Hi all,
I'm looking at the effect of fire occurrence on the number of visits to National Forests and National Parks. I've divided up these parks into spatial units, with multiple units from each park. This gave me panel date with 8 years and 2,500 IDs, and intend to use fixed effects. My dependent variable is count data and is very overdispersed. I'm yet to do a formal over dispersion test after accounting for the fixed effects, but at least the unconditional mean is 5.06 and standard dev is 34.01, so I'm presuming the data will remain over dispersed even after accounting for the fixed effects etc. (I will of course check this is the case formally soon).
I've read Cameron and Trivedi's book on count data, and the default approach seems to be doing a Poisson fixed effects model estimated through maximum likelihood and correcting the standard errors. I have a few questions about this:
1) I'm a little unclear about how to correct the standard errors. They indicate at least for cross section data with a Poisson regression that there is a robust sandwich standard error correction that can easily be implemented in Stata. However, I not only want to correct for over dispersion but also i) the fact that an individual unit's observations over time will be correlated, and ii) there is likely some spatial correlation going on, so I should probably adjust for this sort of correlation between units in the same park. I don't know how I can simultaneously correct standard errors to incorporate all these things. I think the book mentioned that there are panel robust standard errors that deal with the first and second, but I don't know how to incorporate the 3rd.
2) It seems like the benefit of a negative binomial model over Poisson is that they can both give consistent estimators, but neg bin is more efficient if data is over dispersed. Consequently, I was thinking of doing a fixed effects negative binomial model. I've read that the process implemented in Stata isn't truly doing fixed effects, and some researchers suggest just doing a normal neg bin with individual dummies for each unit. There seems to be no clear consensus on whether this results in an incidental parameters problem or not, with one paper (Allison and Waterman) indicating it doesn't and is superior to Poisson fixed effects. Does anyone have any take on this?
Thank you so much!

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