title: Fitting a poisson GLM in R with an aggregated count data
body: <p>I have a dataset of the number of stranded turtles reported at a variety of locations along the Queensland coast of Australia. What I would like to find out is the number of stranded turtles that are NOT reported at each of these locations. In order to estimate that number, I have collected data on the frequency with which a turtle is reported to a stranding location; i.e. how often is a single turtle stranding reported more than one time at about 20 points along the coast? So I have count data which indicates the number of turtles that are reported to a stranding location one time, two times, or three or more times. Ultimately I would like to relate these data to covariates such as local population density and distance to the nearest road, in order to predict the "zero reporting" incidence for the rest of the coastal areas as well.</p>
  
  <p>My data should look something like this, then:</p>
  
  <pre><code>loc&lt;-c("A","B","C")
  rep1&lt;-c(51,24,10)
  rep2&lt;-c(4,8,3)
  rep3ormore&lt;-c(2,1,0)
  pop&lt;-c(50,1000,100)
  turtle- cbind.data.frame(loc, rep1, rep2, rep3ormore, pop)
  </code></pre>
  
  <p>There are other possible covariates, but I'll keep it simple for now! I think this should be able to be done using a Poisson distribution, but I'm having trouble wrapping my head around how to do it. </p>
  
  <p>Additionally, in certain instances I don't have exact numbers for the turtles that have been reported, but instead I have categories; 4-6, 7-10, >10, etc. If there's a way to model that possibility, that would be great as well!</p>