Is there anything wrong with modeling zero-containing non-negative data by first multiplying it by 10^something, then rounding it, and then modeling it as poisson (or negative binomial)?
In my case, I've got data on crop yields that includes complete crop failures, and response vs fitted plots (from OLS) show a lot of fitted values below zero. Furthermore, the measurements are noisy, so I won't really be losing much information by rounding. So multiplying, rounding, and modeling as a count variable seems attractive.
This is longitudinal data with fixed intercepts (to control for all stable covariates), so tobit is out because it also isn't robust to the incidental parameters problem. Adding a small constant and then logging gives ugly residual plots. Gamma is out because gamma regression also isn't robust to the incidental parameters problem, and I've got a lot of fixed intercepts.
I've come across this paper by Paul Allison which shows that poisson and negative binomial with fixed intercepts gives roughly consistent estimates of $\beta$, but that it has too-small SE's.
So, is there something wrong with multiplying data by 100, rounding and treating it as count? Or are there better approaches?
Edit: One idea that has come to me, but that nobody has recommended, is to use a Tweedie distribution, with software that estimates $p$. But again it's not clear that this is robust to the incidental parameters problem.