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Imagine you have data of birds counted in an area - let's say, you count 18 birds in a surveyed area of 1,3 km^2. Imagine you relate this counts to 1km^2, so that you have 13.9 parrots per km^2. Imagine you do the same for several counts in several areas.

I need to evaluate a possible correlation between these birds counted/km^2 and real birds local density, accounting for some variable like Area Size and Time of Sighting.

THE QUESTION IS:

Can values like these (birds counted/km^2) be analysed by a GLM with POISSON DISTRIBUION FAMILY?

The model would be: counts/km^2 ~ real density+area size+time of sighting, family Poisson. Can I do this? If not, what can I use?

My data are not normal, so I cannot use Gaussian family.

Thanks

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Yes. This is called an offset in Poisson regression.

Essentially, you set the coefficient of that parameter to 1.

Here's another question, with an answer, about it: Fitting a Poisson GLM in R - issues with rates vs. counts

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