buggytanya]

Thanks!
% infected was determined digitally. I calculated the number of dark pixels (the fungi is dark, the food is white) on both food sources to get the total area covered by the fungi. Then I divided the number of dark pixels on food source A by the total number of dark pixels to get 'proportion of biomass on food source A'. But since most fungi were either entirely on one or entirely on the other, 95% of my data is 0's and 1's (out of 235 trials, 192 are 1's (all on food source A) and 30 are 0's (none on food source A).

[TheAnalysisFactor]

Hi Buggytanya,

I just came across this in a book today. J. Scott Long's (1997): Regression Models for Categorical and Limited Dependent Variables. It's a great book.

Anyway it says "A common application of [the two-limit tobit model] is when the outcome is a probability or a percentage." p 212

The argument is that values at 1 or 0 are censored. But you might have trouble with the vast majority censored. You might need to do some sort of mixture model, but this book would be a good place to start. It covers logistic, poisson models, etc.

Karen