Can I fit a Poisson model to ln transformed data? This is my first question in stats Stack Exchange and I would say that it is an easy one, but hard to find around! 
I have a set of fish counts which should follow a Poisson Distribution (right ? ). However, due to a high number of outliers, it does not, except if I log transform my data. If I nathurally log transform the data, it fits Poisson very well!! Am I breaking any natural law?
Also, I do not really know what is the point of fitting a model into my data. I want to test for differences across sampling sites and across time, but for that I am already using Kruskal-Wallis (I need the robustness to deal with the outliers). What are the benefits of modelling the data?
Thanks a lot to the stats community!! :)
 A: I thought the (very old fashioned) default transform if you're trying to use ordinary least squares regression was a square root.   However, since 1972, the preferred approach would be to use a generalised linear model where you assume Poisson errors, a log link function and use a standard linear predictor.   You can form a model such that $Y_{st} \sim Poisson(\lambda_{st})$ and then model $\log(\lambda_{st}) = \beta_0 + \beta_{s} + \beta_{t} + \beta_{st}$.   Unpacking this a little:
1. I wouldn't expect your fish counts to follow a Poisson distribution. I might expect your conditional fish counts (conditional on whichever time point and location) to follow a Poisson distribution
2. The advantage of your model is that you can examine the structure of your data. I suggested a very simple log-linear model above, with interactions. But you could modify this so you had a trend for time ($\beta_t \times time$), you could allow the time trend to interact with the sites because you think the trend might be different at different sites, and compare that with a model where all trends are the same. Hence you learn something you can't from a Kruskal-Wallis.   You can even consider mathematical models for growth/death/recruitment etc. if you have them.   All in all, putting this in a model framework opens up a whole world of data interpretation. Hope that helps.
